Public Types | Public Member Functions | Static Public Member Functions | Protected Types | Protected Member Functions | Protected Attributes | Static Protected Attributes | Friends | List of all members
libMesh::FEGenericBase< OutputType > Class Template Referenceabstract

#include <exact_error_estimator.h>

Inheritance diagram for libMesh::FEGenericBase< OutputType >:
Inheritance graph
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Public Types

typedef OutputType OutputShape
 
typedef TensorTools::IncrementRank< OutputShape >::type OutputGradient
 
typedef TensorTools::IncrementRank< OutputGradient >::type OutputTensor
 
typedef TensorTools::DecrementRank< OutputShape >::type OutputDivergence
 
typedef TensorTools::MakeNumber< OutputShape >::type OutputNumber
 
typedef TensorTools::IncrementRank< OutputNumber >::type OutputNumberGradient
 
typedef TensorTools::IncrementRank< OutputNumberGradient >::type OutputNumberTensor
 
typedef TensorTools::DecrementRank< OutputNumber >::type OutputNumberDivergence
 

Public Member Functions

virtual ~FEGenericBase ()
 
const std::vector< std::vector< OutputShape > > & get_phi () const
 
const std::vector< std::vector< OutputGradient > > & get_dphi () const
 
const std::vector< std::vector< OutputShape > > & get_curl_phi () const
 
const std::vector< std::vector< OutputDivergence > > & get_div_phi () const
 
const std::vector< std::vector< OutputShape > > & get_dphidx () const
 
const std::vector< std::vector< OutputShape > > & get_dphidy () const
 
const std::vector< std::vector< OutputShape > > & get_dphidz () const
 
const std::vector< std::vector< OutputShape > > & get_dphidxi () const
 
const std::vector< std::vector< OutputShape > > & get_dphideta () const
 
const std::vector< std::vector< OutputShape > > & get_dphidzeta () const
 
const std::vector< std::vector< OutputTensor > > & get_d2phi () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidx2 () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidxdy () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidxdz () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidy2 () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidydz () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidz2 () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidxi2 () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidxideta () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidxidzeta () const
 
const std::vector< std::vector< OutputShape > > & get_d2phideta2 () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidetadzeta () const
 
const std::vector< std::vector< OutputShape > > & get_d2phidzeta2 () const
 
const std::vector< OutputGradient > & get_dphase () const
 
const std::vector< Real > & get_Sobolev_weight () const
 
const std::vector< RealGradient > & get_Sobolev_dweight () const
 
void print_phi (std::ostream &os) const
 
void print_dphi (std::ostream &os) const
 
void print_d2phi (std::ostream &os) const
 
template<>
std::unique_ptr< FEGenericBase< Real > > build (const unsigned int dim, const FEType &fet)
 
template<>
std::unique_ptr< FEGenericBase< RealGradient > > build (const unsigned int dim, const FEType &fet)
 
template<>
std::unique_ptr< FEGenericBase< Real > > build_InfFE (const unsigned int dim, const FEType &fet)
 
template<>
std::unique_ptr< FEGenericBase< RealGradient > > build_InfFE (const unsigned int, const FEType &)
 
virtual void reinit (const Elem *elem, const std::vector< Point > *const pts=nullptr, const std::vector< Real > *const weights=nullptr)=0
 
virtual void reinit (const Elem *elem, const unsigned int side, const Real tolerance=TOLERANCE, const std::vector< Point > *const pts=nullptr, const std::vector< Real > *const weights=nullptr)=0
 
virtual void edge_reinit (const Elem *elem, const unsigned int edge, const Real tolerance=TOLERANCE, const std::vector< Point > *pts=nullptr, const std::vector< Real > *weights=nullptr)=0
 
virtual void side_map (const Elem *elem, const Elem *side, const unsigned int s, const std::vector< Point > &reference_side_points, std::vector< Point > &reference_points)=0
 
unsigned int get_dim () const
 
const std::vector< Point > & get_xyz () const
 
const std::vector< Real > & get_JxW () const
 
const std::vector< RealGradient > & get_dxyzdxi () const
 
const std::vector< RealGradient > & get_dxyzdeta () const
 
const std::vector< RealGradient > & get_dxyzdzeta () const
 
const std::vector< RealGradient > & get_d2xyzdxi2 () const
 
const std::vector< RealGradient > & get_d2xyzdeta2 () const
 
const std::vector< RealGradient > & get_d2xyzdzeta2 () const
 
const std::vector< RealGradient > & get_d2xyzdxideta () const
 
const std::vector< RealGradient > & get_d2xyzdxidzeta () const
 
const std::vector< RealGradient > & get_d2xyzdetadzeta () const
 
const std::vector< Real > & get_dxidx () const
 
const std::vector< Real > & get_dxidy () const
 
const std::vector< Real > & get_dxidz () const
 
const std::vector< Real > & get_detadx () const
 
const std::vector< Real > & get_detady () const
 
const std::vector< Real > & get_detadz () const
 
const std::vector< Real > & get_dzetadx () const
 
const std::vector< Real > & get_dzetady () const
 
const std::vector< Real > & get_dzetadz () const
 
const std::vector< std::vector< Point > > & get_tangents () const
 
const std::vector< Point > & get_normals () const
 
const std::vector< Real > & get_curvatures () const
 
virtual void attach_quadrature_rule (QBase *q)=0
 
virtual unsigned int n_shape_functions () const =0
 
virtual unsigned int n_quadrature_points () const =0
 
ElemType get_type () const
 
unsigned int get_p_level () const
 
FEType get_fe_type () const
 
Order get_order () const
 
void set_fe_order (int new_order)
 
virtual FEContinuity get_continuity () const =0
 
virtual bool is_hierarchic () const =0
 
FEFamily get_family () const
 
const FEMap & get_fe_map () const
 
void print_JxW (std::ostream &os) const
 
void print_xyz (std::ostream &os) const
 
void print_info (std::ostream &os) const
 

Static Public Member Functions

static std::unique_ptr< FEGenericBase > build (const unsigned int dim, const FEType &type)
 
static std::unique_ptr< FEGenericBase > build_InfFE (const unsigned int dim, const FEType &type)
 
static void compute_proj_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
 
static void coarsened_dof_values (const NumericVector< Number > &global_vector, const DofMap &dof_map, const Elem *coarse_elem, DenseVector< Number > &coarse_dofs, const unsigned int var, const bool use_old_dof_indices=false)
 
static void coarsened_dof_values (const NumericVector< Number > &global_vector, const DofMap &dof_map, const Elem *coarse_elem, DenseVector< Number > &coarse_dofs, const bool use_old_dof_indices=false)
 
static void compute_periodic_constraints (DofConstraints &constraints, DofMap &dof_map, const PeriodicBoundaries &boundaries, const MeshBase &mesh, const PointLocatorBase *point_locator, const unsigned int variable_number, const Elem *elem)
 
static bool on_reference_element (const Point &p, const ElemType t, const Real eps=TOLERANCE)
 
static void get_refspace_nodes (const ElemType t, std::vector< Point > &nodes)
 
static void compute_node_constraints (NodeConstraints &constraints, const Elem *elem)
 
static void compute_periodic_node_constraints (NodeConstraints &constraints, const PeriodicBoundaries &boundaries, const MeshBase &mesh, const PointLocatorBase *point_locator, const Elem *elem)
 
static void print_info (std::ostream &out=libMesh::out)
 
static std::string get_info ()
 
static unsigned int n_objects ()
 
static void enable_print_counter_info ()
 
static void disable_print_counter_info ()
 

Protected Types

typedef std::map< std::string, std::pair< unsigned int, unsigned int > > Counts
 

Protected Member Functions

 FEGenericBase (const unsigned int dim, const FEType &fet)
 
virtual void init_base_shape_functions (const std::vector< Point > &qp, const Elem *e)=0
 
void determine_calculations ()
 
virtual void compute_shape_functions (const Elem *elem, const std::vector< Point > &qp)
 
virtual bool shapes_need_reinit () const =0
 
void increment_constructor_count (const std::string &name)
 
void increment_destructor_count (const std::string &name)
 

Protected Attributes

std::unique_ptr< FETransformationBase< OutputType > > _fe_trans
 
std::vector< std::vector< OutputShape > > phi
 
std::vector< std::vector< OutputGradient > > dphi
 
std::vector< std::vector< OutputShape > > curl_phi
 
std::vector< std::vector< OutputDivergence > > div_phi
 
std::vector< std::vector< OutputShape > > dphidxi
 
std::vector< std::vector< OutputShape > > dphideta
 
std::vector< std::vector< OutputShape > > dphidzeta
 
std::vector< std::vector< OutputShape > > dphidx
 
std::vector< std::vector< OutputShape > > dphidy
 
std::vector< std::vector< OutputShape > > dphidz
 
std::vector< std::vector< OutputTensor > > d2phi
 
std::vector< std::vector< OutputShape > > d2phidxi2
 
std::vector< std::vector< OutputShape > > d2phidxideta
 
std::vector< std::vector< OutputShape > > d2phidxidzeta
 
std::vector< std::vector< OutputShape > > d2phideta2
 
std::vector< std::vector< OutputShape > > d2phidetadzeta
 
std::vector< std::vector< OutputShape > > d2phidzeta2
 
std::vector< std::vector< OutputShape > > d2phidx2
 
std::vector< std::vector< OutputShape > > d2phidxdy
 
std::vector< std::vector< OutputShape > > d2phidxdz
 
std::vector< std::vector< OutputShape > > d2phidy2
 
std::vector< std::vector< OutputShape > > d2phidydz
 
std::vector< std::vector< OutputShape > > d2phidz2
 
std::vector< OutputGradient > dphase
 
std::vector< RealGradient > dweight
 
std::vector< Real > weight
 
std::unique_ptr< FEMap > _fe_map
 
const unsigned int dim
 
bool calculations_started
 
bool calculate_phi
 
bool calculate_dphi
 
bool calculate_d2phi
 
bool calculate_curl_phi
 
bool calculate_div_phi
 
bool calculate_dphiref
 
FEType fe_type
 
ElemType elem_type
 
unsigned int _p_level
 
QBase * qrule
 
bool shapes_on_quadrature
 

Static Protected Attributes

static Counts _counts
 
static Threads::atomic< unsigned int > _n_objects
 
static Threads::spin_mutex _mutex
 
static bool _enable_print_counter = true
 

Friends

template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
class InfFE
 

Detailed Description

template<typename OutputType>
class libMesh::FEGenericBase< OutputType >

This class forms the foundation from which generic finite elements may be derived. In the current implementation the templated derived class FE offers a wide variety of commonly used finite element concepts. Check there for details.

Use the FEGenericBase<OutputType>::build() method to create an object of any of the derived classes which is compatible with OutputType.

Author
Benjamin S. Kirk
Date
2002

Definition at line 39 of file exact_error_estimator.h.

Member Typedef Documentation

◆ Counts

typedef std::map<std::string, std::pair<unsigned int, unsigned int> > libMesh::ReferenceCounter::Counts
protectedinherited

Data structure to log the information. The log is identified by the class name.

Definition at line 117 of file reference_counter.h.

◆ OutputDivergence

template<typename OutputType>
typedef TensorTools::DecrementRank<OutputShape>::type libMesh::FEGenericBase< OutputType >::OutputDivergence

Definition at line 122 of file fe_base.h.

◆ OutputGradient

template<typename OutputType>
typedef TensorTools::IncrementRank<OutputShape>::type libMesh::FEGenericBase< OutputType >::OutputGradient

Definition at line 120 of file fe_base.h.

◆ OutputNumber

template<typename OutputType>
typedef TensorTools::MakeNumber<OutputShape>::type libMesh::FEGenericBase< OutputType >::OutputNumber

Definition at line 123 of file fe_base.h.

◆ OutputNumberDivergence

template<typename OutputType>
typedef TensorTools::DecrementRank<OutputNumber>::type libMesh::FEGenericBase< OutputType >::OutputNumberDivergence

Definition at line 126 of file fe_base.h.

◆ OutputNumberGradient

template<typename OutputType>
typedef TensorTools::IncrementRank<OutputNumber>::type libMesh::FEGenericBase< OutputType >::OutputNumberGradient

Definition at line 124 of file fe_base.h.

◆ OutputNumberTensor

template<typename OutputType>
typedef TensorTools::IncrementRank<OutputNumberGradient>::type libMesh::FEGenericBase< OutputType >::OutputNumberTensor

Definition at line 125 of file fe_base.h.

◆ OutputShape

template<typename OutputType>
typedef OutputType libMesh::FEGenericBase< OutputType >::OutputShape

Convenient typedefs for gradients of output, hessians of output, and potentially-complex-valued versions of same.

Definition at line 119 of file fe_base.h.

◆ OutputTensor

template<typename OutputType>
typedef TensorTools::IncrementRank<OutputGradient>::type libMesh::FEGenericBase< OutputType >::OutputTensor

Definition at line 121 of file fe_base.h.

Constructor & Destructor Documentation

◆ FEGenericBase()

template<typename OutputType >
libMesh::FEGenericBase< OutputType >::FEGenericBase ( const unsigned int  dim,
const FEType &  fet 
)
inlineprotected

Constructor. Optionally initializes required data structures. Protected so that this base class cannot be explicitly instantiated.

Definition at line 676 of file fe_base.h.

677  :
678  FEAbstract(d,fet),
679  _fe_trans( FETransformationBase<OutputType>::build(fet) ),
680  phi(),
681  dphi(),
682  curl_phi(),
683  div_phi(),
684  dphidxi(),
685  dphideta(),
686  dphidzeta(),
687  dphidx(),
688  dphidy(),
689  dphidz()
690 #ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
691  ,d2phi(),
692  d2phidxi2(),
693  d2phidxideta(),
694  d2phidxidzeta(),
695  d2phideta2(),
696  d2phidetadzeta(),
697  d2phidzeta2(),
698  d2phidx2(),
699  d2phidxdy(),
700  d2phidxdz(),
701  d2phidy2(),
702  d2phidydz(),
703  d2phidz2()
704 #endif
705 #ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS
706  ,dphase(),
707  dweight(),
708  weight()
709 #endif
710 {
711 }
712 
713 
714 
715 template <typename OutputType>
716 inline
717 FEGenericBase<OutputType>::~FEGenericBase()
718 {
719 }
libMesh::FEGenericBase::d2phi
std::vector< std::vector< OutputTensor > > d2phi
Definition: fe_base.h:551
libMesh::FEGenericBase::dphidxi
std::vector< std::vector< OutputShape > > dphidxi
Definition: fe_base.h:518
libMesh::FEGenericBase::d2phidxdz
std::vector< std::vector< OutputShape > > d2phidxdz
Definition: fe_base.h:596
libMesh::FEGenericBase::dphidzeta
std::vector< std::vector< OutputShape > > dphidzeta
Definition: fe_base.h:528
libMesh::FEGenericBase::d2phidydz
std::vector< std::vector< OutputShape > > d2phidydz
Definition: fe_base.h:606
libMesh::FEGenericBase::_fe_trans
std::unique_ptr< FETransformationBase< OutputType > > _fe_trans
Definition: fe_base.h:493
libMesh::FEGenericBase::d2phidxideta
std::vector< std::vector< OutputShape > > d2phidxideta
Definition: fe_base.h:561
libMesh::FEAbstract::FEAbstract
FEAbstract(const unsigned int dim, const FEType &fet)
Definition: fe_abstract.C:46
libMesh::FEGenericBase::weight
std::vector< Real > weight
Definition: fe_base.h:643
libMesh::FEGenericBase::d2phidx2
std::vector< std::vector< OutputShape > > d2phidx2
Definition: fe_base.h:586
libMesh::FEGenericBase::curl_phi
std::vector< std::vector< OutputShape > > curl_phi
Definition: fe_base.h:508
libMesh::FEGenericBase::dphidy
std::vector< std::vector< OutputShape > > dphidy
Definition: fe_base.h:538
libMesh::FEGenericBase::d2phidy2
std::vector< std::vector< OutputShape > > d2phidy2
Definition: fe_base.h:601
libMesh::FEGenericBase::d2phidetadzeta
std::vector< std::vector< OutputShape > > d2phidetadzeta
Definition: fe_base.h:576
libMesh::FEGenericBase::d2phidxidzeta
std::vector< std::vector< OutputShape > > d2phidxidzeta
Definition: fe_base.h:566
libMesh::FETransformationBase::build
static std::unique_ptr< FETransformationBase< OutputShape > > build(const FEType &type)
Definition: fe_transformation_base.C:28
libMesh::FEGenericBase::d2phidxdy
std::vector< std::vector< OutputShape > > d2phidxdy
Definition: fe_base.h:591
libMesh::FEGenericBase::dphidx
std::vector< std::vector< OutputShape > > dphidx
Definition: fe_base.h:533
libMesh::FEGenericBase::phi
std::vector< std::vector< OutputShape > > phi
Definition: fe_base.h:498
libMesh::FEGenericBase::d2phideta2
std::vector< std::vector< OutputShape > > d2phideta2
Definition: fe_base.h:571
libMesh::FEGenericBase::dphase
std::vector< OutputGradient > dphase
Definition: fe_base.h:629
libMesh::FEGenericBase::div_phi
std::vector< std::vector< OutputDivergence > > div_phi
Definition: fe_base.h:513
libMesh::FEGenericBase::dphi
std::vector< std::vector< OutputGradient > > dphi
Definition: fe_base.h:503
libMesh::FEGenericBase::d2phidz2
std::vector< std::vector< OutputShape > > d2phidz2
Definition: fe_base.h:611
libMesh::FEGenericBase::d2phidxi2
std::vector< std::vector< OutputShape > > d2phidxi2
Definition: fe_base.h:556
libMesh::FEGenericBase::d2phidzeta2
std::vector< std::vector< OutputShape > > d2phidzeta2
Definition: fe_base.h:581
libMesh::FEGenericBase::dphidz
std::vector< std::vector< OutputShape > > dphidz
Definition: fe_base.h:543
libMesh::FEGenericBase::dphideta
std::vector< std::vector< OutputShape > > dphideta
Definition: fe_base.h:523
libMesh::FEGenericBase::dweight
std::vector< RealGradient > dweight
Definition: fe_base.h:636

◆ ~FEGenericBase()

template<typename OutputType>
virtual libMesh::FEGenericBase< OutputType >::~FEGenericBase ( )
virtual

Destructor.

Member Function Documentation

◆ attach_quadrature_rule()

virtual void libMesh::FEAbstract::attach_quadrature_rule ( QBase *  q)
pure virtualinherited

Provides the class with the quadrature rule. Implement this in derived classes.

Implemented in libMesh::FESubdivision, libMesh::InfFE< Dim, T_radial, T_map >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, and libMesh::FE< Dim, LAGRANGE_VEC >.

◆ build() [1/3]

template<typename OutputType>
static std::unique_ptr<FEGenericBase> libMesh::FEGenericBase< OutputType >::build ( const unsigned int  dim,
const FEType &  type 
)
static

Builds a specific finite element type. A std::unique_ptr<FEGenericBase> is returned to prevent a memory leak. This way the user need not remember to delete the object.

The build call will fail if the OutputType of this class is not compatible with the output required for the requested type

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::UniformRefinementEstimator::_estimate_error(), libMesh::FEMContext::cached_fe(), libMesh::System::calculate_norm(), libMesh::MeshFunction::discontinuous_gradient(), libMesh::ExactErrorEstimator::estimate_error(), libMesh::MeshFunction::gradient(), libMesh::MeshFunction::hessian(), libMesh::InfFE< Dim, T_radial, T_map >::InfFE(), libMesh::InfFE< Dim, T_radial, T_map >::init_face_shape_functions(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::operator()(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::System::point_gradient(), libMesh::System::point_hessian(), libMesh::InfFE< Dim, T_radial, T_map >::reinit(), libMesh::HPCoarsenTest::select_refinement(), and libMesh::Elem::volume().

◆ build() [2/3]

template<>
std::unique_ptr< FEGenericBase< Real > > libMesh::FEGenericBase< Real >::build ( const unsigned int  dim,
const FEType &  fet 
)

Definition at line 182 of file fe_base.C.

184 {
185  switch (dim)
186  {
187  // 0D
188  case 0:
189  {
190  switch (fet.family)
191  {
192  case CLOUGH:
193  return libmesh_make_unique<FE<0,CLOUGH>>(fet);
194 
195  case HERMITE:
196  return libmesh_make_unique<FE<0,HERMITE>>(fet);
197 
198  case LAGRANGE:
199  return libmesh_make_unique<FE<0,LAGRANGE>>(fet);
200 
201  case L2_LAGRANGE:
202  return libmesh_make_unique<FE<0,L2_LAGRANGE>>(fet);
203 
204  case HIERARCHIC:
205  return libmesh_make_unique<FE<0,HIERARCHIC>>(fet);
206 
207  case L2_HIERARCHIC:
208  return libmesh_make_unique<FE<0,L2_HIERARCHIC>>(fet);
209 
210  case MONOMIAL:
211  return libmesh_make_unique<FE<0,MONOMIAL>>(fet);
212 
213 #ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
214  case SZABAB:
215  return libmesh_make_unique<FE<0,SZABAB>>(fet);
216 
217  case BERNSTEIN:
218  return libmesh_make_unique<FE<0,BERNSTEIN>>(fet);
219 #endif
220 
221  case XYZ:
222  return libmesh_make_unique<FEXYZ<0>>(fet);
223 
224  case SCALAR:
225  return libmesh_make_unique<FEScalar<0>>(fet);
226 
227  default:
228  libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
229  }
230  }
231  // 1D
232  case 1:
233  {
234  switch (fet.family)
235  {
236  case CLOUGH:
237  return libmesh_make_unique<FE<1,CLOUGH>>(fet);
238 
239  case HERMITE:
240  return libmesh_make_unique<FE<1,HERMITE>>(fet);
241 
242  case LAGRANGE:
243  return libmesh_make_unique<FE<1,LAGRANGE>>(fet);
244 
245  case L2_LAGRANGE:
246  return libmesh_make_unique<FE<1,L2_LAGRANGE>>(fet);
247 
248  case HIERARCHIC:
249  return libmesh_make_unique<FE<1,HIERARCHIC>>(fet);
250 
251  case L2_HIERARCHIC:
252  return libmesh_make_unique<FE<1,L2_HIERARCHIC>>(fet);
253 
254  case MONOMIAL:
255  return libmesh_make_unique<FE<1,MONOMIAL>>(fet);
256 
257 #ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
258  case SZABAB:
259  return libmesh_make_unique<FE<1,SZABAB>>(fet);
260 
261  case BERNSTEIN:
262  return libmesh_make_unique<FE<1,BERNSTEIN>>(fet);
263 #endif
264 
265  case XYZ:
266  return libmesh_make_unique<FEXYZ<1>>(fet);
267 
268  case SCALAR:
269  return libmesh_make_unique<FEScalar<1>>(fet);
270 
271  default:
272  libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
273  }
274  }
275 
276 
277  // 2D
278  case 2:
279  {
280  switch (fet.family)
281  {
282  case CLOUGH:
283  return libmesh_make_unique<FE<2,CLOUGH>>(fet);
284 
285  case HERMITE:
286  return libmesh_make_unique<FE<2,HERMITE>>(fet);
287 
288  case LAGRANGE:
289  return libmesh_make_unique<FE<2,LAGRANGE>>(fet);
290 
291  case L2_LAGRANGE:
292  return libmesh_make_unique<FE<2,L2_LAGRANGE>>(fet);
293 
294  case HIERARCHIC:
295  return libmesh_make_unique<FE<2,HIERARCHIC>>(fet);
296 
297  case L2_HIERARCHIC:
298  return libmesh_make_unique<FE<2,L2_HIERARCHIC>>(fet);
299 
300  case MONOMIAL:
301  return libmesh_make_unique<FE<2,MONOMIAL>>(fet);
302 
303 #ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
304  case SZABAB:
305  return libmesh_make_unique<FE<2,SZABAB>>(fet);
306 
307  case BERNSTEIN:
308  return libmesh_make_unique<FE<2,BERNSTEIN>>(fet);
309 #endif
310 
311  case XYZ:
312  return libmesh_make_unique<FEXYZ<2>>(fet);
313 
314  case SCALAR:
315  return libmesh_make_unique<FEScalar<2>>(fet);
316 
317  case SUBDIVISION:
318  return libmesh_make_unique<FESubdivision>(fet);
319 
320  default:
321  libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
322  }
323  }
324 
325 
326  // 3D
327  case 3:
328  {
329  switch (fet.family)
330  {
331  case CLOUGH:
332  libmesh_error_msg("ERROR: Clough-Tocher elements currently only support 1D and 2D");
333 
334  case HERMITE:
335  return libmesh_make_unique<FE<3,HERMITE>>(fet);
336 
337  case LAGRANGE:
338  return libmesh_make_unique<FE<3,LAGRANGE>>(fet);
339 
340  case L2_LAGRANGE:
341  return libmesh_make_unique<FE<3,L2_LAGRANGE>>(fet);
342 
343  case HIERARCHIC:
344  return libmesh_make_unique<FE<3,HIERARCHIC>>(fet);
345 
346  case L2_HIERARCHIC:
347  return libmesh_make_unique<FE<3,L2_HIERARCHIC>>(fet);
348 
349  case MONOMIAL:
350  return libmesh_make_unique<FE<3,MONOMIAL>>(fet);
351 
352 #ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
353  case SZABAB:
354  return libmesh_make_unique<FE<3,SZABAB>>(fet);
355 
356  case BERNSTEIN:
357  return libmesh_make_unique<FE<3,BERNSTEIN>>(fet);
358 #endif
359 
360  case XYZ:
361  return libmesh_make_unique<FEXYZ<3>>(fet);
362 
363  case SCALAR:
364  return libmesh_make_unique<FEScalar<3>>(fet);
365 
366  default:
367  libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
368  }
369  }
370 
371  default:
372  libmesh_error_msg("Invalid dimension dim = " << dim);
373  }
374 }
libMesh::FEType::family
FEFamily family
Definition: fe_type.h:204
libMesh::FEAbstract::dim
const unsigned int dim
Definition: fe_abstract.h:531

◆ build() [3/3]

template<>
std::unique_ptr< FEGenericBase< RealGradient > > libMesh::FEGenericBase< RealGradient >::build ( const unsigned int  dim,
const FEType &  fet 
)

Definition at line 380 of file fe_base.C.

382 {
383  switch (dim)
384  {
385  // 0D
386  case 0:
387  {
388  switch (fet.family)
389  {
390  case LAGRANGE_VEC:
391  return libmesh_make_unique<FELagrangeVec<0>>(fet);
392 
393  default:
394  libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
395  }
396  }
397  case 1:
398  {
399  switch (fet.family)
400  {
401  case LAGRANGE_VEC:
402  return libmesh_make_unique<FELagrangeVec<1>>(fet);
403 
404  default:
405  libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
406  }
407  }
408  case 2:
409  {
410  switch (fet.family)
411  {
412  case LAGRANGE_VEC:
413  return libmesh_make_unique<FELagrangeVec<2>>(fet);
414 
415  case NEDELEC_ONE:
416  return libmesh_make_unique<FENedelecOne<2>>(fet);
417 
418  default:
419  libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
420  }
421  }
422  case 3:
423  {
424  switch (fet.family)
425  {
426  case LAGRANGE_VEC:
427  return libmesh_make_unique<FELagrangeVec<3>>(fet);
428 
429  case NEDELEC_ONE:
430  return libmesh_make_unique<FENedelecOne<3>>(fet);
431 
432  default:
433  libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
434  }
435  }
436 
437  default:
438  libmesh_error_msg("Invalid dimension dim = " << dim);
439  } // switch(dim)
440 }
libMesh::FEType::family
FEFamily family
Definition: fe_type.h:204
libMesh::FEAbstract::dim
const unsigned int dim
Definition: fe_abstract.h:531

◆ build_InfFE() [1/3]

template<typename OutputType>
static std::unique_ptr<FEGenericBase> libMesh::FEGenericBase< OutputType >::build_InfFE ( const unsigned int  dim,
const FEType &  type 
)
static

Builds a specific infinite element type. A std::unique_ptr<FEGenericBase> is returned to prevent a memory leak. This way the user need not remember to delete the object.

The build call will fail if the OutputShape of this class is not compatible with the output required for the requested type

Referenced by libMesh::FEMContext::cached_fe().

◆ build_InfFE() [2/3]

template<>
std::unique_ptr< FEGenericBase< Real > > libMesh::FEGenericBase< Real >::build_InfFE ( const unsigned int  dim,
const FEType &  fet 
)

Definition at line 453 of file fe_base.C.

455 {
456  switch (dim)
457  {
458 
459  // 1D
460  case 1:
461  {
462  switch (fet.radial_family)
463  {
464  case INFINITE_MAP:
465  libmesh_error_msg("ERROR: Can't build an infinite element with FEFamily = " << fet.radial_family);
466 
467  case JACOBI_20_00:
468  {
469  switch (fet.inf_map)
470  {
471  case CARTESIAN:
472  return libmesh_make_unique<InfFE<1,JACOBI_20_00,CARTESIAN>>(fet);
473 
474  default:
475  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << fet.inf_map);
476  }
477  }
478 
479  case JACOBI_30_00:
480  {
481  switch (fet.inf_map)
482  {
483  case CARTESIAN:
484  return libmesh_make_unique<InfFE<1,JACOBI_30_00,CARTESIAN>>(fet);
485 
486  default:
487  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << fet.inf_map);
488  }
489  }
490 
491  case LEGENDRE:
492  {
493  switch (fet.inf_map)
494  {
495  case CARTESIAN:
496  return libmesh_make_unique<InfFE<1,LEGENDRE,CARTESIAN>>(fet);
497 
498  default:
499  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << fet.inf_map);
500  }
501  }
502 
503  case LAGRANGE:
504  {
505  switch (fet.inf_map)
506  {
507  case CARTESIAN:
508  return libmesh_make_unique<InfFE<1,LAGRANGE,CARTESIAN>>(fet);
509 
510  default:
511  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << fet.inf_map);
512  }
513  }
514 
515  default:
516  libmesh_error_msg("ERROR: Bad FEType.radial_family= " << fet.radial_family);
517  }
518  }
519 
520 
521 
522 
523  // 2D
524  case 2:
525  {
526  switch (fet.radial_family)
527  {
528  case INFINITE_MAP:
529  libmesh_error_msg("ERROR: Can't build an infinite element with FEFamily = " << fet.radial_family);
530 
531  case JACOBI_20_00:
532  {
533  switch (fet.inf_map)
534  {
535  case CARTESIAN:
536  return libmesh_make_unique<InfFE<2,JACOBI_20_00,CARTESIAN>>(fet);
537 
538  default:
539  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
540  }
541  }
542 
543  case JACOBI_30_00:
544  {
545  switch (fet.inf_map)
546  {
547  case CARTESIAN:
548  return libmesh_make_unique<InfFE<2,JACOBI_30_00,CARTESIAN>>(fet);
549 
550  default:
551  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
552  }
553  }
554 
555  case LEGENDRE:
556  {
557  switch (fet.inf_map)
558  {
559  case CARTESIAN:
560  return libmesh_make_unique<InfFE<2,LEGENDRE,CARTESIAN>>(fet);
561 
562  default:
563  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
564  }
565  }
566 
567  case LAGRANGE:
568  {
569  switch (fet.inf_map)
570  {
571  case CARTESIAN:
572  return libmesh_make_unique<InfFE<2,LAGRANGE,CARTESIAN>>(fet);
573 
574  default:
575  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
576  }
577  }
578 
579  default:
580  libmesh_error_msg("ERROR: Bad FEType.radial_family= " << fet.radial_family);
581  }
582  }
583 
584 
585 
586 
587  // 3D
588  case 3:
589  {
590  switch (fet.radial_family)
591  {
592  case INFINITE_MAP:
593  libmesh_error_msg("ERROR: Don't build an infinite element with FEFamily = " << fet.radial_family);
594 
595  case JACOBI_20_00:
596  {
597  switch (fet.inf_map)
598  {
599  case CARTESIAN:
600  return libmesh_make_unique<InfFE<3,JACOBI_20_00,CARTESIAN>>(fet);
601 
602  default:
603  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
604  }
605  }
606 
607  case JACOBI_30_00:
608  {
609  switch (fet.inf_map)
610  {
611  case CARTESIAN:
612  return libmesh_make_unique<InfFE<3,JACOBI_30_00,CARTESIAN>>(fet);
613 
614  default:
615  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
616  }
617  }
618 
619  case LEGENDRE:
620  {
621  switch (fet.inf_map)
622  {
623  case CARTESIAN:
624  return libmesh_make_unique<InfFE<3,LEGENDRE,CARTESIAN>>(fet);
625 
626  default:
627  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
628  }
629  }
630 
631  case LAGRANGE:
632  {
633  switch (fet.inf_map)
634  {
635  case CARTESIAN:
636  return libmesh_make_unique<InfFE<3,LAGRANGE,CARTESIAN>>(fet);
637 
638  default:
639  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
640  }
641  }
642 
643  default:
644  libmesh_error_msg("ERROR: Bad FEType.radial_family= " << fet.radial_family);
645  }
646  }
647 
648  default:
649  libmesh_error_msg("Invalid dimension dim = " << dim);
650  }
651 }
libMesh::FEAbstract::dim
const unsigned int dim
Definition: fe_abstract.h:531
libMesh::FEType::inf_map
InfMapType inf_map
Definition: fe_type.h:258
libMesh::FEType::radial_family
FEFamily radial_family
Definition: fe_type.h:250

◆ build_InfFE() [3/3]

template<>
std::unique_ptr< FEGenericBase< RealGradient > > libMesh::FEGenericBase< RealGradient >::build_InfFE ( const unsigned  int,
const FEType &   
)

Definition at line 657 of file fe_base.C.

659 {
660  // No vector types defined... YET.
661  libmesh_not_implemented();
662  return std::unique_ptr<FEVectorBase>();
663 }

◆ coarsened_dof_values() [1/2]

template<typename OutputType >
void libMesh::FEGenericBase< OutputType >::coarsened_dof_values ( const NumericVector< Number > &  global_vector,
const DofMap &  dof_map,
const Elem *  coarse_elem,
DenseVector< Number > &  coarse_dofs,
const unsigned int  var,
const bool  use_old_dof_indices = false 
)
static

Creates a local projection on coarse_elem, based on the DoF values in global_vector for it's children. Computes a vector of coefficients corresponding to dof_indices for only the single given var

Definition at line 791 of file fe_base.C.

Referenced by libMesh::JumpErrorEstimator::estimate_error(), and libMesh::ExactErrorEstimator::estimate_error().

797 {
798  // Side/edge local DOF indices
799  std::vector<unsigned int> new_side_dofs, old_side_dofs;
800 
801  // FIXME: what about 2D shells in 3D space?
802  unsigned int dim = elem->dim();
803 
804  // Cache n_children(); it's a virtual call but it's const.
805  const unsigned int n_children = elem->n_children();
806 
807  // We use local FE objects for now
808  // FIXME: we should use more, external objects instead for efficiency
809  const FEType & base_fe_type = dof_map.variable_type(var);
810  std::unique_ptr<FEGenericBase<OutputShape>> fe
811  (FEGenericBase<OutputShape>::build(dim, base_fe_type));
812  std::unique_ptr<FEGenericBase<OutputShape>> fe_coarse
813  (FEGenericBase<OutputShape>::build(dim, base_fe_type));
814 
815  std::unique_ptr<QBase> qrule (base_fe_type.default_quadrature_rule(dim));
816  std::unique_ptr<QBase> qedgerule (base_fe_type.default_quadrature_rule(1));
817  std::unique_ptr<QBase> qsiderule (base_fe_type.default_quadrature_rule(dim-1));
818  std::vector<Point> coarse_qpoints;
819 
820  // The values of the shape functions at the quadrature
821  // points
822  const std::vector<std::vector<OutputShape>> & phi_values =
823  fe->get_phi();
824  const std::vector<std::vector<OutputShape>> & phi_coarse =
825  fe_coarse->get_phi();
826 
827  // The gradients of the shape functions at the quadrature
828  // points on the child element.
829  const std::vector<std::vector<OutputGradient>> * dphi_values =
830  nullptr;
831  const std::vector<std::vector<OutputGradient>> * dphi_coarse =
832  nullptr;
833 
834  const FEContinuity cont = fe->get_continuity();
835 
836  if (cont == C_ONE)
837  {
838  const std::vector<std::vector<OutputGradient>> &
839  ref_dphi_values = fe->get_dphi();
840  dphi_values = &ref_dphi_values;
841  const std::vector<std::vector<OutputGradient>> &
842  ref_dphi_coarse = fe_coarse->get_dphi();
843  dphi_coarse = &ref_dphi_coarse;
844  }
845 
846  // The Jacobian * quadrature weight at the quadrature points
847  const std::vector<Real> & JxW =
848  fe->get_JxW();
849 
850  // The XYZ locations of the quadrature points on the
851  // child element
852  const std::vector<Point> & xyz_values =
853  fe->get_xyz();
854 
855 
856 
857  FEType fe_type = base_fe_type, temp_fe_type;
858  const ElemType elem_type = elem->type();
859  fe_type.order = static_cast<Order>(fe_type.order +
860  elem->max_descendant_p_level());
861 
862  // Number of nodes on parent element
863  const unsigned int n_nodes = elem->n_nodes();
864 
865  // Number of dofs on parent element
866  const unsigned int new_n_dofs =
867  FEInterface::n_dofs(dim, fe_type, elem_type);
868 
869  // Fixed vs. free DoFs on edge/face projections
870  std::vector<char> dof_is_fixed(new_n_dofs, false); // bools
871  std::vector<int> free_dof(new_n_dofs, 0);
872 
873  DenseMatrix<Real> Ke;
874  DenseVector<Number> Fe;
875  Ue.resize(new_n_dofs); Ue.zero();
876 
877 
878  // When coarsening, in general, we need a series of
879  // projections to ensure a unique and continuous
880  // solution. We start by interpolating nodes, then
881  // hold those fixed and project edges, then
882  // hold those fixed and project faces, then
883  // hold those fixed and project interiors
884 
885  // Copy node values first
886  {
887  std::vector<dof_id_type> node_dof_indices;
888  if (use_old_dof_indices)
889  dof_map.old_dof_indices (elem, node_dof_indices, var);
890  else
891  dof_map.dof_indices (elem, node_dof_indices, var);
892 
893  unsigned int current_dof = 0;
894  for (unsigned int n=0; n!= n_nodes; ++n)
895  {
896  // FIXME: this should go through the DofMap,
897  // not duplicate dof_indices code badly!
898  const unsigned int my_nc =
899  FEInterface::n_dofs_at_node (dim, fe_type,
900  elem_type, n);
901  if (!elem->is_vertex(n))
902  {
903  current_dof += my_nc;
904  continue;
905  }
906 
907  temp_fe_type = base_fe_type;
908  // We're assuming here that child n shares vertex n,
909  // which is wrong on non-simplices right now
910  // ... but this code isn't necessary except on elements
911  // where p refinement creates more vertex dofs; we have
912  // no such elements yet.
913  /*
914  if (elem->child_ptr(n)->p_level() < elem->p_level())
915  {
916  temp_fe_type.order =
917  static_cast<Order>(temp_fe_type.order +
918  elem->child_ptr(n)->p_level());
919  }
920  */
921  const unsigned int nc =
922  FEInterface::n_dofs_at_node (dim, temp_fe_type,
923  elem_type, n);
924  for (unsigned int i=0; i!= nc; ++i)
925  {
926  Ue(current_dof) =
927  old_vector(node_dof_indices[current_dof]);
928  dof_is_fixed[current_dof] = true;
929  current_dof++;
930  }
931  }
932  }
933 
934  // In 3D, project any edge values next
935  if (dim > 2 && cont != DISCONTINUOUS)
936  for (auto e : elem->edge_index_range())
937  {
938  FEInterface::dofs_on_edge(elem, dim, fe_type,
939  e, new_side_dofs);
940 
941  const unsigned int n_new_side_dofs =
942  cast_int<unsigned int>(new_side_dofs.size());
943 
944  // Some edge dofs are on nodes and already
945  // fixed, others are free to calculate
946  unsigned int free_dofs = 0;
947  for (unsigned int i=0; i != n_new_side_dofs; ++i)
948  if (!dof_is_fixed[new_side_dofs[i]])
949  free_dof[free_dofs++] = i;
950  Ke.resize (free_dofs, free_dofs); Ke.zero();
951  Fe.resize (free_dofs); Fe.zero();
952  // The new edge coefficients
953  DenseVector<Number> Uedge(free_dofs);
954 
955  // Add projection terms from each child sharing
956  // this edge
957  for (unsigned int c=0; c != n_children; ++c)
958  {
959  if (!elem->is_child_on_edge(c,e))
960  continue;
961  const Elem * child = elem->child_ptr(c);
962 
963  std::vector<dof_id_type> child_dof_indices;
964  if (use_old_dof_indices)
965  dof_map.old_dof_indices (child,
966  child_dof_indices, var);
967  else
968  dof_map.dof_indices (child,
969  child_dof_indices, var);
970  const unsigned int child_n_dofs =
971  cast_int<unsigned int>
972  (child_dof_indices.size());
973 
974  temp_fe_type = base_fe_type;
975  temp_fe_type.order =
976  static_cast<Order>(temp_fe_type.order +
977  child->p_level());
978 
979  FEInterface::dofs_on_edge(child, dim,
980  temp_fe_type, e, old_side_dofs);
981 
982  // Initialize both child and parent FE data
983  // on the child's edge
984  fe->attach_quadrature_rule (qedgerule.get());
985  fe->edge_reinit (child, e);
986  const unsigned int n_qp = qedgerule->n_points();
987 
988  FEInterface::inverse_map (dim, fe_type, elem,
989  xyz_values, coarse_qpoints);
990 
991  fe_coarse->reinit(elem, &coarse_qpoints);
992 
993  // Loop over the quadrature points
994  for (unsigned int qp=0; qp<n_qp; qp++)
995  {
996  // solution value at the quadrature point
997  OutputNumber fineval = libMesh::zero;
998  // solution grad at the quadrature point
999  OutputNumberGradient finegrad;
1000 
1001  // Sum the solution values * the DOF
1002  // values at the quadrature point to
1003  // get the solution value and gradient.
1004  for (unsigned int i=0; i<child_n_dofs;
1005  i++)
1006  {
1007  fineval +=
1008  (old_vector(child_dof_indices[i])*
1009  phi_values[i][qp]);
1010  if (cont == C_ONE)
1011  finegrad += (*dphi_values)[i][qp] *
1012  old_vector(child_dof_indices[i]);
1013  }
1014 
1015  // Form edge projection matrix
1016  for (unsigned int sidei=0, freei=0; sidei != n_new_side_dofs; ++sidei)
1017  {
1018  unsigned int i = new_side_dofs[sidei];
1019  // fixed DoFs aren't test functions
1020  if (dof_is_fixed[i])
1021  continue;
1022  for (unsigned int sidej=0, freej=0; sidej != n_new_side_dofs; ++sidej)
1023  {
1024  unsigned int j =
1025  new_side_dofs[sidej];
1026  if (dof_is_fixed[j])
1027  Fe(freei) -=
1028  TensorTools::inner_product(phi_coarse[i][qp],
1029  phi_coarse[j][qp]) *
1030  JxW[qp] * Ue(j);
1031  else
1032  Ke(freei,freej) +=
1033  TensorTools::inner_product(phi_coarse[i][qp],
1034  phi_coarse[j][qp]) *
1035  JxW[qp];
1036  if (cont == C_ONE)
1037  {
1038  if (dof_is_fixed[j])
1039  Fe(freei) -=
1040  TensorTools::inner_product((*dphi_coarse)[i][qp],
1041  (*dphi_coarse)[j][qp]) *
1042  JxW[qp] * Ue(j);
1043  else
1044  Ke(freei,freej) +=
1045  TensorTools::inner_product((*dphi_coarse)[i][qp],
1046  (*dphi_coarse)[j][qp]) *
1047  JxW[qp];
1048  }
1049  if (!dof_is_fixed[j])
1050  freej++;
1051  }
1052  Fe(freei) += TensorTools::inner_product(phi_coarse[i][qp],
1053  fineval) * JxW[qp];
1054  if (cont == C_ONE)
1055  Fe(freei) +=
1056  TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
1057  freei++;
1058  }
1059  }
1060  }
1061  Ke.cholesky_solve(Fe, Uedge);
1062 
1063  // Transfer new edge solutions to element
1064  for (unsigned int i=0; i != free_dofs; ++i)
1065  {
1066  Number & ui = Ue(new_side_dofs[free_dof[i]]);
1067  libmesh_assert(std::abs(ui) < TOLERANCE ||
1068  std::abs(ui - Uedge(i)) < TOLERANCE);
1069  ui = Uedge(i);
1070  dof_is_fixed[new_side_dofs[free_dof[i]]] = true;
1071  }
1072  }
1073 
1074  // Project any side values (edges in 2D, faces in 3D)
1075  if (dim > 1 && cont != DISCONTINUOUS)
1076  for (auto s : elem->side_index_range())
1077  {
1078  FEInterface::dofs_on_side(elem, dim, fe_type,
1079  s, new_side_dofs);
1080 
1081  const unsigned int n_new_side_dofs =
1082  cast_int<unsigned int>(new_side_dofs.size());
1083 
1084  // Some side dofs are on nodes/edges and already
1085  // fixed, others are free to calculate
1086  unsigned int free_dofs = 0;
1087  for (unsigned int i=0; i != n_new_side_dofs; ++i)
1088  if (!dof_is_fixed[new_side_dofs[i]])
1089  free_dof[free_dofs++] = i;
1090  Ke.resize (free_dofs, free_dofs); Ke.zero();
1091  Fe.resize (free_dofs); Fe.zero();
1092  // The new side coefficients
1093  DenseVector<Number> Uside(free_dofs);
1094 
1095  // Add projection terms from each child sharing
1096  // this side
1097  for (unsigned int c=0; c != n_children; ++c)
1098  {
1099  if (!elem->is_child_on_side(c,s))
1100  continue;
1101  const Elem * child = elem->child_ptr(c);
1102 
1103  std::vector<dof_id_type> child_dof_indices;
1104  if (use_old_dof_indices)
1105  dof_map.old_dof_indices (child,
1106  child_dof_indices, var);
1107  else
1108  dof_map.dof_indices (child,
1109  child_dof_indices, var);
1110  const unsigned int child_n_dofs =
1111  cast_int<unsigned int>
1112  (child_dof_indices.size());
1113 
1114  temp_fe_type = base_fe_type;
1115  temp_fe_type.order =
1116  static_cast<Order>(temp_fe_type.order +
1117  child->p_level());
1118 
1119  FEInterface::dofs_on_side(child, dim,
1120  temp_fe_type, s, old_side_dofs);
1121 
1122  // Initialize both child and parent FE data
1123  // on the child's side
1124  fe->attach_quadrature_rule (qsiderule.get());
1125  fe->reinit (child, s);
1126  const unsigned int n_qp = qsiderule->n_points();
1127 
1128  FEInterface::inverse_map (dim, fe_type, elem,
1129  xyz_values, coarse_qpoints);
1130 
1131  fe_coarse->reinit(elem, &coarse_qpoints);
1132 
1133  // Loop over the quadrature points
1134  for (unsigned int qp=0; qp<n_qp; qp++)
1135  {
1136  // solution value at the quadrature point
1137  OutputNumber fineval = libMesh::zero;
1138  // solution grad at the quadrature point
1139  OutputNumberGradient finegrad;
1140 
1141  // Sum the solution values * the DOF
1142  // values at the quadrature point to
1143  // get the solution value and gradient.
1144  for (unsigned int i=0; i<child_n_dofs;
1145  i++)
1146  {
1147  fineval +=
1148  old_vector(child_dof_indices[i]) *
1149  phi_values[i][qp];
1150  if (cont == C_ONE)
1151  finegrad += (*dphi_values)[i][qp] *
1152  old_vector(child_dof_indices[i]);
1153  }
1154 
1155  // Form side projection matrix
1156  for (unsigned int sidei=0, freei=0; sidei != n_new_side_dofs; ++sidei)
1157  {
1158  unsigned int i = new_side_dofs[sidei];
1159  // fixed DoFs aren't test functions
1160  if (dof_is_fixed[i])
1161  continue;
1162  for (unsigned int sidej=0, freej=0; sidej != n_new_side_dofs; ++sidej)
1163  {
1164  unsigned int j =
1165  new_side_dofs[sidej];
1166  if (dof_is_fixed[j])
1167  Fe(freei) -=
1168  TensorTools::inner_product(phi_coarse[i][qp],
1169  phi_coarse[j][qp]) *
1170  JxW[qp] * Ue(j);
1171  else
1172  Ke(freei,freej) +=
1173  TensorTools::inner_product(phi_coarse[i][qp],
1174  phi_coarse[j][qp]) *
1175  JxW[qp];
1176  if (cont == C_ONE)
1177  {
1178  if (dof_is_fixed[j])
1179  Fe(freei) -=
1180  TensorTools::inner_product((*dphi_coarse)[i][qp],
1181  (*dphi_coarse)[j][qp]) *
1182  JxW[qp] * Ue(j);
1183  else
1184  Ke(freei,freej) +=
1185  TensorTools::inner_product((*dphi_coarse)[i][qp],
1186  (*dphi_coarse)[j][qp]) *
1187  JxW[qp];
1188  }
1189  if (!dof_is_fixed[j])
1190  freej++;
1191  }
1192  Fe(freei) += TensorTools::inner_product(fineval, phi_coarse[i][qp]) * JxW[qp];
1193  if (cont == C_ONE)
1194  Fe(freei) +=
1195  TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
1196  freei++;
1197  }
1198  }
1199  }
1200  Ke.cholesky_solve(Fe, Uside);
1201 
1202  // Transfer new side solutions to element
1203  for (unsigned int i=0; i != free_dofs; ++i)
1204  {
1205  Number & ui = Ue(new_side_dofs[free_dof[i]]);
1206  libmesh_assert(std::abs(ui) < TOLERANCE ||
1207  std::abs(ui - Uside(i)) < TOLERANCE);
1208  ui = Uside(i);
1209  dof_is_fixed[new_side_dofs[free_dof[i]]] = true;
1210  }
1211  }
1212 
1213  // Project the interior values, finally
1214 
1215  // Some interior dofs are on nodes/edges/sides and
1216  // already fixed, others are free to calculate
1217  unsigned int free_dofs = 0;
1218  for (unsigned int i=0; i != new_n_dofs; ++i)
1219  if (!dof_is_fixed[i])
1220  free_dof[free_dofs++] = i;
1221  Ke.resize (free_dofs, free_dofs); Ke.zero();
1222  Fe.resize (free_dofs); Fe.zero();
1223  // The new interior coefficients
1224  DenseVector<Number> Uint(free_dofs);
1225 
1226  // Add projection terms from each child
1227  for (auto & child : elem->child_ref_range())
1228  {
1229  std::vector<dof_id_type> child_dof_indices;
1230  if (use_old_dof_indices)
1231  dof_map.old_dof_indices (&child,
1232  child_dof_indices, var);
1233  else
1234  dof_map.dof_indices (&child,
1235  child_dof_indices, var);
1236  const unsigned int child_n_dofs =
1237  cast_int<unsigned int>
1238  (child_dof_indices.size());
1239 
1240  // Initialize both child and parent FE data
1241  // on the child's quadrature points
1242  fe->attach_quadrature_rule (qrule.get());
1243  fe->reinit (&child);
1244  const unsigned int n_qp = qrule->n_points();
1245 
1246  FEInterface::inverse_map (dim, fe_type, elem,
1247  xyz_values, coarse_qpoints);
1248 
1249  fe_coarse->reinit(elem, &coarse_qpoints);
1250 
1251  // Loop over the quadrature points
1252  for (unsigned int qp=0; qp<n_qp; qp++)
1253  {
1254  // solution value at the quadrature point
1255  OutputNumber fineval = libMesh::zero;
1256  // solution grad at the quadrature point
1257  OutputNumberGradient finegrad;
1258 
1259  // Sum the solution values * the DOF
1260  // values at the quadrature point to
1261  // get the solution value and gradient.
1262  for (unsigned int i=0; i<child_n_dofs; i++)
1263  {
1264  fineval +=
1265  (old_vector(child_dof_indices[i]) *
1266  phi_values[i][qp]);
1267  if (cont == C_ONE)
1268  finegrad += (*dphi_values)[i][qp] *
1269  old_vector(child_dof_indices[i]);
1270  }
1271 
1272  // Form interior projection matrix
1273  for (unsigned int i=0, freei=0;
1274  i != new_n_dofs; ++i)
1275  {
1276  // fixed DoFs aren't test functions
1277  if (dof_is_fixed[i])
1278  continue;
1279  for (unsigned int j=0, freej=0; j !=
1280  new_n_dofs; ++j)
1281  {
1282  if (dof_is_fixed[j])
1283  Fe(freei) -=
1284  TensorTools::inner_product(phi_coarse[i][qp],
1285  phi_coarse[j][qp]) *
1286  JxW[qp] * Ue(j);
1287  else
1288  Ke(freei,freej) +=
1289  TensorTools::inner_product(phi_coarse[i][qp],
1290  phi_coarse[j][qp]) *
1291  JxW[qp];
1292  if (cont == C_ONE)
1293  {
1294  if (dof_is_fixed[j])
1295  Fe(freei) -=
1296  TensorTools::inner_product((*dphi_coarse)[i][qp],
1297  (*dphi_coarse)[j][qp]) *
1298  JxW[qp] * Ue(j);
1299  else
1300  Ke(freei,freej) +=
1301  TensorTools::inner_product((*dphi_coarse)[i][qp],
1302  (*dphi_coarse)[j][qp]) *
1303  JxW[qp];
1304  }
1305  if (!dof_is_fixed[j])
1306  freej++;
1307  }
1308  Fe(freei) += TensorTools::inner_product(phi_coarse[i][qp], fineval) *
1309  JxW[qp];
1310  if (cont == C_ONE)
1311  Fe(freei) += TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
1312  freei++;
1313  }
1314  }
1315  }
1316  Ke.cholesky_solve(Fe, Uint);
1317 
1318  // Transfer new interior solutions to element
1319  for (unsigned int i=0; i != free_dofs; ++i)
1320  {
1321  Number & ui = Ue(free_dof[i]);
1322  libmesh_assert(std::abs(ui) < TOLERANCE ||
1323  std::abs(ui - Uint(i)) < TOLERANCE);
1324  ui = Uint(i);
1325  // We should be fixing all dofs by now; no need to keep track of
1326  // that unless we're debugging
1327 #ifndef NDEBUG
1328  dof_is_fixed[free_dof[i]] = true;
1329 #endif
1330  }
1331 
1332 #ifndef NDEBUG
1333  // Make sure every DoF got reached!
1334  for (unsigned int i=0; i != new_n_dofs; ++i)
1335  libmesh_assert(dof_is_fixed[i]);
1336 #endif
1337 }
libMesh::FEInterface::dofs_on_edge
static void dofs_on_edge(const Elem *const elem, const unsigned int dim, const FEType &fe_t, unsigned int e, std::vector< unsigned int > &di)
Definition: fe_interface.C:536
libMesh::FEType
Manages the family, order, etc. parameters for a given FE.
Definition: fe_type.h:179
std::abs
double abs(double a)
Definition: libmesh_augment_std_namespace.h:59
libMesh::FEInterface::n_dofs
static unsigned int n_dofs(const unsigned int dim, const FEType &fe_t, const ElemType t)
Definition: fe_interface.C:454
libMesh::DofMap::dof_indices
void dof_indices(const Elem *const elem, std::vector< dof_id_type > &di) const
Definition: dof_map.C:1930
libMesh::FEInterface::dofs_on_side
static void dofs_on_side(const Elem *const elem, const unsigned int dim, const FEType &fe_t, unsigned int s, std::vector< unsigned int > &di)
Definition: fe_interface.C:523
libMesh::DenseVector::resize
void resize(const unsigned int n)
Definition: dense_vector.h:355
libMesh::DofMap::variable_type
const FEType & variable_type(const unsigned int c) const
Definition: dof_map.h:1792
libMesh::Elem
The base class for all geometric element types.
Definition: elem.h:100
libMesh::FEGenericBase::OutputNumberGradient
TensorTools::IncrementRank< OutputNumber >::type OutputNumberGradient
Definition: fe_base.h:124
libMesh::Elem::p_level
unsigned int p_level() const
Definition: elem.h:2555
libMesh::FEType::order
OrderWrapper order
Definition: fe_type.h:198
libMesh::TOLERANCE
static const Real TOLERANCE
Definition: libmesh_common.h:139
libMesh::zero
const Number zero
Definition: libmesh.h:239
libMesh::DofMap::old_dof_indices
void old_dof_indices(const Elem *const elem, std::vector< dof_id_type > &di, const unsigned int vn=libMesh::invalid_uint) const
Definition: dof_map.C:2434
libMesh::FEType::default_quadrature_rule
std::unique_ptr< QBase > default_quadrature_rule(const unsigned int dim, const int extraorder=0) const
Definition: fe_type.C:31
n_nodes
const dof_id_type n_nodes
Definition: tecplot_io.C:68
libMesh::FEAbstract::dim
const unsigned int dim
Definition: fe_abstract.h:531
libMesh::FEInterface::inverse_map
static Point inverse_map(const unsigned int dim, const FEType &fe_t, const Elem *elem, const Point &p, const Real tolerance=TOLERANCE, const bool secure=true)
Definition: fe_interface.C:590
libMesh::QBase::n_points
unsigned int n_points() const
Definition: quadrature.h:127
libMesh::FEGenericBase::OutputNumber
TensorTools::MakeNumber< OutputShape >::type OutputNumber
Definition: fe_base.h:123
libMesh::FEInterface::n_dofs_at_node
static unsigned int n_dofs_at_node(const unsigned int dim, const FEType &fe_t, const ElemType t, const unsigned int n)
Definition: fe_interface.C:473
libMesh::DenseMatrix::zero
virtual void zero() override
Definition: dense_matrix.h:808
libMesh::DenseMatrix::resize
void resize(const unsigned int new_m, const unsigned int new_n)
Definition: dense_matrix.h:792
libMesh::DenseMatrix::cholesky_solve
void cholesky_solve(const DenseVector< T2 > &b, DenseVector< T2 > &x)
Definition: dense_matrix_impl.h:929
libMesh::DenseMatrix
A matrix object used for finite element assembly and numerics.
Definition: dense_matrix.h:54
libMesh::TensorTools::inner_product
boostcopy::enable_if_c< ScalarTraits< T >::value &&ScalarTraits< T2 >::value, typename CompareTypes< T, T2 >::supertype >::type inner_product(const T &a, const T2 &b)
Definition: tensor_tools.h:47
libMesh::Elem::child_ptr
const Elem * child_ptr(unsigned int i) const
Definition: elem.h:2578
libMesh::DenseVector::zero
virtual void zero() override
Definition: dense_vector.h:379

◆ coarsened_dof_values() [2/2]

template<typename OutputType >
void libMesh::FEGenericBase< OutputType >::coarsened_dof_values ( const NumericVector< Number > &  global_vector,
const DofMap &  dof_map,
const Elem *  coarse_elem,
DenseVector< Number > &  coarse_dofs,
const bool  use_old_dof_indices = false 
)
static

Creates a local projection on coarse_elem, based on the DoF values in global_vector for it's children. Computes a vector of coefficients corresponding to all dof_indices.

Definition at line 1343 of file fe_base.C.

1348 {
1349  Ue.resize(0);
1350 
1351  for (unsigned int v=0; v != dof_map.n_variables(); ++v)
1352  {
1353  DenseVector<Number> Usub;
1354 
1355  coarsened_dof_values(old_vector, dof_map, elem, Usub,
1356  use_old_dof_indices);
1357 
1358  Ue.append (Usub);
1359  }
1360 }
libMesh::DofMap::n_variables
unsigned int n_variables() const
Definition: dof_map.h:541
libMesh::FEGenericBase::coarsened_dof_values
static void coarsened_dof_values(const NumericVector< Number > &global_vector, const DofMap &dof_map, const Elem *coarse_elem, DenseVector< Number > &coarse_dofs, const unsigned int var, const bool use_old_dof_indices=false)
Definition: fe_base.C:791

◆ compute_node_constraints()

void libMesh::FEAbstract::compute_node_constraints ( NodeConstraints &  constraints,
const Elem *  elem 
)
staticinherited

Computes the nodal constraint contributions (for non-conforming adapted meshes), using Lagrange geometry

Definition at line 820 of file fe_abstract.C.

References std::abs(), libMesh::Elem::build_side_ptr(), libMesh::Elem::default_order(), libMesh::Elem::dim(), libMesh::FEAbstract::fe_type, libMesh::FEInterface::inverse_map(), libMesh::LAGRANGE, libMesh::Elem::level(), libMesh::FEInterface::n_dofs(), libMesh::Elem::neighbor_ptr(), libMesh::Elem::parent(), libMesh::Real, libMesh::remote_elem, libMesh::FEInterface::shape(), libMesh::Elem::side_index_range(), libMesh::Threads::spin_mtx, and libMesh::Elem::subactive().

822 {
823  libmesh_assert(elem);
824 
825  const unsigned int Dim = elem->dim();
826 
827  // Only constrain elements in 2,3D.
828  if (Dim == 1)
829  return;
830 
831  // Only constrain active and ancestor elements
832  if (elem->subactive())
833  return;
834 
835  // We currently always use LAGRANGE mappings for geometry
836  const FEType fe_type(elem->default_order(), LAGRANGE);
837 
838  // Pull objects out of the loop to reduce heap operations
839  std::vector<const Node *> my_nodes, parent_nodes;
840  std::unique_ptr<const Elem> my_side, parent_side;
841 
842  // Look at the element faces. Check to see if we need to
843  // build constraints.
844  for (auto s : elem->side_index_range())
845  if (elem->neighbor_ptr(s) != nullptr &&
846  elem->neighbor_ptr(s) != remote_elem)
847  if (elem->neighbor_ptr(s)->level() < elem->level()) // constrain dofs shared between
848  { // this element and ones coarser
849  // than this element.
850  // Get pointers to the elements of interest and its parent.
851  const Elem * parent = elem->parent();
852 
853  // This can't happen... Only level-0 elements have nullptr
854  // parents, and no level-0 elements can be at a higher
855  // level than their neighbors!
856  libmesh_assert(parent);
857 
858  elem->build_side_ptr(my_side, s);
859  parent->build_side_ptr(parent_side, s);
860 
861  const unsigned int n_side_nodes = my_side->n_nodes();
862 
863  my_nodes.clear();
864  my_nodes.reserve (n_side_nodes);
865  parent_nodes.clear();
866  parent_nodes.reserve (n_side_nodes);
867 
868  for (unsigned int n=0; n != n_side_nodes; ++n)
869  my_nodes.push_back(my_side->node_ptr(n));
870 
871  for (unsigned int n=0; n != n_side_nodes; ++n)
872  parent_nodes.push_back(parent_side->node_ptr(n));
873 
874  for (unsigned int my_side_n=0;
875  my_side_n < n_side_nodes;
876  my_side_n++)
877  {
878  libmesh_assert_less (my_side_n, FEInterface::n_dofs(Dim-1, fe_type, my_side->type()));
879 
880  const Node * my_node = my_nodes[my_side_n];
881 
882  // The support point of the DOF
883  const Point & support_point = *my_node;
884 
885  // Figure out where my node lies on their reference element.
886  const Point mapped_point = FEInterface::inverse_map(Dim-1, fe_type,
887  parent_side.get(),
888  support_point);
889 
890  // Compute the parent's side shape function values.
891  for (unsigned int their_side_n=0;
892  their_side_n < n_side_nodes;
893  their_side_n++)
894  {
895  libmesh_assert_less (their_side_n, FEInterface::n_dofs(Dim-1, fe_type, parent_side->type()));
896 
897  const Node * their_node = parent_nodes[their_side_n];
898  libmesh_assert(their_node);
899 
900  const Real their_value = FEInterface::shape(Dim-1,
901  fe_type,
902  parent_side->type(),
903  their_side_n,
904  mapped_point);
905 
906  const Real their_mag = std::abs(their_value);
907 #ifdef DEBUG
908  // Protect for the case u_i ~= u_j,
909  // in which case i better equal j.
910  if (their_mag > 0.999)
911  {
912  libmesh_assert_equal_to (my_node, their_node);
913  libmesh_assert_less (std::abs(their_value - 1.), 0.001);
914  }
915  else
916 #endif
917  // To make nodal constraints useful for constructing
918  // sparsity patterns faster, we need to get EVERY
919  // POSSIBLE constraint coupling identified, even if
920  // there is no coupling in the isoparametric
921  // Lagrange case.
922  if (their_mag < 1.e-5)
923  {
924  // since we may be running this method concurrently
925  // on multiple threads we need to acquire a lock
926  // before modifying the shared constraint_row object.
927  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
928 
929  // A reference to the constraint row.
930  NodeConstraintRow & constraint_row = constraints[my_node].first;
931 
932  constraint_row.insert(std::make_pair (their_node,
933  0.));
934  }
935  // To get nodal coordinate constraints right, only
936  // add non-zero and non-identity values for Lagrange
937  // basis functions.
938  else // (1.e-5 <= their_mag <= .999)
939  {
940  // since we may be running this method concurrently
941  // on multiple threads we need to acquire a lock
942  // before modifying the shared constraint_row object.
943  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
944 
945  // A reference to the constraint row.
946  NodeConstraintRow & constraint_row = constraints[my_node].first;
947 
948  constraint_row.insert(std::make_pair (their_node,
949  their_value));
950  }
951  }
952  }
953  }
954 }
std::abs
double abs(double a)
Definition: libmesh_augment_std_namespace.h:59
libMesh::FEInterface::n_dofs
static unsigned int n_dofs(const unsigned int dim, const FEType &fe_t, const ElemType t)
Definition: fe_interface.C:454
libMesh::Threads::spin_mtx
spin_mutex spin_mtx
Definition: threads.C:29
libMesh::FEInterface::shape
static Real shape(const unsigned int dim, const FEType &fe_t, const ElemType t, const unsigned int i, const Point &p)
Definition: fe_interface.C:657
libMesh::FEInterface::inverse_map
static Point inverse_map(const unsigned int dim, const FEType &fe_t, const Elem *elem, const Point &p, const Real tolerance=TOLERANCE, const bool secure=true)
Definition: fe_interface.C:590
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:131
libMesh::NodeConstraintRow
std::map< const Node *, Real, std::less< const Node * >, Threads::scalable_allocator< std::pair< const Node *const, Real > > > NodeConstraintRow
Definition: dof_map.h:145
libMesh::remote_elem
const RemoteElem * remote_elem
Definition: remote_elem.C:57

◆ compute_periodic_constraints()

template<typename OutputType >
void libMesh::FEGenericBase< OutputType >::compute_periodic_constraints ( DofConstraints &  constraints,
DofMap &  dof_map,
const PeriodicBoundaries &  boundaries,
const MeshBase &  mesh,
const PointLocatorBase *  point_locator,
const unsigned int  variable_number,
const Elem *  elem 
)
static

Computes the constraint matrix contributions (for meshes with periodic boundary conditions) corresponding to variable number var_number, using generic projections.

Definition at line 1650 of file fe_base.C.

Referenced by libMesh::FEInterface::compute_periodic_constraints().

1657 {
1658  // Only bother if we truly have periodic boundaries
1659  if (boundaries.empty())
1660  return;
1661 
1662  libmesh_assert(elem);
1663 
1664  // Only constrain active elements with this method
1665  if (!elem->active())
1666  return;
1667 
1668  const unsigned int Dim = elem->dim();
1669 
1670  // We need sys_number and variable_number for DofObject methods
1671  // later
1672  const unsigned int sys_number = dof_map.sys_number();
1673 
1674  const FEType & base_fe_type = dof_map.variable_type(variable_number);
1675 
1676  // Construct FE objects for this element and its pseudo-neighbors.
1677  std::unique_ptr<FEGenericBase<OutputShape>> my_fe
1678  (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
1679  const FEContinuity cont = my_fe->get_continuity();
1680 
1681  // We don't need to constrain discontinuous elements
1682  if (cont == DISCONTINUOUS)
1683  return;
1684  libmesh_assert (cont == C_ZERO || cont == C_ONE);
1685 
1686  // We'll use element size to generate relative tolerances later
1687  const Real primary_hmin = elem->hmin();
1688 
1689  std::unique_ptr<FEGenericBase<OutputShape>> neigh_fe
1690  (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
1691 
1692  QGauss my_qface(Dim-1, base_fe_type.default_quadrature_order());
1693  my_fe->attach_quadrature_rule (&my_qface);
1694  std::vector<Point> neigh_qface;
1695 
1696  const std::vector<Real> & JxW = my_fe->get_JxW();
1697  const std::vector<Point> & q_point = my_fe->get_xyz();
1698  const std::vector<std::vector<OutputShape>> & phi = my_fe->get_phi();
1699  const std::vector<std::vector<OutputShape>> & neigh_phi =
1700  neigh_fe->get_phi();
1701  const std::vector<Point> * face_normals = nullptr;
1702  const std::vector<std::vector<OutputGradient>> * dphi = nullptr;
1703  const std::vector<std::vector<OutputGradient>> * neigh_dphi = nullptr;
1704  std::vector<dof_id_type> my_dof_indices, neigh_dof_indices;
1705  std::vector<unsigned int> my_side_dofs, neigh_side_dofs;
1706 
1707  if (cont != C_ZERO)
1708  {
1709  const std::vector<Point> & ref_face_normals =
1710  my_fe->get_normals();
1711  face_normals = &ref_face_normals;
1712  const std::vector<std::vector<OutputGradient>> & ref_dphi =
1713  my_fe->get_dphi();
1714  dphi = &ref_dphi;
1715  const std::vector<std::vector<OutputGradient>> & ref_neigh_dphi =
1716  neigh_fe->get_dphi();
1717  neigh_dphi = &ref_neigh_dphi;
1718  }
1719 
1720  DenseMatrix<Real> Ke;
1721  DenseVector<Real> Fe;
1722  std::vector<DenseVector<Real>> Ue;
1723 
1724  // Container to catch the boundary ids that BoundaryInfo hands us.
1725  std::vector<boundary_id_type> bc_ids;
1726 
1727  // Look at the element faces. Check to see if we need to
1728  // build constraints.
1729  const unsigned short int max_ns = elem->n_sides();
1730  for (unsigned short int s = 0; s != max_ns; ++s)
1731  {
1732  if (elem->neighbor_ptr(s))
1733  continue;
1734 
1735  mesh.get_boundary_info().boundary_ids (elem, s, bc_ids);
1736 
1737  for (const auto & boundary_id : bc_ids)
1738  {
1739  const PeriodicBoundaryBase * periodic = boundaries.boundary(boundary_id);
1740  if (periodic && periodic->is_my_variable(variable_number))
1741  {
1742  libmesh_assert(point_locator);
1743 
1744  // Get pointers to the element's neighbor.
1745  const Elem * neigh = boundaries.neighbor(boundary_id, *point_locator, elem, s);
1746 
1747  if (neigh == nullptr)
1748  libmesh_error_msg("PeriodicBoundaries point locator object returned nullptr!");
1749 
1750  // periodic (and possibly h refinement) constraints:
1751  // constrain dofs shared between
1752  // this element and ones as coarse
1753  // as or coarser than this element.
1754  if (neigh->level() <= elem->level())
1755  {
1756  unsigned int s_neigh =
1757  mesh.get_boundary_info().side_with_boundary_id(neigh, periodic->pairedboundary);
1758  libmesh_assert_not_equal_to (s_neigh, libMesh::invalid_uint);
1759 
1760 #ifdef LIBMESH_ENABLE_AMR
1761  // Find the minimum p level; we build the h constraint
1762  // matrix with this and then constrain away all higher p
1763  // DoFs.
1764  libmesh_assert(neigh->active());
1765  const unsigned int min_p_level =
1766  std::min(elem->p_level(), neigh->p_level());
1767 
1768  // we may need to make the FE objects reinit with the
1769  // minimum shared p_level
1770  // FIXME - I hate using const_cast<> and avoiding
1771  // accessor functions; there's got to be a
1772  // better way to do this!
1773  const unsigned int old_elem_level = elem->p_level();
1774  if (old_elem_level != min_p_level)
1775  (const_cast<Elem *>(elem))->hack_p_level(min_p_level);
1776  const unsigned int old_neigh_level = neigh->p_level();
1777  if (old_neigh_level != min_p_level)
1778  (const_cast<Elem *>(neigh))->hack_p_level(min_p_level);
1779 #endif // #ifdef LIBMESH_ENABLE_AMR
1780 
1781  // We can do a projection with a single integration,
1782  // due to the assumption of nested finite element
1783  // subspaces.
1784  // FIXME: it might be more efficient to do nodes,
1785  // then edges, then side, to reduce the size of the
1786  // Cholesky factorization(s)
1787  my_fe->reinit(elem, s);
1788 
1789  dof_map.dof_indices (elem, my_dof_indices,
1790  variable_number);
1791  dof_map.dof_indices (neigh, neigh_dof_indices,
1792  variable_number);
1793 
1794  // We use neigh_dof_indices_all_variables in the case that the
1795  // periodic boundary condition involves mappings between multiple
1796  // variables.
1797  std::vector<std::vector<dof_id_type>> neigh_dof_indices_all_variables;
1798  if(periodic->has_transformation_matrix())
1799  {
1800  const std::set<unsigned int> & variables = periodic->get_variables();
1801  neigh_dof_indices_all_variables.resize(variables.size());
1802  unsigned int index = 0;
1803  for(unsigned int var : variables)
1804  {
1805  dof_map.dof_indices (neigh, neigh_dof_indices_all_variables[index],
1806  var);
1807  index++;
1808  }
1809  }
1810 
1811  const unsigned int n_qp = my_qface.n_points();
1812 
1813  // Translate the quadrature points over to the
1814  // neighbor's boundary
1815  std::vector<Point> neigh_point(q_point.size());
1816  for (auto i : index_range(neigh_point))
1817  neigh_point[i] = periodic->get_corresponding_pos(q_point[i]);
1818 
1819  FEInterface::inverse_map (Dim, base_fe_type, neigh,
1820  neigh_point, neigh_qface);
1821 
1822  neigh_fe->reinit(neigh, &neigh_qface);
1823 
1824  // We're only concerned with DOFs whose values (and/or first
1825  // derivatives for C1 elements) are supported on side nodes
1826  FEInterface::dofs_on_side(elem, Dim, base_fe_type, s, my_side_dofs);
1827  FEInterface::dofs_on_side(neigh, Dim, base_fe_type, s_neigh, neigh_side_dofs);
1828 
1829  // We're done with functions that examine Elem::p_level(),
1830  // so let's unhack those levels
1831 #ifdef LIBMESH_ENABLE_AMR
1832  if (elem->p_level() != old_elem_level)
1833  (const_cast<Elem *>(elem))->hack_p_level(old_elem_level);
1834  if (neigh->p_level() != old_neigh_level)
1835  (const_cast<Elem *>(neigh))->hack_p_level(old_neigh_level);
1836 #endif // #ifdef LIBMESH_ENABLE_AMR
1837 
1838  const unsigned int n_side_dofs =
1839  cast_int<unsigned int>
1840  (my_side_dofs.size());
1841  libmesh_assert_equal_to (n_side_dofs, neigh_side_dofs.size());
1842 
1843  Ke.resize (n_side_dofs, n_side_dofs);
1844  Ue.resize(n_side_dofs);
1845 
1846  // Form the projection matrix, (inner product of fine basis
1847  // functions against fine test functions)
1848  for (unsigned int is = 0; is != n_side_dofs; ++is)
1849  {
1850  const unsigned int i = my_side_dofs[is];
1851  for (unsigned int js = 0; js != n_side_dofs; ++js)
1852  {
1853  const unsigned int j = my_side_dofs[js];
1854  for (unsigned int qp = 0; qp != n_qp; ++qp)
1855  {
1856  Ke(is,js) += JxW[qp] *
1857  TensorTools::inner_product(phi[i][qp],
1858  phi[j][qp]);
1859  if (cont != C_ZERO)
1860  Ke(is,js) += JxW[qp] *
1861  TensorTools::inner_product((*dphi)[i][qp] *
1862  (*face_normals)[qp],
1863  (*dphi)[j][qp] *
1864  (*face_normals)[qp]);
1865  }
1866  }
1867  }
1868 
1869  // Form the right hand sides, (inner product of coarse basis
1870  // functions against fine test functions)
1871  for (unsigned int is = 0; is != n_side_dofs; ++is)
1872  {
1873  const unsigned int i = neigh_side_dofs[is];
1874  Fe.resize (n_side_dofs);
1875  for (unsigned int js = 0; js != n_side_dofs; ++js)
1876  {
1877  const unsigned int j = my_side_dofs[js];
1878  for (unsigned int qp = 0; qp != n_qp; ++qp)
1879  {
1880  Fe(js) += JxW[qp] *
1881  TensorTools::inner_product(neigh_phi[i][qp],
1882  phi[j][qp]);
1883  if (cont != C_ZERO)
1884  Fe(js) += JxW[qp] *
1885  TensorTools::inner_product((*neigh_dphi)[i][qp] *
1886  (*face_normals)[qp],
1887  (*dphi)[j][qp] *
1888  (*face_normals)[qp]);
1889  }
1890  }
1891  Ke.cholesky_solve(Fe, Ue[is]);
1892  }
1893 
1894  // Make sure we're not adding recursive constraints
1895  // due to the redundancy in the way we add periodic
1896  // boundary constraints
1897  //
1898  // In order for this to work while threaded or on
1899  // distributed meshes, we need a rigorous way to
1900  // avoid recursive constraints. Here it is:
1901  //
1902  // For vertex DoFs, if there is a "prior" element
1903  // (i.e. a coarser element or an equally refined
1904  // element with a lower id) on this boundary which
1905  // contains the vertex point, then we will avoid
1906  // generating constraints; the prior element (or
1907  // something prior to it) may do so. If we are the
1908  // most prior (or "primary") element on this
1909  // boundary sharing this point, then we look at the
1910  // boundary periodic to us, we find the primary
1911  // element there, and if that primary is coarser or
1912  // equal-but-lower-id, then our vertex dofs are
1913  // constrained in terms of that element.
1914  //
1915  // For edge DoFs, if there is a coarser element
1916  // on this boundary sharing this edge, then we will
1917  // avoid generating constraints (we will be
1918  // constrained indirectly via AMR constraints
1919  // connecting us to the coarser element's DoFs). If
1920  // we are the coarsest element sharing this edge,
1921  // then we generate constraints if and only if we
1922  // are finer than the coarsest element on the
1923  // boundary periodic to us sharing the corresponding
1924  // periodic edge, or if we are at equal level but
1925  // our edge nodes have higher ids than the periodic
1926  // edge nodes (sorted from highest to lowest, then
1927  // compared lexicographically)
1928  //
1929  // For face DoFs, we generate constraints if we are
1930  // finer than our periodic neighbor, or if we are at
1931  // equal level but our element id is higher than its
1932  // element id.
1933  //
1934  // If the primary neighbor is also the current elem
1935  // (a 1-element-thick mesh) then we choose which
1936  // vertex dofs to constrain via lexicographic
1937  // ordering on point locations
1938 
1939  // FIXME: This code doesn't yet properly handle
1940  // cases where multiple different periodic BCs
1941  // intersect.
1942  std::set<dof_id_type> my_constrained_dofs;
1943 
1944  // Container to catch boundary IDs handed back by BoundaryInfo.
1945  std::vector<boundary_id_type> new_bc_ids;
1946 
1947  for (unsigned int n = 0; n != elem->n_nodes(); ++n)
1948  {
1949  if (!elem->is_node_on_side(n,s))
1950  continue;
1951 
1952  const Node & my_node = elem->node_ref(n);
1953 
1954  if (elem->is_vertex(n))
1955  {
1956  // Find all boundary ids that include this
1957  // point and have periodic boundary
1958  // conditions for this variable
1959  std::set<boundary_id_type> point_bcids;
1960 
1961  for (unsigned int new_s = 0;
1962  new_s != max_ns; ++new_s)
1963  {
1964  if (!elem->is_node_on_side(n,new_s))
1965  continue;
1966 
1967  mesh.get_boundary_info().boundary_ids (elem, s, new_bc_ids);
1968 
1969  for (const auto & new_boundary_id : new_bc_ids)
1970  {
1971  const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
1972  if (new_periodic && new_periodic->is_my_variable(variable_number))
1973  point_bcids.insert(new_boundary_id);
1974  }
1975  }
1976 
1977  // See if this vertex has point neighbors to
1978  // defer to
1979  if (primary_boundary_point_neighbor
1980  (elem, my_node, mesh.get_boundary_info(), point_bcids)
1981  != elem)
1982  continue;
1983 
1984  // Find the complementary boundary id set
1985  std::set<boundary_id_type> point_pairedids;
1986  for (const auto & new_boundary_id : point_bcids)
1987  {
1988  const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
1989  point_pairedids.insert(new_periodic->pairedboundary);
1990  }
1991 
1992  // What do we want to constrain against?
1993  const Elem * primary_elem = nullptr;
1994  const Elem * main_neigh = nullptr;
1995  Point main_pt = my_node,
1996  primary_pt = my_node;
1997 
1998  for (const auto & new_boundary_id : point_bcids)
1999  {
2000  // Find the corresponding periodic point and
2001  // its primary neighbor
2002  const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
2003 
2004  const Point neigh_pt =
2005  new_periodic->get_corresponding_pos(my_node);
2006 
2007  // If the point is getting constrained
2008  // to itself by this PBC then we don't
2009  // generate any constraints
2010  if (neigh_pt.absolute_fuzzy_equals
2011  (my_node, primary_hmin*TOLERANCE))
2012  continue;
2013 
2014  // Otherwise we'll have a constraint in
2015  // one direction or another
2016  if (!primary_elem)
2017  primary_elem = elem;
2018 
2019  const Elem * primary_neigh =
2020  primary_boundary_point_neighbor(neigh, neigh_pt,
2021  mesh.get_boundary_info(),
2022  point_pairedids);
2023 
2024  libmesh_assert(primary_neigh);
2025 
2026  if (new_boundary_id == boundary_id)
2027  {
2028  main_neigh = primary_neigh;
2029  main_pt = neigh_pt;
2030  }
2031 
2032  // Finer elements will get constrained in
2033  // terms of coarser neighbors, not the
2034  // other way around
2035  if ((primary_neigh->level() > primary_elem->level()) ||
2036 
2037  // For equal-level elements, the one with
2038  // higher id gets constrained in terms of
2039  // the one with lower id
2040  (primary_neigh->level() == primary_elem->level() &&
2041  primary_neigh->id() > primary_elem->id()) ||
2042 
2043  // On a one-element-thick mesh, we compare
2044  // points to see what side gets constrained
2045  (primary_neigh == primary_elem &&
2046  (neigh_pt > primary_pt)))
2047  continue;
2048 
2049  primary_elem = primary_neigh;
2050  primary_pt = neigh_pt;
2051  }
2052 
2053  if (!primary_elem ||
2054  primary_elem != main_neigh ||
2055  primary_pt != main_pt)
2056  continue;
2057  }
2058  else if (elem->is_edge(n))
2059  {
2060  // Find which edge we're on
2061  unsigned int e=0;
2062  for (; e != elem->n_edges(); ++e)
2063  {
2064  if (elem->is_node_on_edge(n,e))
2065  break;
2066  }
2067  libmesh_assert_less (e, elem->n_edges());
2068 
2069  // Find the edge end nodes
2070  const Node
2071  * e1 = nullptr,
2072  * e2 = nullptr;
2073  for (unsigned int nn = 0; nn != elem->n_nodes(); ++nn)
2074  {
2075  if (nn == n)
2076  continue;
2077 
2078  if (elem->is_node_on_edge(nn, e))
2079  {
2080  if (e1 == nullptr)
2081  {
2082  e1 = elem->node_ptr(nn);
2083  }
2084  else
2085  {
2086  e2 = elem->node_ptr(nn);
2087  break;
2088  }
2089  }
2090  }
2091  libmesh_assert (e1 && e2);
2092 
2093  // Find all boundary ids that include this
2094  // edge and have periodic boundary
2095  // conditions for this variable
2096  std::set<boundary_id_type> edge_bcids;
2097 
2098  for (unsigned int new_s = 0;
2099  new_s != max_ns; ++new_s)
2100  {
2101  if (!elem->is_node_on_side(n,new_s))
2102  continue;
2103 
2104  // We're reusing the new_bc_ids vector created outside the loop over nodes.
2105  mesh.get_boundary_info().boundary_ids (elem, s, new_bc_ids);
2106 
2107  for (const auto & new_boundary_id : new_bc_ids)
2108  {
2109  const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
2110  if (new_periodic && new_periodic->is_my_variable(variable_number))
2111  edge_bcids.insert(new_boundary_id);
2112  }
2113  }
2114 
2115 
2116  // See if this edge has neighbors to defer to
2117  if (primary_boundary_edge_neighbor
2118  (elem, *e1, *e2, mesh.get_boundary_info(), edge_bcids)
2119  != elem)
2120  continue;
2121 
2122  // Find the complementary boundary id set
2123  std::set<boundary_id_type> edge_pairedids;
2124  for (const auto & new_boundary_id : edge_bcids)
2125  {
2126  const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
2127  edge_pairedids.insert(new_periodic->pairedboundary);
2128  }
2129 
2130  // What do we want to constrain against?
2131  const Elem * primary_elem = nullptr;
2132  const Elem * main_neigh = nullptr;
2133  Point main_pt1 = *e1,
2134  main_pt2 = *e2,
2135  primary_pt1 = *e1,
2136  primary_pt2 = *e2;
2137 
2138  for (const auto & new_boundary_id : edge_bcids)
2139  {
2140  // Find the corresponding periodic edge and
2141  // its primary neighbor
2142  const PeriodicBoundaryBase * new_periodic = boundaries.boundary(new_boundary_id);
2143 
2144  Point neigh_pt1 = new_periodic->get_corresponding_pos(*e1),
2145  neigh_pt2 = new_periodic->get_corresponding_pos(*e2);
2146 
2147  // If the edge is getting constrained
2148  // to itself by this PBC then we don't
2149  // generate any constraints
2150  if (neigh_pt1.absolute_fuzzy_equals
2151  (*e1, primary_hmin*TOLERANCE) &&
2152  neigh_pt2.absolute_fuzzy_equals
2153  (*e2, primary_hmin*TOLERANCE))
2154  continue;
2155 
2156  // Otherwise we'll have a constraint in
2157  // one direction or another
2158  if (!primary_elem)
2159  primary_elem = elem;
2160 
2161  const Elem * primary_neigh = primary_boundary_edge_neighbor
2162  (neigh, neigh_pt1, neigh_pt2,
2163  mesh.get_boundary_info(), edge_pairedids);
2164 
2165  libmesh_assert(primary_neigh);
2166 
2167  if (new_boundary_id == boundary_id)
2168  {
2169  main_neigh = primary_neigh;
2170  main_pt1 = neigh_pt1;
2171  main_pt2 = neigh_pt2;
2172  }
2173 
2174  // If we have a one-element thick mesh,
2175  // we'll need to sort our points to get a
2176  // consistent ordering rule
2177  //
2178  // Use >= in this test to make sure that,
2179  // for angular constraints, no node gets
2180  // constrained to itself.
2181  if (primary_neigh == primary_elem)
2182  {
2183  if (primary_pt1 > primary_pt2)
2184  std::swap(primary_pt1, primary_pt2);
2185  if (neigh_pt1 > neigh_pt2)
2186  std::swap(neigh_pt1, neigh_pt2);
2187 
2188  if (neigh_pt2 >= primary_pt2)
2189  continue;
2190  }
2191 
2192  // Otherwise:
2193  // Finer elements will get constrained in
2194  // terms of coarser ones, not the other way
2195  // around
2196  if ((primary_neigh->level() > primary_elem->level()) ||
2197 
2198  // For equal-level elements, the one with
2199  // higher id gets constrained in terms of
2200  // the one with lower id
2201  (primary_neigh->level() == primary_elem->level() &&
2202  primary_neigh->id() > primary_elem->id()))
2203  continue;
2204 
2205  primary_elem = primary_neigh;
2206  primary_pt1 = neigh_pt1;
2207  primary_pt2 = neigh_pt2;
2208  }
2209 
2210  if (!primary_elem ||
2211  primary_elem != main_neigh ||
2212  primary_pt1 != main_pt1 ||
2213  primary_pt2 != main_pt2)
2214  continue;
2215  }
2216  else if (elem->is_face(n))
2217  {
2218  // If we have a one-element thick mesh,
2219  // use the ordering of the face node and its
2220  // periodic counterpart to determine what
2221  // gets constrained
2222  if (neigh == elem)
2223  {
2224  const Point neigh_pt =
2225  periodic->get_corresponding_pos(my_node);
2226  if (neigh_pt > my_node)
2227  continue;
2228  }
2229 
2230  // Otherwise:
2231  // Finer elements will get constrained in
2232  // terms of coarser ones, not the other way
2233  // around
2234  if ((neigh->level() > elem->level()) ||
2235 
2236  // For equal-level elements, the one with
2237  // higher id gets constrained in terms of
2238  // the one with lower id
2239  (neigh->level() == elem->level() &&
2240  neigh->id() > elem->id()))
2241  continue;
2242  }
2243 
2244  // If we made it here without hitting a continue
2245  // statement, then we're at a node whose dofs
2246  // should be constrained by this element's
2247  // calculations.
2248  const unsigned int n_comp =
2249  my_node.n_comp(sys_number, variable_number);
2250 
2251  for (unsigned int i=0; i != n_comp; ++i)
2252  my_constrained_dofs.insert
2253  (my_node.dof_number
2254  (sys_number, variable_number, i));
2255  }
2256 
2257  // FIXME: old code for disambiguating periodic BCs:
2258  // this is not threadsafe nor safe to run on a
2259  // non-serialized mesh.
2260  /*
2261  std::vector<bool> recursive_constraint(n_side_dofs, false);
2262 
2263  for (unsigned int is = 0; is != n_side_dofs; ++is)
2264  {
2265  const unsigned int i = neigh_side_dofs[is];
2266  const dof_id_type their_dof_g = neigh_dof_indices[i];
2267  libmesh_assert_not_equal_to (their_dof_g, DofObject::invalid_id);
2268 
2269  {
2270  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
2271 
2272  if (!dof_map.is_constrained_dof(their_dof_g))
2273  continue;
2274  }
2275 
2276  DofConstraintRow & their_constraint_row =
2277  constraints[their_dof_g].first;
2278 
2279  for (unsigned int js = 0; js != n_side_dofs; ++js)
2280  {
2281  const unsigned int j = my_side_dofs[js];
2282  const dof_id_type my_dof_g = my_dof_indices[j];
2283  libmesh_assert_not_equal_to (my_dof_g, DofObject::invalid_id);
2284 
2285  if (their_constraint_row.count(my_dof_g))
2286  recursive_constraint[js] = true;
2287  }
2288  }
2289  */
2290 
2291  for (unsigned int js = 0; js != n_side_dofs; ++js)
2292  {
2293  // FIXME: old code path
2294  // if (recursive_constraint[js])
2295  // continue;
2296 
2297  const unsigned int j = my_side_dofs[js];
2298  const dof_id_type my_dof_g = my_dof_indices[j];
2299  libmesh_assert_not_equal_to (my_dof_g, DofObject::invalid_id);
2300 
2301  // FIXME: new code path
2302  if (!my_constrained_dofs.count(my_dof_g))
2303  continue;
2304 
2305  DofConstraintRow * constraint_row;
2306 
2307  // we may be running constraint methods concurrently
2308  // on multiple threads, so we need a lock to
2309  // ensure that this constraint is "ours"
2310  {
2311  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
2312 
2313  if (dof_map.is_constrained_dof(my_dof_g))
2314  continue;
2315 
2316  constraint_row = &(constraints[my_dof_g]);
2317  libmesh_assert(constraint_row->empty());
2318  }
2319 
2320  for (unsigned int is = 0; is != n_side_dofs; ++is)
2321  {
2322  const unsigned int i = neigh_side_dofs[is];
2323  const dof_id_type their_dof_g = neigh_dof_indices[i];
2324  libmesh_assert_not_equal_to (their_dof_g, DofObject::invalid_id);
2325 
2326  // Periodic constraints should never be
2327  // self-constraints
2328  // libmesh_assert_not_equal_to (their_dof_g, my_dof_g);
2329 
2330  const Real their_dof_value = Ue[is](js);
2331 
2332  if (their_dof_g == my_dof_g)
2333  {
2334  libmesh_assert_less (std::abs(their_dof_value-1.), 1.e-5);
2335  for (unsigned int k = 0; k != n_side_dofs; ++k)
2336  libmesh_assert(k == is || std::abs(Ue[k](js)) < 1.e-5);
2337  continue;
2338  }
2339 
2340  if (std::abs(their_dof_value) < 10*TOLERANCE)
2341  continue;
2342 
2343  if(!periodic->has_transformation_matrix())
2344  {
2345  constraint_row->insert(std::make_pair(their_dof_g,
2346  their_dof_value));
2347  }
2348  else
2349  {
2350  // In this case the current variable is constrained in terms of other variables.
2351  // We assume that all variables in this constraint have the same FE type (this
2352  // is asserted below), and hence we can create the constraint row contribution
2353  // by multiplying their_dof_value by the corresponding row of the transformation
2354  // matrix.
2355 
2356  const std::set<unsigned int> & variables = periodic->get_variables();
2357  neigh_dof_indices_all_variables.resize(variables.size());
2358  unsigned int index = 0;
2359  for(unsigned int other_var : variables)
2360  {
2361  libmesh_assert_msg(base_fe_type == dof_map.variable_type(other_var), "FE types must match for all variables involved in constraint");
2362 
2363  Real var_weighting = periodic->get_transformation_matrix()(variable_number, other_var);
2364  constraint_row->insert(std::make_pair(neigh_dof_indices_all_variables[index][i],
2365  var_weighting*their_dof_value));
2366  index++;
2367  }
2368  }
2369 
2370  }
2371  }
2372  }
2373  // p refinement constraints:
2374  // constrain dofs shared between
2375  // active elements and neighbors with
2376  // lower polynomial degrees
2377 #ifdef LIBMESH_ENABLE_AMR
2378  const unsigned int min_p_level =
2379  neigh->min_p_level_by_neighbor(elem, elem->p_level());
2380  if (min_p_level < elem->p_level())
2381  {
2382  // Adaptive p refinement of non-hierarchic bases will
2383  // require more coding
2384  libmesh_assert(my_fe->is_hierarchic());
2385  dof_map.constrain_p_dofs(variable_number, elem,
2386  s, min_p_level);
2387  }
2388 #endif // #ifdef LIBMESH_ENABLE_AMR
2389  }
2390  }
2391  }
2392 }
libMesh::FEType
Manages the family, order, etc. parameters for a given FE.
Definition: fe_type.h:179
std::abs
double abs(double a)
Definition: libmesh_augment_std_namespace.h:59
libMesh::DofObject::dof_number
dof_id_type dof_number(const unsigned int s, const unsigned int var, const unsigned int comp) const
Definition: dof_object.h:833
libMesh::Node
A geometric point in (x,y,z) space associated with a DOF.
Definition: node.h:52
libMesh::invalid_uint
const unsigned int invalid_uint
Definition: libmesh.h:245
libMesh::DofObject::n_comp
unsigned int n_comp(const unsigned int s, const unsigned int var) const
Definition: dof_object.h:803
libMesh::Elem::is_face
virtual bool is_face(const unsigned int i) const =0
libMesh::DofMap::dof_indices
void dof_indices(const Elem *const elem, std::vector< dof_id_type > &di) const
Definition: dof_map.C:1930
libMesh::FEInterface::dofs_on_side
static void dofs_on_side(const Elem *const elem, const unsigned int dim, const FEType &fe_t, unsigned int s, std::vector< unsigned int > &di)
Definition: fe_interface.C:523
libMesh::PeriodicBoundaryBase::get_variables
const std::set< unsigned int > & get_variables() const
Definition: periodic_boundary_base.C:106
libMesh::DenseVector::resize
void resize(const unsigned int n)
Definition: dense_vector.h:355
libMesh::DofMap::variable_type
const FEType & variable_type(const unsigned int c) const
Definition: dof_map.h:1792
libMesh::BoundaryInfo::side_with_boundary_id
unsigned int side_with_boundary_id(const Elem *const elem, const boundary_id_type boundary_id) const
Definition: boundary_info.C:1558
libMesh::Elem
The base class for all geometric element types.
Definition: elem.h:100
mesh
MeshBase & mesh
Definition: mesh_communication.C:1245
libMesh::index_range
IntRange< std::size_t > index_range(const std::vector< T > &vec)
Definition: int_range.h:104
libMesh::PeriodicBoundaries::boundary
PeriodicBoundaryBase * boundary(boundary_id_type id)
Definition: periodic_boundaries.C:40
libMesh::Elem::is_node_on_side
virtual bool is_node_on_side(const unsigned int n, const unsigned int s) const =0
libMesh::FEType::default_quadrature_order
Order default_quadrature_order() const
Definition: fe_type.h:333
libMesh::Elem::p_level
unsigned int p_level() const
Definition: elem.h:2555
libMesh::TOLERANCE
static const Real TOLERANCE
Definition: libmesh_common.h:139
libMesh::MeshBase::get_boundary_info
const BoundaryInfo & get_boundary_info() const
Definition: mesh_base.h:131
libMesh::Elem::min_p_level_by_neighbor
unsigned int min_p_level_by_neighbor(const Elem *neighbor, unsigned int current_min) const
Definition: elem.C:1870
libMesh::DofMap::sys_number
unsigned int sys_number() const
Definition: dof_map.h:1744
libMesh::BoundaryInfo::boundary_ids
std::vector< boundary_id_type > boundary_ids(const Node *node) const
Definition: boundary_info.C:948
libMesh::Elem::is_node_on_edge
virtual bool is_node_on_edge(const unsigned int n, const unsigned int e) const =0
libMesh::PeriodicBoundaryBase::get_corresponding_pos
virtual Point get_corresponding_pos(const Point &pt) const =0
libMesh::Threads::spin_mtx
spin_mutex spin_mtx
Definition: threads.C:29
libMesh::FEGenericBase::phi
std::vector< std::vector< OutputShape > > phi
Definition: fe_base.h:498
libMesh::Elem::node_ref
const Node & node_ref(const unsigned int i) const
Definition: elem.h:1979
libMesh::DofObject::id
dof_id_type id() const
Definition: dof_object.h:655
libMesh::Elem::hmin
virtual Real hmin() const
Definition: elem.C:356
libMesh::Elem::n_nodes
virtual unsigned int n_nodes() const =0
libMesh::DofMap::is_constrained_dof
bool is_constrained_dof(const dof_id_type dof) const
Definition: dof_map.h:1829
libMesh::DofObject::invalid_id
static const dof_id_type invalid_id
Definition: dof_object.h:347
libMesh::FEInterface::inverse_map
static Point inverse_map(const unsigned int dim, const FEType &fe_t, const Elem *elem, const Point &p, const Real tolerance=TOLERANCE, const bool secure=true)
Definition: fe_interface.C:590
libMesh::Elem::n_edges
virtual unsigned int n_edges() const =0
libMesh::TypeVector::absolute_fuzzy_equals
bool absolute_fuzzy_equals(const TypeVector< T > &rhs, Real tol=TOLERANCE) const
Definition: type_vector.h:965
libMesh::FEGenericBase::dphi
std::vector< std::vector< OutputGradient > > dphi
Definition: fe_base.h:503
libMesh::PeriodicBoundaryBase::get_transformation_matrix
const DenseMatrix< Real > & get_transformation_matrix() const
Definition: periodic_boundary_base.C:81
libMesh::Elem::n_sides
virtual unsigned int n_sides() const =0
libMesh::Elem::neighbor_ptr
const Elem * neighbor_ptr(unsigned int i) const
Definition: elem.h:2050
libMesh::Elem::level
unsigned int level() const
Definition: elem.h:2521
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:131
libMesh::PeriodicBoundaries::neighbor
const Elem * neighbor(boundary_id_type boundary_id, const PointLocatorBase &point_locator, const Elem *e, unsigned int side) const
Definition: periodic_boundaries.C:61
libMesh::Elem::dim
virtual unsigned short dim() const =0
libMesh::Elem::node_ptr
const Node * node_ptr(const unsigned int i) const
Definition: elem.h:1957
libMesh::Elem::is_vertex
virtual bool is_vertex(const unsigned int i) const =0
swap
void swap(Iterator &lhs, Iterator &rhs)
Definition: variant_filter_iterator.h:478
libMesh::PeriodicBoundaryBase::is_my_variable
bool is_my_variable(unsigned int var_num) const
Definition: periodic_boundary_base.C:66
libMesh::DofConstraintRow
std::map< dof_id_type, Real, std::less< dof_id_type >, Threads::scalable_allocator< std::pair< const dof_id_type, Real > > > DofConstraintRow
Definition: dof_map.h:97
libMesh::DenseMatrix::resize
void resize(const unsigned int new_m, const unsigned int new_n)
Definition: dense_matrix.h:792
libMesh::QGauss
Implements 1, 2, and 3D "Gaussian" quadrature rules.
Definition: quadrature_gauss.h:39
libMesh::PeriodicBoundaryBase
Base class for all PeriodicBoundary implementations.
Definition: periodic_boundary_base.h:49
libMesh::DenseMatrix::cholesky_solve
void cholesky_solve(const DenseVector< T2 > &b, DenseVector< T2 > &x)
Definition: dense_matrix_impl.h:929
libMesh::DenseMatrix
A matrix object used for finite element assembly and numerics.
Definition: dense_matrix.h:54
libMesh::Elem::active
bool active() const
Definition: elem.h:2390
std::min
long double min(long double a, double b)
Definition: libmesh_augment_std_namespace.h:29
libMesh::Point
A geometric point in (x,y,z) space.
Definition: point.h:38
libMesh::Elem::is_edge
virtual bool is_edge(const unsigned int i) const =0
libMesh::TensorTools::inner_product
boostcopy::enable_if_c< ScalarTraits< T >::value &&ScalarTraits< T2 >::value, typename CompareTypes< T, T2 >::supertype >::type inner_product(const T &a, const T2 &b)
Definition: tensor_tools.h:47
libMesh::DofMap::constrain_p_dofs
void constrain_p_dofs(unsigned int var, const Elem *elem, unsigned int s, unsigned int p)
Definition: dof_map_constraints.C:4208
libMesh::dof_id_type
uint8_t dof_id_type
Definition: id_types.h:64

◆ compute_periodic_node_constraints()

void libMesh::FEAbstract::compute_periodic_node_constraints ( NodeConstraints &  constraints,
const PeriodicBoundaries &  boundaries,
const MeshBase &  mesh,
const PointLocatorBase *  point_locator,
const Elem *  elem 
)
staticinherited

Computes the node position constraint equation contributions (for meshes with periodic boundary conditions)

Definition at line 965 of file fe_abstract.C.

References libMesh::Elem::active(), libMesh::PeriodicBoundaries::boundary(), libMesh::Elem::build_side_ptr(), libMesh::Elem::default_order(), libMesh::Elem::dim(), libMesh::FEAbstract::fe_type, libMesh::PeriodicBoundaryBase::get_corresponding_pos(), libMesh::invalid_uint, libMesh::FEInterface::inverse_map(), libMesh::LAGRANGE, libMesh::Elem::level(), mesh, libMesh::FEInterface::n_dofs(), libMesh::PeriodicBoundaries::neighbor(), libMesh::Elem::neighbor_ptr(), libMesh::PeriodicBoundaryBase::pairedboundary, libMesh::Real, libMesh::FEInterface::shape(), libMesh::Elem::side_index_range(), and libMesh::Threads::spin_mtx.

970 {
971  // Only bother if we truly have periodic boundaries
972  if (boundaries.empty())
973  return;
974 
975  libmesh_assert(elem);
976 
977  // Only constrain active elements with this method
978  if (!elem->active())
979  return;
980 
981  const unsigned int Dim = elem->dim();
982 
983  // We currently always use LAGRANGE mappings for geometry
984  const FEType fe_type(elem->default_order(), LAGRANGE);
985 
986  // Pull objects out of the loop to reduce heap operations
987  std::vector<const Node *> my_nodes, neigh_nodes;
988  std::unique_ptr<const Elem> my_side, neigh_side;
989 
990  // Look at the element faces. Check to see if we need to
991  // build constraints.
992  std::vector<boundary_id_type> bc_ids;
993  for (auto s : elem->side_index_range())
994  {
995  if (elem->neighbor_ptr(s))
996  continue;
997 
998  mesh.get_boundary_info().boundary_ids (elem, s, bc_ids);
999  for (const auto & boundary_id : bc_ids)
1000  {
1001  const PeriodicBoundaryBase * periodic = boundaries.boundary(boundary_id);
1002  if (periodic)
1003  {
1004  libmesh_assert(point_locator);
1005 
1006  // Get pointers to the element's neighbor.
1007  const Elem * neigh = boundaries.neighbor(boundary_id, *point_locator, elem, s);
1008 
1009  // h refinement constraints:
1010  // constrain dofs shared between
1011  // this element and ones as coarse
1012  // as or coarser than this element.
1013  if (neigh->level() <= elem->level())
1014  {
1015  unsigned int s_neigh =
1016  mesh.get_boundary_info().side_with_boundary_id(neigh, periodic->pairedboundary);
1017  libmesh_assert_not_equal_to (s_neigh, libMesh::invalid_uint);
1018 
1019 #ifdef LIBMESH_ENABLE_AMR
1020  libmesh_assert(neigh->active());
1021 #endif // #ifdef LIBMESH_ENABLE_AMR
1022 
1023  elem->build_side_ptr(my_side, s);
1024  neigh->build_side_ptr(neigh_side, s_neigh);
1025 
1026  const unsigned int n_side_nodes = my_side->n_nodes();
1027 
1028  my_nodes.clear();
1029  my_nodes.reserve (n_side_nodes);
1030  neigh_nodes.clear();
1031  neigh_nodes.reserve (n_side_nodes);
1032 
1033  for (unsigned int n=0; n != n_side_nodes; ++n)
1034  my_nodes.push_back(my_side->node_ptr(n));
1035 
1036  for (unsigned int n=0; n != n_side_nodes; ++n)
1037  neigh_nodes.push_back(neigh_side->node_ptr(n));
1038 
1039  // Make sure we're not adding recursive constraints
1040  // due to the redundancy in the way we add periodic
1041  // boundary constraints, or adding constraints to
1042  // nodes that already have AMR constraints
1043  std::vector<bool> skip_constraint(n_side_nodes, false);
1044 
1045  for (unsigned int my_side_n=0;
1046  my_side_n < n_side_nodes;
1047  my_side_n++)
1048  {
1049  libmesh_assert_less (my_side_n, FEInterface::n_dofs(Dim-1, fe_type, my_side->type()));
1050 
1051  const Node * my_node = my_nodes[my_side_n];
1052 
1053  // Figure out where my node lies on their reference element.
1054  const Point neigh_point = periodic->get_corresponding_pos(*my_node);
1055 
1056  const Point mapped_point = FEInterface::inverse_map(Dim-1, fe_type,
1057  neigh_side.get(),
1058  neigh_point);
1059 
1060  // If we've already got a constraint on this
1061  // node, then the periodic constraint is
1062  // redundant
1063  {
1064  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
1065 
1066  if (constraints.count(my_node))
1067  {
1068  skip_constraint[my_side_n] = true;
1069  continue;
1070  }
1071  }
1072 
1073  // Compute the neighbors's side shape function values.
1074  for (unsigned int their_side_n=0;
1075  their_side_n < n_side_nodes;
1076  their_side_n++)
1077  {
1078  libmesh_assert_less (their_side_n, FEInterface::n_dofs(Dim-1, fe_type, neigh_side->type()));
1079 
1080  const Node * their_node = neigh_nodes[their_side_n];
1081 
1082  // If there's a constraint on an opposing node,
1083  // we need to see if it's constrained by
1084  // *our side* making any periodic constraint
1085  // on us recursive
1086  {
1087  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
1088 
1089  if (!constraints.count(their_node))
1090  continue;
1091 
1092  const NodeConstraintRow & their_constraint_row =
1093  constraints[their_node].first;
1094 
1095  for (unsigned int orig_side_n=0;
1096  orig_side_n < n_side_nodes;
1097  orig_side_n++)
1098  {
1099  libmesh_assert_less (orig_side_n, FEInterface::n_dofs(Dim-1, fe_type, my_side->type()));
1100 
1101  const Node * orig_node = my_nodes[orig_side_n];
1102 
1103  if (their_constraint_row.count(orig_node))
1104  skip_constraint[orig_side_n] = true;
1105  }
1106  }
1107  }
1108  }
1109  for (unsigned int my_side_n=0;
1110  my_side_n < n_side_nodes;
1111  my_side_n++)
1112  {
1113  libmesh_assert_less (my_side_n, FEInterface::n_dofs(Dim-1, fe_type, my_side->type()));
1114 
1115  if (skip_constraint[my_side_n])
1116  continue;
1117 
1118  const Node * my_node = my_nodes[my_side_n];
1119 
1120  // Figure out where my node lies on their reference element.
1121  const Point neigh_point = periodic->get_corresponding_pos(*my_node);
1122 
1123  // Figure out where my node lies on their reference element.
1124  const Point mapped_point = FEInterface::inverse_map(Dim-1, fe_type,
1125  neigh_side.get(),
1126  neigh_point);
1127 
1128  for (unsigned int their_side_n=0;
1129  their_side_n < n_side_nodes;
1130  their_side_n++)
1131  {
1132  libmesh_assert_less (their_side_n, FEInterface::n_dofs(Dim-1, fe_type, neigh_side->type()));
1133 
1134  const Node * their_node = neigh_nodes[their_side_n];
1135  libmesh_assert(their_node);
1136 
1137  const Real their_value = FEInterface::shape(Dim-1,
1138  fe_type,
1139  neigh_side->type(),
1140  their_side_n,
1141  mapped_point);
1142 
1143  // since we may be running this method concurrently
1144  // on multiple threads we need to acquire a lock
1145  // before modifying the shared constraint_row object.
1146  {
1147  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
1148 
1149  NodeConstraintRow & constraint_row =
1150  constraints[my_node].first;
1151 
1152  constraint_row.insert(std::make_pair(their_node,
1153  their_value));
1154  }
1155  }
1156  }
1157  }
1158  }
1159  }
1160  }
1161 }
libMesh::FEInterface::n_dofs
static unsigned int n_dofs(const unsigned int dim, const FEType &fe_t, const ElemType t)
Definition: fe_interface.C:454
libMesh::invalid_uint
const unsigned int invalid_uint
Definition: libmesh.h:245
mesh
MeshBase & mesh
Definition: mesh_communication.C:1245
libMesh::Threads::spin_mtx
spin_mutex spin_mtx
Definition: threads.C:29
libMesh::FEInterface::shape
static Real shape(const unsigned int dim, const FEType &fe_t, const ElemType t, const unsigned int i, const Point &p)
Definition: fe_interface.C:657
libMesh::FEInterface::inverse_map
static Point inverse_map(const unsigned int dim, const FEType &fe_t, const Elem *elem, const Point &p, const Real tolerance=TOLERANCE, const bool secure=true)
Definition: fe_interface.C:590
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:131
libMesh::NodeConstraintRow
std::map< const Node *, Real, std::less< const Node * >, Threads::scalable_allocator< std::pair< const Node *const, Real > > > NodeConstraintRow
Definition: dof_map.h:145

◆ compute_proj_constraints()

template<typename OutputType >
void libMesh::FEGenericBase< OutputType >::compute_proj_constraints ( DofConstraints &  constraints,
DofMap &  dof_map,
const unsigned int  variable_number,
const Elem *  elem 
)
static

Computes the constraint matrix contributions (for non-conforming adapted meshes) corresponding to variable number var_number, using generic projections.

Definition at line 1366 of file fe_base.C.

Referenced by libMesh::FE< Dim, LAGRANGE_VEC >::compute_constraints().

1370 {
1371  libmesh_assert(elem);
1372 
1373  const unsigned int Dim = elem->dim();
1374 
1375  // Only constrain elements in 2,3D.
1376  if (Dim == 1)
1377  return;
1378 
1379  // Only constrain active elements with this method
1380  if (!elem->active())
1381  return;
1382 
1383  const FEType & base_fe_type = dof_map.variable_type(variable_number);
1384 
1385  // Construct FE objects for this element and its neighbors.
1386  std::unique_ptr<FEGenericBase<OutputShape>> my_fe
1387  (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
1388  const FEContinuity cont = my_fe->get_continuity();
1389 
1390  // We don't need to constrain discontinuous elements
1391  if (cont == DISCONTINUOUS)
1392  return;
1393  libmesh_assert (cont == C_ZERO || cont == C_ONE);
1394 
1395  std::unique_ptr<FEGenericBase<OutputShape>> neigh_fe
1396  (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
1397 
1398  QGauss my_qface(Dim-1, base_fe_type.default_quadrature_order());
1399  my_fe->attach_quadrature_rule (&my_qface);
1400  std::vector<Point> neigh_qface;
1401 
1402  const std::vector<Real> & JxW = my_fe->get_JxW();
1403  const std::vector<Point> & q_point = my_fe->get_xyz();
1404  const std::vector<std::vector<OutputShape>> & phi = my_fe->get_phi();
1405  const std::vector<std::vector<OutputShape>> & neigh_phi =
1406  neigh_fe->get_phi();
1407  const std::vector<Point> * face_normals = nullptr;
1408  const std::vector<std::vector<OutputGradient>> * dphi = nullptr;
1409  const std::vector<std::vector<OutputGradient>> * neigh_dphi = nullptr;
1410 
1411  std::vector<dof_id_type> my_dof_indices, neigh_dof_indices;
1412  std::vector<unsigned int> my_side_dofs, neigh_side_dofs;
1413 
1414  if (cont != C_ZERO)
1415  {
1416  const std::vector<Point> & ref_face_normals =
1417  my_fe->get_normals();
1418  face_normals = &ref_face_normals;
1419  const std::vector<std::vector<OutputGradient>> & ref_dphi =
1420  my_fe->get_dphi();
1421  dphi = &ref_dphi;
1422  const std::vector<std::vector<OutputGradient>> & ref_neigh_dphi =
1423  neigh_fe->get_dphi();
1424  neigh_dphi = &ref_neigh_dphi;
1425  }
1426 
1427  DenseMatrix<Real> Ke;
1428  DenseVector<Real> Fe;
1429  std::vector<DenseVector<Real>> Ue;
1430 
1431  // Look at the element faces. Check to see if we need to
1432  // build constraints.
1433  for (auto s : elem->side_index_range())
1434  if (elem->neighbor_ptr(s) != nullptr)
1435  {
1436  // Get pointers to the element's neighbor.
1437  const Elem * neigh = elem->neighbor_ptr(s);
1438 
1439  // h refinement constraints:
1440  // constrain dofs shared between
1441  // this element and ones coarser
1442  // than this element.
1443  if (neigh->level() < elem->level())
1444  {
1445  unsigned int s_neigh = neigh->which_neighbor_am_i(elem);
1446  libmesh_assert_less (s_neigh, neigh->n_neighbors());
1447 
1448  // Find the minimum p level; we build the h constraint
1449  // matrix with this and then constrain away all higher p
1450  // DoFs.
1451  libmesh_assert(neigh->active());
1452  const unsigned int min_p_level =
1453  std::min(elem->p_level(), neigh->p_level());
1454 
1455  // we may need to make the FE objects reinit with the
1456  // minimum shared p_level
1457  const unsigned int old_elem_level = elem->p_level();
1458  if (elem->p_level() != min_p_level)
1459  my_fe->set_fe_order(my_fe->get_fe_type().order.get_order() - old_elem_level + min_p_level);
1460  const unsigned int old_neigh_level = neigh->p_level();
1461  if (old_neigh_level != min_p_level)
1462  neigh_fe->set_fe_order(neigh_fe->get_fe_type().order.get_order() - old_neigh_level + min_p_level);
1463 
1464  my_fe->reinit(elem, s);
1465 
1466  // This function gets called element-by-element, so there
1467  // will be a lot of memory allocation going on. We can
1468  // at least minimize this for the case of the dof indices
1469  // by efficiently preallocating the requisite storage.
1470  // n_nodes is not necessarily n_dofs, but it is better
1471  // than nothing!
1472  my_dof_indices.reserve (elem->n_nodes());
1473  neigh_dof_indices.reserve (neigh->n_nodes());
1474 
1475  dof_map.dof_indices (elem, my_dof_indices,
1476  variable_number,
1477  min_p_level);
1478  dof_map.dof_indices (neigh, neigh_dof_indices,
1479  variable_number,
1480  min_p_level);
1481 
1482  const unsigned int n_qp = my_qface.n_points();
1483 
1484  FEInterface::inverse_map (Dim, base_fe_type, neigh,
1485  q_point, neigh_qface);
1486 
1487  neigh_fe->reinit(neigh, &neigh_qface);
1488 
1489  // We're only concerned with DOFs whose values (and/or first
1490  // derivatives for C1 elements) are supported on side nodes
1491  FEType elem_fe_type = base_fe_type;
1492  if (old_elem_level != min_p_level)
1493  elem_fe_type.order = base_fe_type.order.get_order() - old_elem_level + min_p_level;
1494  FEType neigh_fe_type = base_fe_type;
1495  if (old_neigh_level != min_p_level)
1496  neigh_fe_type.order = base_fe_type.order.get_order() - old_neigh_level + min_p_level;
1497  FEInterface::dofs_on_side(elem, Dim, elem_fe_type, s, my_side_dofs);
1498  FEInterface::dofs_on_side(neigh, Dim, neigh_fe_type, s_neigh, neigh_side_dofs);
1499 
1500  const unsigned int n_side_dofs =
1501  cast_int<unsigned int>(my_side_dofs.size());
1502  libmesh_assert_equal_to (n_side_dofs, neigh_side_dofs.size());
1503 
1504  Ke.resize (n_side_dofs, n_side_dofs);
1505  Ue.resize(n_side_dofs);
1506 
1507  // Form the projection matrix, (inner product of fine basis
1508  // functions against fine test functions)
1509  for (unsigned int is = 0; is != n_side_dofs; ++is)
1510  {
1511  const unsigned int i = my_side_dofs[is];
1512  for (unsigned int js = 0; js != n_side_dofs; ++js)
1513  {
1514  const unsigned int j = my_side_dofs[js];
1515  for (unsigned int qp = 0; qp != n_qp; ++qp)
1516  {
1517  Ke(is,js) += JxW[qp] * TensorTools::inner_product(phi[i][qp], phi[j][qp]);
1518  if (cont != C_ZERO)
1519  Ke(is,js) += JxW[qp] *
1520  TensorTools::inner_product((*dphi)[i][qp] *
1521  (*face_normals)[qp],
1522  (*dphi)[j][qp] *
1523  (*face_normals)[qp]);
1524  }
1525  }
1526  }
1527 
1528  // Form the right hand sides, (inner product of coarse basis
1529  // functions against fine test functions)
1530  for (unsigned int is = 0; is != n_side_dofs; ++is)
1531  {
1532  const unsigned int i = neigh_side_dofs[is];
1533  Fe.resize (n_side_dofs);
1534  for (unsigned int js = 0; js != n_side_dofs; ++js)
1535  {
1536  const unsigned int j = my_side_dofs[js];
1537  for (unsigned int qp = 0; qp != n_qp; ++qp)
1538  {
1539  Fe(js) += JxW[qp] *
1540  TensorTools::inner_product(neigh_phi[i][qp],
1541  phi[j][qp]);
1542  if (cont != C_ZERO)
1543  Fe(js) += JxW[qp] *
1544  TensorTools::inner_product((*neigh_dphi)[i][qp] *
1545  (*face_normals)[qp],
1546  (*dphi)[j][qp] *
1547  (*face_normals)[qp]);
1548  }
1549  }
1550  Ke.cholesky_solve(Fe, Ue[is]);
1551  }
1552 
1553  for (unsigned int js = 0; js != n_side_dofs; ++js)
1554  {
1555  const unsigned int j = my_side_dofs[js];
1556  const dof_id_type my_dof_g = my_dof_indices[j];
1557  libmesh_assert_not_equal_to (my_dof_g, DofObject::invalid_id);
1558 
1559  // Hunt for "constraining against myself" cases before
1560  // we bother creating a constraint row
1561  bool self_constraint = false;
1562  for (unsigned int is = 0; is != n_side_dofs; ++is)
1563  {
1564  const unsigned int i = neigh_side_dofs[is];
1565  const dof_id_type their_dof_g = neigh_dof_indices[i];
1566  libmesh_assert_not_equal_to (their_dof_g, DofObject::invalid_id);
1567 
1568  if (their_dof_g == my_dof_g)
1569  {
1570 #ifndef NDEBUG
1571  const Real their_dof_value = Ue[is](js);
1572  libmesh_assert_less (std::abs(their_dof_value-1.),
1573  10*TOLERANCE);
1574 
1575  for (unsigned int k = 0; k != n_side_dofs; ++k)
1576  libmesh_assert(k == is ||
1577  std::abs(Ue[k](js)) <
1578  10*TOLERANCE);
1579 #endif
1580 
1581  self_constraint = true;
1582  break;
1583  }
1584  }
1585 
1586  if (self_constraint)
1587  continue;
1588 
1589  DofConstraintRow * constraint_row;
1590 
1591  // we may be running constraint methods concurrently
1592  // on multiple threads, so we need a lock to
1593  // ensure that this constraint is "ours"
1594  {
1595  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
1596 
1597  if (dof_map.is_constrained_dof(my_dof_g))
1598  continue;
1599 
1600  constraint_row = &(constraints[my_dof_g]);
1601  libmesh_assert(constraint_row->empty());
1602  }
1603 
1604  for (unsigned int is = 0; is != n_side_dofs; ++is)
1605  {
1606  const unsigned int i = neigh_side_dofs[is];
1607  const dof_id_type their_dof_g = neigh_dof_indices[i];
1608  libmesh_assert_not_equal_to (their_dof_g, DofObject::invalid_id);
1609  libmesh_assert_not_equal_to (their_dof_g, my_dof_g);
1610 
1611  const Real their_dof_value = Ue[is](js);
1612 
1613  if (std::abs(their_dof_value) < 10*TOLERANCE)
1614  continue;
1615 
1616  constraint_row->insert(std::make_pair(their_dof_g,
1617  their_dof_value));
1618  }
1619  }
1620 
1621  my_fe->set_fe_order(my_fe->get_fe_type().order.get_order() + old_elem_level - min_p_level);
1622  neigh_fe->set_fe_order(neigh_fe->get_fe_type().order.get_order() + old_neigh_level - min_p_level);
1623  }
1624 
1625  // p refinement constraints:
1626  // constrain dofs shared between
1627  // active elements and neighbors with
1628  // lower polynomial degrees
1629  const unsigned int min_p_level =
1630  neigh->min_p_level_by_neighbor(elem, elem->p_level());
1631  if (min_p_level < elem->p_level())
1632  {
1633  // Adaptive p refinement of non-hierarchic bases will
1634  // require more coding
1635  libmesh_assert(my_fe->is_hierarchic());
1636  dof_map.constrain_p_dofs(variable_number, elem,
1637  s, min_p_level);
1638  }
1639  }
1640 }
libMesh::FEType
Manages the family, order, etc. parameters for a given FE.
Definition: fe_type.h:179
std::abs
double abs(double a)
Definition: libmesh_augment_std_namespace.h:59
libMesh::Elem::side_index_range
IntRange< unsigned short > side_index_range() const
Definition: elem.h:2166
libMesh::DofMap::dof_indices
void dof_indices(const Elem *const elem, std::vector< dof_id_type > &di) const
Definition: dof_map.C:1930
libMesh::FEInterface::dofs_on_side
static void dofs_on_side(const Elem *const elem, const unsigned int dim, const FEType &fe_t, unsigned int s, std::vector< unsigned int > &di)
Definition: fe_interface.C:523
libMesh::DenseVector::resize
void resize(const unsigned int n)
Definition: dense_vector.h:355
libMesh::DofMap::variable_type
const FEType & variable_type(const unsigned int c) const
Definition: dof_map.h:1792
libMesh::Elem
The base class for all geometric element types.
Definition: elem.h:100
libMesh::FEType::default_quadrature_order
Order default_quadrature_order() const
Definition: fe_type.h:333
libMesh::Elem::p_level
unsigned int p_level() const
Definition: elem.h:2555
libMesh::FEType::order
OrderWrapper order
Definition: fe_type.h:198
libMesh::TOLERANCE
static const Real TOLERANCE
Definition: libmesh_common.h:139
libMesh::Elem::min_p_level_by_neighbor
unsigned int min_p_level_by_neighbor(const Elem *neighbor, unsigned int current_min) const
Definition: elem.C:1870
libMesh::Threads::spin_mtx
spin_mutex spin_mtx
Definition: threads.C:29
libMesh::FEGenericBase::phi
std::vector< std::vector< OutputShape > > phi
Definition: fe_base.h:498
libMesh::Elem::n_nodes
virtual unsigned int n_nodes() const =0
libMesh::Elem::which_neighbor_am_i
unsigned int which_neighbor_am_i(const Elem *e) const
Definition: elem.h:2314
libMesh::DofMap::is_constrained_dof
bool is_constrained_dof(const dof_id_type dof) const
Definition: dof_map.h:1829
libMesh::DofObject::invalid_id
static const dof_id_type invalid_id
Definition: dof_object.h:347
libMesh::FEInterface::inverse_map
static Point inverse_map(const unsigned int dim, const FEType &fe_t, const Elem *elem, const Point &p, const Real tolerance=TOLERANCE, const bool secure=true)
Definition: fe_interface.C:590
libMesh::FEGenericBase::dphi
std::vector< std::vector< OutputGradient > > dphi
Definition: fe_base.h:503
libMesh::OrderWrapper::get_order
int get_order() const
Definition: fe_type.h:78
libMesh::Elem::neighbor_ptr
const Elem * neighbor_ptr(unsigned int i) const
Definition: elem.h:2050
libMesh::Elem::level
unsigned int level() const
Definition: elem.h:2521
libMesh::Real
DIE A HORRIBLE DEATH HERE typedef LIBMESH_DEFAULT_SCALAR_TYPE Real
Definition: libmesh_common.h:131
libMesh::Elem::dim
virtual unsigned short dim() const =0
libMesh::Elem::n_neighbors
unsigned int n_neighbors() const
Definition: elem.h:644
libMesh::DofConstraintRow
std::map< dof_id_type, Real, std::less< dof_id_type >, Threads::scalable_allocator< std::pair< const dof_id_type, Real > > > DofConstraintRow
Definition: dof_map.h:97
libMesh::DenseMatrix::resize
void resize(const unsigned int new_m, const unsigned int new_n)
Definition: dense_matrix.h:792
libMesh::QGauss
Implements 1, 2, and 3D "Gaussian" quadrature rules.
Definition: quadrature_gauss.h:39
libMesh::DenseMatrix::cholesky_solve
void cholesky_solve(const DenseVector< T2 > &b, DenseVector< T2 > &x)
Definition: dense_matrix_impl.h:929
libMesh::DenseMatrix
A matrix object used for finite element assembly and numerics.
Definition: dense_matrix.h:54
libMesh::Elem::active
bool active() const
Definition: elem.h:2390
std::min
long double min(long double a, double b)
Definition: libmesh_augment_std_namespace.h:29
libMesh::TensorTools::inner_product
boostcopy::enable_if_c< ScalarTraits< T >::value &&ScalarTraits< T2 >::value, typename CompareTypes< T, T2 >::supertype >::type inner_product(const T &a, const T2 &b)
Definition: tensor_tools.h:47
libMesh::DofMap::constrain_p_dofs
void constrain_p_dofs(unsigned int var, const Elem *elem, unsigned int s, unsigned int p)
Definition: dof_map_constraints.C:4208
libMesh::dof_id_type
uint8_t dof_id_type
Definition: id_types.h:64

◆ compute_shape_functions()

template<typename OutputType >
void libMesh::FEGenericBase< OutputType >::compute_shape_functions ( const Elem *  elem,
const std::vector< Point > &  qp 
)
protectedvirtual

After having updated the jacobian and the transformation from local to global coordinates in FEAbstract::compute_map(), the first derivatives of the shape functions are transformed to global coordinates, giving dphi, dphidx, dphidy, and dphidz. This method should rarely be re-defined in derived classes, but still should be usable for children. Therefore, keep it protected.

Implements libMesh::FEAbstract.

Reimplemented in libMesh::FEXYZ< Dim >, and libMesh::InfFE< Dim, T_radial, T_map >.

Definition at line 669 of file fe_base.C.

671 {
672  //-------------------------------------------------------------------------
673  // Compute the shape function values (and derivatives)
674  // at the Quadrature points. Note that the actual values
675  // have already been computed via init_shape_functions
676 
677  // Start logging the shape function computation
678  LOG_SCOPE("compute_shape_functions()", "FE");
679 
680  this->determine_calculations();
681 
682  if (calculate_phi)
683  this->_fe_trans->map_phi(this->dim, elem, qp, (*this), this->phi);
684 
685  if (calculate_dphi)
686  this->_fe_trans->map_dphi(this->dim, elem, qp, (*this), this->dphi,
687  this->dphidx, this->dphidy, this->dphidz);
688 
689 #ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
690  if (calculate_d2phi)
691  this->_fe_trans->map_d2phi(this->dim, qp, (*this), this->d2phi,
692  this->d2phidx2, this->d2phidxdy, this->d2phidxdz,
693  this->d2phidy2, this->d2phidydz, this->d2phidz2);
694 #endif //LIBMESH_ENABLE_SECOND_DERIVATIVES
695 
696  // Only compute curl for vector-valued elements
697  if (calculate_curl_phi && TypesEqual<OutputType,RealGradient>::value)
698  this->_fe_trans->map_curl(this->dim, elem, qp, (*this), this->curl_phi);
699 
700  // Only compute div for vector-valued elements
701  if (calculate_div_phi && TypesEqual<OutputType,RealGradient>::value)
702  this->_fe_trans->map_div(this->dim, elem, qp, (*this), this->div_phi);
703 }
libMesh::FEGenericBase::d2phi
std::vector< std::vector< OutputTensor > > d2phi
Definition: fe_base.h:551
libMesh::FEGenericBase::d2phidxdz
std::vector< std::vector< OutputShape > > d2phidxdz
Definition: fe_base.h:596
libMesh::FEGenericBase::d2phidydz
std::vector< std::vector< OutputShape > > d2phidydz
Definition: fe_base.h:606
libMesh::FEGenericBase::_fe_trans
std::unique_ptr< FETransformationBase< OutputType > > _fe_trans
Definition: fe_base.h:493
libMesh::FEGenericBase::d2phidx2
std::vector< std::vector< OutputShape > > d2phidx2
Definition: fe_base.h:586
libMesh::FEGenericBase::curl_phi
std::vector< std::vector< OutputShape > > curl_phi
Definition: fe_base.h:508
libMesh::FEGenericBase::dphidy
std::vector< std::vector< OutputShape > > dphidy
Definition: fe_base.h:538
libMesh::FEGenericBase::d2phidy2
std::vector< std::vector< OutputShape > > d2phidy2
Definition: fe_base.h:601
libMesh::FEGenericBase::d2phidxdy
std::vector< std::vector< OutputShape > > d2phidxdy
Definition: fe_base.h:591
libMesh::FEGenericBase::dphidx
std::vector< std::vector< OutputShape > > dphidx
Definition: fe_base.h:533
libMesh::FEGenericBase::phi
std::vector< std::vector< OutputShape > > phi
Definition: fe_base.h:498
libMesh::FEAbstract::dim
const unsigned int dim
Definition: fe_abstract.h:531
libMesh::FEGenericBase::div_phi
std::vector< std::vector< OutputDivergence > > div_phi
Definition: fe_base.h:513
libMesh::FEGenericBase::determine_calculations
void determine_calculations()
Definition: fe_base.C:728
libMesh::FEGenericBase::dphi
std::vector< std::vector< OutputGradient > > dphi
Definition: fe_base.h:503
libMesh::FEGenericBase::d2phidz2
std::vector< std::vector< OutputShape > > d2phidz2
Definition: fe_base.h:611
libMesh::FEGenericBase::dphidz
std::vector< std::vector< OutputShape > > dphidz
Definition: fe_base.h:543

◆ determine_calculations()

template<typename OutputType >
void libMesh::FEGenericBase< OutputType >::determine_calculations ( )
protected

Determine which values are to be calculated, for both the FE itself and for the FEMap.

Definition at line 728 of file fe_base.C.

729 {
730  this->calculations_started = true;
731 
732  // If the user forgot to request anything, we'll be safe and
733  // calculate everything:
734 #ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
735  if (!this->calculate_phi && !this->calculate_dphi && !this->calculate_d2phi
736  && !this->calculate_curl_phi && !this->calculate_div_phi)
737  {
738  this->calculate_phi = this->calculate_dphi = this->calculate_d2phi = this->calculate_dphiref = true;
739  if (FEInterface::field_type(fe_type.family) == TYPE_VECTOR)
740  {
741  this->calculate_curl_phi = true;
742  this->calculate_div_phi = true;
743  }
744  }
745 #else
746  if (!this->calculate_phi && !this->calculate_dphi && !this->calculate_curl_phi && !this->calculate_div_phi)
747  {
748  this->calculate_phi = this->calculate_dphi = this->calculate_dphiref = true;
749  if (FEInterface::field_type(fe_type.family) == TYPE_VECTOR)
750  {
751  this->calculate_curl_phi = true;
752  this->calculate_div_phi = true;
753  }
754  }
755 #endif // LIBMESH_ENABLE_SECOND_DERIVATIVES
756 
757  // Request whichever terms are necessary from the FEMap
758  if (this->calculate_phi)
759  this->_fe_trans->init_map_phi(*this);
760 
761  if (this->calculate_dphiref)
762  this->_fe_trans->init_map_dphi(*this);
763 
764 #ifdef LIBMESH_ENABLE_SECOND_DERIVATIVES
765  if (this->calculate_d2phi)
766  this->_fe_trans->init_map_d2phi(*this);
767 #endif //LIBMESH_ENABLE_SECOND_DERIVATIVES
768 }
libMesh::FEType::family
FEFamily family
Definition: fe_type.h:204
libMesh::FEGenericBase::_fe_trans
std::unique_ptr< FETransformationBase< OutputType > > _fe_trans
Definition: fe_base.h:493
libMesh::FEInterface::field_type
static FEFieldType field_type(const FEType &fe_type)
Definition: fe_interface.C:1437

◆ disable_print_counter_info()

void libMesh::ReferenceCounter::disable_print_counter_info ( )
staticinherited

Definition at line 106 of file reference_counter.C.

References libMesh::ReferenceCounter::_enable_print_counter.

Referenced by libMesh::LibMeshInit::LibMeshInit().

107 {
108  _enable_print_counter = false;
109  return;
110 }

◆ edge_reinit()

virtual void libMesh::FEAbstract::edge_reinit ( const Elem *  elem,
const unsigned int  edge,
const Real  tolerance = TOLERANCE,
const std::vector< Point > *  pts = nullptr,
const std::vector< Real > *  weights = nullptr 
)
pure virtualinherited

Reinitializes all the physical element-dependent data based on the edge of the element elem. The tolerance parameter is passed to the involved call to inverse_map(). By default the element data are computed at the quadrature points specified by the quadrature rule qrule, but any set of points on the reference edge element may be specified in the optional argument pts.

Implemented in libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::InfFE< Dim, T_radial, T_map >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, and libMesh::FE< Dim, LAGRANGE_VEC >.

◆ enable_print_counter_info()

void libMesh::ReferenceCounter::enable_print_counter_info ( )
staticinherited

Methods to enable/disable the reference counter output from print_info()

Definition at line 100 of file reference_counter.C.

References libMesh::ReferenceCounter::_enable_print_counter.

101 {
102  _enable_print_counter = true;
103  return;
104 }

◆ get_continuity()

virtual FEContinuity libMesh::FEAbstract::get_continuity ( ) const
pure virtualinherited
Returns
The continuity level of the finite element.

Implemented in libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::InfFE< Dim, T_radial, T_map >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, and libMesh::FE< Dim, LAGRANGE_VEC >.

Referenced by libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::operator()().

◆ get_curl_phi()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_curl_phi ( ) const
inline
Returns
The curl of the shape function at the quadrature points.

Definition at line 223 of file fe_base.h.

Referenced by libMesh::ExactSolution::_compute_error(), and libMesh::FEMContext::interior_curl().

224  { libmesh_assert(!calculations_started || calculate_curl_phi);
225  calculate_curl_phi = calculate_dphiref = true; return curl_phi; }
libMesh::FEGenericBase::curl_phi
std::vector< std::vector< OutputShape > > curl_phi
Definition: fe_base.h:508

◆ get_curvatures()

const std::vector<Real>& libMesh::FEAbstract::get_curvatures ( ) const
inlineinherited
Returns
The curvatures for use in face integration.

Definition at line 391 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

392  { return this->_fe_map->get_curvatures();}
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_d2phi()

template<typename OutputType>
const std::vector<std::vector<OutputTensor> >& libMesh::FEGenericBase< OutputType >::get_d2phi ( ) const
inline
Returns
The shape function second derivatives at the quadrature points.

Definition at line 289 of file fe_base.h.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::System::calculate_norm(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::LaplacianErrorEstimator::init_context(), libMesh::ParsedFEMFunction< T >::init_context(), libMesh::FEMContext::interior_hessians(), libMesh::LaplacianErrorEstimator::internal_side_integration(), libMesh::FEMContext::side_hessians(), and libMesh::FEMContext::some_hessian().

290  { libmesh_assert(!calculations_started || calculate_d2phi);
291  calculate_d2phi = calculate_dphiref = true; return d2phi; }
libMesh::FEGenericBase::d2phi
std::vector< std::vector< OutputTensor > > d2phi
Definition: fe_base.h:551

◆ get_d2phideta2()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phideta2 ( ) const
inline
Returns
The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 369 of file fe_base.h.

Referenced by libMesh::H1FETransformation< OutputShape >::map_d2phi().

370  { libmesh_assert(!calculations_started || calculate_d2phi);
371  calculate_d2phi = calculate_dphiref = true; return d2phideta2; }
libMesh::FEGenericBase::d2phideta2
std::vector< std::vector< OutputShape > > d2phideta2
Definition: fe_base.h:571

◆ get_d2phidetadzeta()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidetadzeta ( ) const
inline
Returns
The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 377 of file fe_base.h.

Referenced by libMesh::H1FETransformation< OutputShape >::map_d2phi().

378  { libmesh_assert(!calculations_started || calculate_d2phi);
379  calculate_d2phi = calculate_dphiref = true; return d2phidetadzeta; }
libMesh::FEGenericBase::d2phidetadzeta
std::vector< std::vector< OutputShape > > d2phidetadzeta
Definition: fe_base.h:576

◆ get_d2phidx2()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidx2 ( ) const
inline
Returns
The shape function second derivatives at the quadrature points.

Definition at line 297 of file fe_base.h.

298  { libmesh_assert(!calculations_started || calculate_d2phi);
299  calculate_d2phi = calculate_dphiref = true; return d2phidx2; }
libMesh::FEGenericBase::d2phidx2
std::vector< std::vector< OutputShape > > d2phidx2
Definition: fe_base.h:586

◆ get_d2phidxdy()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidxdy ( ) const
inline
Returns
The shape function second derivatives at the quadrature points.

Definition at line 305 of file fe_base.h.

306  { libmesh_assert(!calculations_started || calculate_d2phi);
307  calculate_d2phi = calculate_dphiref = true; return d2phidxdy; }
libMesh::FEGenericBase::d2phidxdy
std::vector< std::vector< OutputShape > > d2phidxdy
Definition: fe_base.h:591

◆ get_d2phidxdz()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidxdz ( ) const
inline
Returns
The shape function second derivatives at the quadrature points.

Definition at line 313 of file fe_base.h.

314  { libmesh_assert(!calculations_started || calculate_d2phi);
315  calculate_d2phi = calculate_dphiref = true; return d2phidxdz; }
libMesh::FEGenericBase::d2phidxdz
std::vector< std::vector< OutputShape > > d2phidxdz
Definition: fe_base.h:596

◆ get_d2phidxi2()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidxi2 ( ) const
inline
Returns
The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 345 of file fe_base.h.

Referenced by libMesh::H1FETransformation< OutputShape >::map_d2phi().

346  { libmesh_assert(!calculations_started || calculate_d2phi);
347  calculate_d2phi = calculate_dphiref = true; return d2phidxi2; }
libMesh::FEGenericBase::d2phidxi2
std::vector< std::vector< OutputShape > > d2phidxi2
Definition: fe_base.h:556

◆ get_d2phidxideta()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidxideta ( ) const
inline
Returns
The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 353 of file fe_base.h.

Referenced by libMesh::H1FETransformation< OutputShape >::map_d2phi().

354  { libmesh_assert(!calculations_started || calculate_d2phi);
355  calculate_d2phi = calculate_dphiref = true; return d2phidxideta; }
libMesh::FEGenericBase::d2phidxideta
std::vector< std::vector< OutputShape > > d2phidxideta
Definition: fe_base.h:561

◆ get_d2phidxidzeta()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidxidzeta ( ) const
inline
Returns
The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 361 of file fe_base.h.

Referenced by libMesh::H1FETransformation< OutputShape >::map_d2phi().

362  { libmesh_assert(!calculations_started || calculate_d2phi);
363  calculate_d2phi = calculate_dphiref = true; return d2phidxidzeta; }
libMesh::FEGenericBase::d2phidxidzeta
std::vector< std::vector< OutputShape > > d2phidxidzeta
Definition: fe_base.h:566

◆ get_d2phidy2()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidy2 ( ) const
inline
Returns
The shape function second derivatives at the quadrature points.

Definition at line 321 of file fe_base.h.

322  { libmesh_assert(!calculations_started || calculate_d2phi);
323  calculate_d2phi = calculate_dphiref = true; return d2phidy2; }
libMesh::FEGenericBase::d2phidy2
std::vector< std::vector< OutputShape > > d2phidy2
Definition: fe_base.h:601

◆ get_d2phidydz()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidydz ( ) const
inline
Returns
The shape function second derivatives at the quadrature points.

Definition at line 329 of file fe_base.h.

330  { libmesh_assert(!calculations_started || calculate_d2phi);
331  calculate_d2phi = calculate_dphiref = true; return d2phidydz; }
libMesh::FEGenericBase::d2phidydz
std::vector< std::vector< OutputShape > > d2phidydz
Definition: fe_base.h:606

◆ get_d2phidz2()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidz2 ( ) const
inline
Returns
The shape function second derivatives at the quadrature points.

Definition at line 337 of file fe_base.h.

338  { libmesh_assert(!calculations_started || calculate_d2phi);
339  calculate_d2phi = calculate_dphiref = true; return d2phidz2; }
libMesh::FEGenericBase::d2phidz2
std::vector< std::vector< OutputShape > > d2phidz2
Definition: fe_base.h:611

◆ get_d2phidzeta2()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_d2phidzeta2 ( ) const
inline
Returns
The shape function second derivatives at the quadrature points, in reference coordinates

Definition at line 385 of file fe_base.h.

Referenced by libMesh::H1FETransformation< OutputShape >::map_d2phi().

386  { libmesh_assert(!calculations_started || calculate_d2phi);
387  calculate_d2phi = calculate_dphiref = true; return d2phidzeta2; }
libMesh::FEGenericBase::d2phidzeta2
std::vector< std::vector< OutputShape > > d2phidzeta2
Definition: fe_base.h:581

◆ get_d2xyzdeta2()

const std::vector<RealGradient>& libMesh::FEAbstract::get_d2xyzdeta2 ( ) const
inlineinherited
Returns
The second partial derivatives in eta.

Definition at line 278 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

279  { return this->_fe_map->get_d2xyzdeta2(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_d2xyzdetadzeta()

const std::vector<RealGradient>& libMesh::FEAbstract::get_d2xyzdetadzeta ( ) const
inlineinherited
Returns
The second partial derivatives in eta-zeta.

Definition at line 308 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

309  { return this->_fe_map->get_d2xyzdetadzeta(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_d2xyzdxi2()

const std::vector<RealGradient>& libMesh::FEAbstract::get_d2xyzdxi2 ( ) const
inlineinherited
Returns
The second partial derivatives in xi.

Definition at line 272 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

273  { return this->_fe_map->get_d2xyzdxi2(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_d2xyzdxideta()

const std::vector<RealGradient>& libMesh::FEAbstract::get_d2xyzdxideta ( ) const
inlineinherited
Returns
The second partial derivatives in xi-eta.

Definition at line 294 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

295  { return this->_fe_map->get_d2xyzdxideta(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_d2xyzdxidzeta()

const std::vector<RealGradient>& libMesh::FEAbstract::get_d2xyzdxidzeta ( ) const
inlineinherited
Returns
The second partial derivatives in xi-zeta.

Definition at line 302 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

303  { return this->_fe_map->get_d2xyzdxidzeta(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_d2xyzdzeta2()

const std::vector<RealGradient>& libMesh::FEAbstract::get_d2xyzdzeta2 ( ) const
inlineinherited
Returns
The second partial derivatives in zeta.

Definition at line 286 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

287  { return this->_fe_map->get_d2xyzdzeta2(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_detadx()

const std::vector<Real>& libMesh::FEAbstract::get_detadx ( ) const
inlineinherited
Returns
The deta/dx entry in the transformation matrix from physical to local coordinates.

Definition at line 338 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

339  { return this->_fe_map->get_detadx(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_detady()

const std::vector<Real>& libMesh::FEAbstract::get_detady ( ) const
inlineinherited
Returns
The deta/dy entry in the transformation matrix from physical to local coordinates.

Definition at line 345 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

346  { return this->_fe_map->get_detady(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_detadz()

const std::vector<Real>& libMesh::FEAbstract::get_detadz ( ) const
inlineinherited
Returns
The deta/dz entry in the transformation matrix from physical to local coordinates.

Definition at line 352 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

353  { return this->_fe_map->get_detadz(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dim()

unsigned int libMesh::FEAbstract::get_dim ( ) const
inlineinherited
Returns
the dimension of this FE

Definition at line 231 of file fe_abstract.h.

References libMesh::FEAbstract::dim.

232  { return dim; }
libMesh::FEAbstract::dim
const unsigned int dim
Definition: fe_abstract.h:531

◆ get_div_phi()

template<typename OutputType>
const std::vector<std::vector<OutputDivergence> >& libMesh::FEGenericBase< OutputType >::get_div_phi ( ) const
inline
Returns
The divergence of the shape function at the quadrature points.

Definition at line 231 of file fe_base.h.

Referenced by libMesh::ExactSolution::_compute_error(), and libMesh::FEMContext::interior_div().

232  { libmesh_assert(!calculations_started || calculate_div_phi);
233  calculate_div_phi = calculate_dphiref = true; return div_phi; }
libMesh::FEGenericBase::div_phi
std::vector< std::vector< OutputDivergence > > div_phi
Definition: fe_base.h:513

◆ get_dphase()

template<typename OutputType>
const std::vector<OutputGradient>& libMesh::FEGenericBase< OutputType >::get_dphase ( ) const
inline
Returns
The global first derivative of the phase term which is used in infinite elements, evaluated at the quadrature points.

In case of the general finite element class FE this field is initialized to all zero, so that the variational formulation for an infinite element produces correct element matrices for a mesh using both finite and infinite elements.

Definition at line 403 of file fe_base.h.

404  { return dphase; }
libMesh::FEGenericBase::dphase
std::vector< OutputGradient > dphase
Definition: fe_base.h:629

◆ get_dphi()

template<typename OutputType>
const std::vector<std::vector<OutputGradient> >& libMesh::FEGenericBase< OutputType >::get_dphi ( ) const
inline
Returns
The shape function derivatives at the quadrature points.

Definition at line 215 of file fe_base.h.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::System::calculate_norm(), libMesh::OldSolutionCoefs< Output, point_output >::eval_at_point(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::OldSolutionBase< Output, point_output >::get_shape_outputs(), libMesh::ParsedFEMFunction< T >::init_context(), libMesh::KellyErrorEstimator::init_context(), libMesh::FEMContext::interior_gradients(), libMesh::KellyErrorEstimator::internal_side_integration(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::operator()(), libMesh::FEMContext::side_gradient(), libMesh::FEMContext::side_gradients(), and libMesh::FEMContext::some_gradient().

216  { libmesh_assert(!calculations_started || calculate_dphi);
217  calculate_dphi = calculate_dphiref = true; return dphi; }
libMesh::FEGenericBase::dphi
std::vector< std::vector< OutputGradient > > dphi
Definition: fe_base.h:503

◆ get_dphideta()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_dphideta ( ) const
inline
Returns
The shape function eta-derivative at the quadrature points.

Definition at line 271 of file fe_base.h.

Referenced by libMesh::HCurlFETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_d2phi(), libMesh::H1FETransformation< OutputShape >::map_div(), and libMesh::H1FETransformation< OutputShape >::map_dphi().

272  { libmesh_assert(!calculations_started || calculate_dphiref);
273  calculate_dphiref = true; return dphideta; }
libMesh::FEGenericBase::dphideta
std::vector< std::vector< OutputShape > > dphideta
Definition: fe_base.h:523

◆ get_dphidx()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_dphidx ( ) const
inline
Returns
The shape function x-derivative at the quadrature points.

Definition at line 239 of file fe_base.h.

240  { libmesh_assert(!calculations_started || calculate_dphi);
241  calculate_dphi = calculate_dphiref = true; return dphidx; }
libMesh::FEGenericBase::dphidx
std::vector< std::vector< OutputShape > > dphidx
Definition: fe_base.h:533

◆ get_dphidxi()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_dphidxi ( ) const
inline
Returns
The shape function xi-derivative at the quadrature points.

Definition at line 263 of file fe_base.h.

Referenced by libMesh::HCurlFETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_d2phi(), libMesh::H1FETransformation< OutputShape >::map_div(), and libMesh::H1FETransformation< OutputShape >::map_dphi().

264  { libmesh_assert(!calculations_started || calculate_dphiref);
265  calculate_dphiref = true; return dphidxi; }
libMesh::FEGenericBase::dphidxi
std::vector< std::vector< OutputShape > > dphidxi
Definition: fe_base.h:518

◆ get_dphidy()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_dphidy ( ) const
inline
Returns
The shape function y-derivative at the quadrature points.

Definition at line 247 of file fe_base.h.

248  { libmesh_assert(!calculations_started || calculate_dphi);
249  calculate_dphi = calculate_dphiref = true; return dphidy; }
libMesh::FEGenericBase::dphidy
std::vector< std::vector< OutputShape > > dphidy
Definition: fe_base.h:538

◆ get_dphidz()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_dphidz ( ) const
inline
Returns
The shape function z-derivative at the quadrature points.

Definition at line 255 of file fe_base.h.

256  { libmesh_assert(!calculations_started || calculate_dphi);
257  calculate_dphi = calculate_dphiref = true; return dphidz; }
libMesh::FEGenericBase::dphidz
std::vector< std::vector< OutputShape > > dphidz
Definition: fe_base.h:543

◆ get_dphidzeta()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_dphidzeta ( ) const
inline
Returns
The shape function zeta-derivative at the quadrature points.

Definition at line 279 of file fe_base.h.

Referenced by libMesh::HCurlFETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_d2phi(), libMesh::H1FETransformation< OutputShape >::map_div(), and libMesh::H1FETransformation< OutputShape >::map_dphi().

280  { libmesh_assert(!calculations_started || calculate_dphiref);
281  calculate_dphiref = true; return dphidzeta; }
libMesh::FEGenericBase::dphidzeta
std::vector< std::vector< OutputShape > > dphidzeta
Definition: fe_base.h:528

◆ get_dxidx()

const std::vector<Real>& libMesh::FEAbstract::get_dxidx ( ) const
inlineinherited
Returns
The dxi/dx entry in the transformation matrix from physical to local coordinates.

Definition at line 317 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

318  { return this->_fe_map->get_dxidx(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dxidy()

const std::vector<Real>& libMesh::FEAbstract::get_dxidy ( ) const
inlineinherited
Returns
The dxi/dy entry in the transformation matrix from physical to local coordinates.

Definition at line 324 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

325  { return this->_fe_map->get_dxidy(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dxidz()

const std::vector<Real>& libMesh::FEAbstract::get_dxidz ( ) const
inlineinherited
Returns
The dxi/dz entry in the transformation matrix from physical to local coordinates.

Definition at line 331 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

332  { return this->_fe_map->get_dxidz(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dxyzdeta()

const std::vector<RealGradient>& libMesh::FEAbstract::get_dxyzdeta ( ) const
inlineinherited
Returns
The element tangents in eta-direction at the quadrature points.

Definition at line 259 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

260  { return this->_fe_map->get_dxyzdeta(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dxyzdxi()

const std::vector<RealGradient>& libMesh::FEAbstract::get_dxyzdxi ( ) const
inlineinherited
Returns
The element tangents in xi-direction at the quadrature points.

Definition at line 252 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

253  { return this->_fe_map->get_dxyzdxi(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dxyzdzeta()

const std::vector<RealGradient>& libMesh::FEAbstract::get_dxyzdzeta ( ) const
inlineinherited
Returns
The element tangents in zeta-direction at the quadrature points.

Definition at line 266 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

267  { return _fe_map->get_dxyzdzeta(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dzetadx()

const std::vector<Real>& libMesh::FEAbstract::get_dzetadx ( ) const
inlineinherited
Returns
The dzeta/dx entry in the transformation matrix from physical to local coordinates.

Definition at line 359 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

360  { return this->_fe_map->get_dzetadx(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dzetady()

const std::vector<Real>& libMesh::FEAbstract::get_dzetady ( ) const
inlineinherited
Returns
The dzeta/dy entry in the transformation matrix from physical to local coordinates.

Definition at line 366 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

367  { return this->_fe_map->get_dzetady(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_dzetadz()

const std::vector<Real>& libMesh::FEAbstract::get_dzetadz ( ) const
inlineinherited
Returns
The dzeta/dz entry in the transformation matrix from physical to local coordinates.

Definition at line 373 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

374  { return this->_fe_map->get_dzetadz(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_family()

FEFamily libMesh::FEAbstract::get_family ( ) const
inlineinherited
Returns
The finite element family of this element.

Definition at line 455 of file fe_abstract.h.

References libMesh::FEType::family, and libMesh::FEAbstract::fe_type.

455 { return fe_type.family; }
libMesh::FEType::family
FEFamily family
Definition: fe_type.h:204

◆ get_fe_map()

const FEMap& libMesh::FEAbstract::get_fe_map ( ) const
inlineinherited
Returns
The mapping object

Definition at line 460 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

Referenced by libMesh::HCurlFETransformation< OutputShape >::init_map_d2phi(), libMesh::H1FETransformation< OutputShape >::init_map_d2phi(), libMesh::HCurlFETransformation< OutputShape >::init_map_dphi(), libMesh::H1FETransformation< OutputShape >::init_map_dphi(), libMesh::HCurlFETransformation< OutputShape >::init_map_phi(), libMesh::HCurlFETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_curl(), libMesh::H1FETransformation< OutputShape >::map_d2phi(), libMesh::H1FETransformation< OutputShape >::map_div(), libMesh::H1FETransformation< OutputShape >::map_dphi(), and libMesh::HCurlFETransformation< OutputShape >::map_phi().

460 { return *_fe_map.get(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_fe_type()

FEType libMesh::FEAbstract::get_fe_type ( ) const
inlineinherited
Returns
The FE Type (approximation order and family) of the finite element.

Definition at line 429 of file fe_abstract.h.

References libMesh::FEAbstract::fe_type.

Referenced by libMesh::FEMContext::build_new_fe(), libMesh::HCurlFETransformation< OutputShape >::map_phi(), libMesh::H1FETransformation< OutputShape >::map_phi(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::operator()(), and libMesh::JumpErrorEstimator::reinit_sides().

429 { return fe_type; }

◆ get_info()

std::string libMesh::ReferenceCounter::get_info ( )
staticinherited

Gets a string containing the reference information.

Definition at line 47 of file reference_counter.C.

References libMesh::ReferenceCounter::_counts, and libMesh::Quality::name().

Referenced by libMesh::ReferenceCounter::print_info().

48 {
49 #if defined(LIBMESH_ENABLE_REFERENCE_COUNTING) && defined(DEBUG)
50 
51  std::ostringstream oss;
52 
53  oss << '\n'
54  << " ---------------------------------------------------------------------------- \n"
55  << "| Reference count information |\n"
56  << " ---------------------------------------------------------------------------- \n";
57 
58  for (const auto & pr : _counts)
59  {
60  const std::string name(pr.first);
61  const unsigned int creations = pr.second.first;
62  const unsigned int destructions = pr.second.second;
63 
64  oss << "| " << name << " reference count information:\n"
65  << "| Creations: " << creations << '\n'
66  << "| Destructions: " << destructions << '\n';
67  }
68 
69  oss << " ---------------------------------------------------------------------------- \n";
70 
71  return oss.str();
72 
73 #else
74 
75  return "";
76 
77 #endif
78 }
libMesh::Quality::name
std::string name(const ElemQuality q)
Definition: elem_quality.C:42

◆ get_JxW()

const std::vector<Real>& libMesh::FEAbstract::get_JxW ( ) const
inlineinherited
Returns
The element Jacobian times the quadrature weight for each quadrature point.

Definition at line 245 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::System::calculate_norm(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::FEMSystem::init_context(), libMesh::LaplacianErrorEstimator::internal_side_integration(), libMesh::DiscontinuityMeasure::internal_side_integration(), libMesh::KellyErrorEstimator::internal_side_integration(), and libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::operator()().

246  { return this->_fe_map->get_JxW(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_normals()

const std::vector<Point>& libMesh::FEAbstract::get_normals ( ) const
inlineinherited
Returns
The outward pointing normal vectors for face integration.

Definition at line 385 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

Referenced by libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::ParsedFEMFunction< T >::eval_args(), libMesh::ParsedFEMFunction< T >::init_context(), libMesh::KellyErrorEstimator::init_context(), and libMesh::KellyErrorEstimator::internal_side_integration().

386  { return this->_fe_map->get_normals(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_order()

Order libMesh::FEAbstract::get_order ( ) const
inlineinherited
Returns
The approximation order of the finite element.

Definition at line 434 of file fe_abstract.h.

References libMesh::FEAbstract::_p_level, libMesh::FEAbstract::fe_type, and libMesh::FEType::order.

434 { return static_cast<Order>(fe_type.order + _p_level); }
libMesh::FEAbstract::_p_level
unsigned int _p_level
Definition: fe_abstract.h:587
libMesh::FEType::order
OrderWrapper order
Definition: fe_type.h:198

◆ get_p_level()

unsigned int libMesh::FEAbstract::get_p_level ( ) const
inlineinherited
Returns
The p refinement level that the current shape functions have been calculated for.

Definition at line 424 of file fe_abstract.h.

References libMesh::FEAbstract::_p_level.

424 { return _p_level; }
libMesh::FEAbstract::_p_level
unsigned int _p_level
Definition: fe_abstract.h:587

◆ get_phi()

template<typename OutputType>
const std::vector<std::vector<OutputShape> >& libMesh::FEGenericBase< OutputType >::get_phi ( ) const
inline
Returns
The shape function values at the quadrature points on the element.

Definition at line 207 of file fe_base.h.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::System::calculate_norm(), libMesh::OldSolutionCoefs< Output, point_output >::eval_at_point(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::OldSolutionBase< Output, point_output >::get_shape_outputs(), libMesh::DiscontinuityMeasure::init_context(), libMesh::ParsedFEMFunction< T >::init_context(), libMesh::FEMSystem::init_context(), libMesh::FEMContext::interior_values(), libMesh::DiscontinuityMeasure::internal_side_integration(), libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::operator()(), libMesh::FEMContext::side_values(), and libMesh::FEMContext::some_value().

208  { libmesh_assert(!calculations_started || calculate_phi);
209  calculate_phi = true; return phi; }
libMesh::FEGenericBase::phi
std::vector< std::vector< OutputShape > > phi
Definition: fe_base.h:498

◆ get_refspace_nodes()

void libMesh::FEAbstract::get_refspace_nodes ( const ElemType  t,
std::vector< Point > &  nodes 
)
staticinherited
Returns
The reference space coordinates of nodes based on the element type.

Definition at line 283 of file fe_abstract.C.

References libMesh::EDGE2, libMesh::EDGE3, libMesh::HEX20, libMesh::HEX27, libMesh::HEX8, libMesh::PRISM15, libMesh::PRISM18, libMesh::PRISM6, libMesh::PYRAMID13, libMesh::PYRAMID14, libMesh::PYRAMID5, libMesh::QUAD4, libMesh::QUAD8, libMesh::QUAD9, libMesh::QUADSHELL4, libMesh::QUADSHELL8, libMesh::TET10, libMesh::TET4, libMesh::TRI3, libMesh::TRI6, and libMesh::TRISHELL3.

284 {
285  switch(itemType)
286  {
287  case EDGE2:
288  {
289  nodes.resize(2);
290  nodes[0] = Point (-1.,0.,0.);
291  nodes[1] = Point (1.,0.,0.);
292  return;
293  }
294  case EDGE3:
295  {
296  nodes.resize(3);
297  nodes[0] = Point (-1.,0.,0.);
298  nodes[1] = Point (1.,0.,0.);
299  nodes[2] = Point (0.,0.,0.);
300  return;
301  }
302  case TRI3:
303  case TRISHELL3:
304  {
305  nodes.resize(3);
306  nodes[0] = Point (0.,0.,0.);
307  nodes[1] = Point (1.,0.,0.);
308  nodes[2] = Point (0.,1.,0.);
309  return;
310  }
311  case TRI6:
312  {
313  nodes.resize(6);
314  nodes[0] = Point (0.,0.,0.);
315  nodes[1] = Point (1.,0.,0.);
316  nodes[2] = Point (0.,1.,0.);
317  nodes[3] = Point (.5,0.,0.);
318  nodes[4] = Point (.5,.5,0.);
319  nodes[5] = Point (0.,.5,0.);
320  return;
321  }
322  case QUAD4:
323  case QUADSHELL4:
324  {
325  nodes.resize(4);
326  nodes[0] = Point (-1.,-1.,0.);
327  nodes[1] = Point (1.,-1.,0.);
328  nodes[2] = Point (1.,1.,0.);
329  nodes[3] = Point (-1.,1.,0.);
330  return;
331  }
332  case QUAD8:
333  case QUADSHELL8:
334  {
335  nodes.resize(8);
336  nodes[0] = Point (-1.,-1.,0.);
337  nodes[1] = Point (1.,-1.,0.);
338  nodes[2] = Point (1.,1.,0.);
339  nodes[3] = Point (-1.,1.,0.);
340  nodes[4] = Point (0.,-1.,0.);
341  nodes[5] = Point (1.,0.,0.);
342  nodes[6] = Point (0.,1.,0.);
343  nodes[7] = Point (-1.,0.,0.);
344  return;
345  }
346  case QUAD9:
347  {
348  nodes.resize(9);
349  nodes[0] = Point (-1.,-1.,0.);
350  nodes[1] = Point (1.,-1.,0.);
351  nodes[2] = Point (1.,1.,0.);
352  nodes[3] = Point (-1.,1.,0.);
353  nodes[4] = Point (0.,-1.,0.);
354  nodes[5] = Point (1.,0.,0.);
355  nodes[6] = Point (0.,1.,0.);
356  nodes[7] = Point (-1.,0.,0.);
357  nodes[8] = Point (0.,0.,0.);
358  return;
359  }
360  case TET4:
361  {
362  nodes.resize(4);
363  nodes[0] = Point (0.,0.,0.);
364  nodes[1] = Point (1.,0.,0.);
365  nodes[2] = Point (0.,1.,0.);
366  nodes[3] = Point (0.,0.,1.);
367  return;
368  }
369  case TET10:
370  {
371  nodes.resize(10);
372  nodes[0] = Point (0.,0.,0.);
373  nodes[1] = Point (1.,0.,0.);
374  nodes[2] = Point (0.,1.,0.);
375  nodes[3] = Point (0.,0.,1.);
376  nodes[4] = Point (.5,0.,0.);
377  nodes[5] = Point (.5,.5,0.);
378  nodes[6] = Point (0.,.5,0.);
379  nodes[7] = Point (0.,0.,.5);
380  nodes[8] = Point (.5,0.,.5);
381  nodes[9] = Point (0.,.5,.5);
382  return;
383  }
384  case HEX8:
385  {
386  nodes.resize(8);
387  nodes[0] = Point (-1.,-1.,-1.);
388  nodes[1] = Point (1.,-1.,-1.);
389  nodes[2] = Point (1.,1.,-1.);
390  nodes[3] = Point (-1.,1.,-1.);
391  nodes[4] = Point (-1.,-1.,1.);
392  nodes[5] = Point (1.,-1.,1.);
393  nodes[6] = Point (1.,1.,1.);
394  nodes[7] = Point (-1.,1.,1.);
395  return;
396  }
397  case HEX20:
398  {
399  nodes.resize(20);
400  nodes[0] = Point (-1.,-1.,-1.);
401  nodes[1] = Point (1.,-1.,-1.);
402  nodes[2] = Point (1.,1.,-1.);
403  nodes[3] = Point (-1.,1.,-1.);
404  nodes[4] = Point (-1.,-1.,1.);
405  nodes[5] = Point (1.,-1.,1.);
406  nodes[6] = Point (1.,1.,1.);
407  nodes[7] = Point (-1.,1.,1.);
408  nodes[8] = Point (0.,-1.,-1.);
409  nodes[9] = Point (1.,0.,-1.);
410  nodes[10] = Point (0.,1.,-1.);
411  nodes[11] = Point (-1.,0.,-1.);
412  nodes[12] = Point (-1.,-1.,0.);
413  nodes[13] = Point (1.,-1.,0.);
414  nodes[14] = Point (1.,1.,0.);
415  nodes[15] = Point (-1.,1.,0.);
416  nodes[16] = Point (0.,-1.,1.);
417  nodes[17] = Point (1.,0.,1.);
418  nodes[18] = Point (0.,1.,1.);
419  nodes[19] = Point (-1.,0.,1.);
420  return;
421  }
422  case HEX27:
423  {
424  nodes.resize(27);
425  nodes[0] = Point (-1.,-1.,-1.);
426  nodes[1] = Point (1.,-1.,-1.);
427  nodes[2] = Point (1.,1.,-1.);
428  nodes[3] = Point (-1.,1.,-1.);
429  nodes[4] = Point (-1.,-1.,1.);
430  nodes[5] = Point (1.,-1.,1.);
431  nodes[6] = Point (1.,1.,1.);
432  nodes[7] = Point (-1.,1.,1.);
433  nodes[8] = Point (0.,-1.,-1.);
434  nodes[9] = Point (1.,0.,-1.);
435  nodes[10] = Point (0.,1.,-1.);
436  nodes[11] = Point (-1.,0.,-1.);
437  nodes[12] = Point (-1.,-1.,0.);
438  nodes[13] = Point (1.,-1.,0.);
439  nodes[14] = Point (1.,1.,0.);
440  nodes[15] = Point (-1.,1.,0.);
441  nodes[16] = Point (0.,-1.,1.);
442  nodes[17] = Point (1.,0.,1.);
443  nodes[18] = Point (0.,1.,1.);
444  nodes[19] = Point (-1.,0.,1.);
445  nodes[20] = Point (0.,0.,-1.);
446  nodes[21] = Point (0.,-1.,0.);
447  nodes[22] = Point (1.,0.,0.);
448  nodes[23] = Point (0.,1.,0.);
449  nodes[24] = Point (-1.,0.,0.);
450  nodes[25] = Point (0.,0.,1.);
451  nodes[26] = Point (0.,0.,0.);
452  return;
453  }
454  case PRISM6:
455  {
456  nodes.resize(6);
457  nodes[0] = Point (0.,0.,-1.);
458  nodes[1] = Point (1.,0.,-1.);
459  nodes[2] = Point (0.,1.,-1.);
460  nodes[3] = Point (0.,0.,1.);
461  nodes[4] = Point (1.,0.,1.);
462  nodes[5] = Point (0.,1.,1.);
463  return;
464  }
465  case PRISM15:
466  {
467  nodes.resize(15);
468  nodes[0] = Point (0.,0.,-1.);
469  nodes[1] = Point (1.,0.,-1.);
470  nodes[2] = Point (0.,1.,-1.);
471  nodes[3] = Point (0.,0.,1.);
472  nodes[4] = Point (1.,0.,1.);
473  nodes[5] = Point (0.,1.,1.);
474  nodes[6] = Point (.5,0.,-1.);
475  nodes[7] = Point (.5,.5,-1.);
476  nodes[8] = Point (0.,.5,-1.);
477  nodes[9] = Point (0.,0.,0.);
478  nodes[10] = Point (1.,0.,0.);
479  nodes[11] = Point (0.,1.,0.);
480  nodes[12] = Point (.5,0.,1.);
481  nodes[13] = Point (.5,.5,1.);
482  nodes[14] = Point (0.,.5,1.);
483  return;
484  }
485  case PRISM18:
486  {
487  nodes.resize(18);
488  nodes[0] = Point (0.,0.,-1.);
489  nodes[1] = Point (1.,0.,-1.);
490  nodes[2] = Point (0.,1.,-1.);
491  nodes[3] = Point (0.,0.,1.);
492  nodes[4] = Point (1.,0.,1.);
493  nodes[5] = Point (0.,1.,1.);
494  nodes[6] = Point (.5,0.,-1.);
495  nodes[7] = Point (.5,.5,-1.);
496  nodes[8] = Point (0.,.5,-1.);
497  nodes[9] = Point (0.,0.,0.);
498  nodes[10] = Point (1.,0.,0.);
499  nodes[11] = Point (0.,1.,0.);
500  nodes[12] = Point (.5,0.,1.);
501  nodes[13] = Point (.5,.5,1.);
502  nodes[14] = Point (0.,.5,1.);
503  nodes[15] = Point (.5,0.,0.);
504  nodes[16] = Point (.5,.5,0.);
505  nodes[17] = Point (0.,.5,0.);
506  return;
507  }
508  case PYRAMID5:
509  {
510  nodes.resize(5);
511  nodes[0] = Point (-1.,-1.,0.);
512  nodes[1] = Point (1.,-1.,0.);
513  nodes[2] = Point (1.,1.,0.);
514  nodes[3] = Point (-1.,1.,0.);
515  nodes[4] = Point (0.,0.,1.);
516  return;
517  }
518  case PYRAMID13:
519  {
520  nodes.resize(13);
521 
522  // base corners
523  nodes[0] = Point (-1.,-1.,0.);
524  nodes[1] = Point (1.,-1.,0.);
525  nodes[2] = Point (1.,1.,0.);
526  nodes[3] = Point (-1.,1.,0.);
527 
528  // apex
529  nodes[4] = Point (0.,0.,1.);
530 
531  // base midedge
532  nodes[5] = Point (0.,-1.,0.);
533  nodes[6] = Point (1.,0.,0.);
534  nodes[7] = Point (0.,1.,0.);
535  nodes[8] = Point (-1,0.,0.);
536 
537  // lateral midedge
538  nodes[9] = Point (-.5,-.5,.5);
539  nodes[10] = Point (.5,-.5,.5);
540  nodes[11] = Point (.5,.5,.5);
541  nodes[12] = Point (-.5,.5,.5);
542 
543  return;
544  }
545  case PYRAMID14:
546  {
547  nodes.resize(14);
548 
549  // base corners
550  nodes[0] = Point (-1.,-1.,0.);
551  nodes[1] = Point (1.,-1.,0.);
552  nodes[2] = Point (1.,1.,0.);
553  nodes[3] = Point (-1.,1.,0.);
554 
555  // apex
556  nodes[4] = Point (0.,0.,1.);
557 
558  // base midedge
559  nodes[5] = Point (0.,-1.,0.);
560  nodes[6] = Point (1.,0.,0.);
561  nodes[7] = Point (0.,1.,0.);
562  nodes[8] = Point (-1,0.,0.);
563 
564  // lateral midedge
565  nodes[9] = Point (-.5,-.5,.5);
566  nodes[10] = Point (.5,-.5,.5);
567  nodes[11] = Point (.5,.5,.5);
568  nodes[12] = Point (-.5,.5,.5);
569 
570  // base center
571  nodes[13] = Point (0.,0.,0.);
572 
573  return;
574  }
575 
576  default:
577  libmesh_error_msg("ERROR: Unknown element type " << itemType);
578  }
579 }

◆ get_Sobolev_dweight()

template<typename OutputType>
const std::vector<RealGradient>& libMesh::FEGenericBase< OutputType >::get_Sobolev_dweight ( ) const
inline
Returns
The first global derivative of the multiplicative weight at each quadrature point. See get_Sobolev_weight() for details. In case of FE initialized to all zero.

Definition at line 427 of file fe_base.h.

428  { return dweight; }
libMesh::FEGenericBase::dweight
std::vector< RealGradient > dweight
Definition: fe_base.h:636

◆ get_Sobolev_weight()

template<typename OutputType>
const std::vector<Real>& libMesh::FEGenericBase< OutputType >::get_Sobolev_weight ( ) const
inline
Returns
The multiplicative weight at each quadrature point. This weight is used for certain infinite element weak formulations, so that weighted Sobolev spaces are used for the trial function space. This renders the variational form easily computable.

In case of the general finite element class FE this field is initialized to all ones, so that the variational formulation for an infinite element produces correct element matrices for a mesh using both finite and infinite elements.

Definition at line 419 of file fe_base.h.

420  { return weight; }
libMesh::FEGenericBase::weight
std::vector< Real > weight
Definition: fe_base.h:643

◆ get_tangents()

const std::vector<std::vector<Point> >& libMesh::FEAbstract::get_tangents ( ) const
inlineinherited
Returns
The tangent vectors for face integration.

Definition at line 379 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

380  { return this->_fe_map->get_tangents(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ get_type()

ElemType libMesh::FEAbstract::get_type ( ) const
inlineinherited
Returns
The element type that the current shape functions have been calculated for. Useful in determining when shape functions must be recomputed.

Definition at line 418 of file fe_abstract.h.

References libMesh::FEAbstract::elem_type.

418 { return elem_type; }

◆ get_xyz()

const std::vector<Point>& libMesh::FEAbstract::get_xyz ( ) const
inlineinherited
Returns
The xyz spatial locations of the quadrature points on the element.

Definition at line 238 of file fe_abstract.h.

References libMesh::FEAbstract::_fe_map.

Referenced by libMesh::ExactSolution::_compute_error(), libMesh::DiscontinuityMeasure::boundary_side_integration(), libMesh::KellyErrorEstimator::boundary_side_integration(), libMesh::JumpErrorEstimator::estimate_error(), libMesh::ParsedFEMFunction< T >::eval_args(), libMesh::ExactErrorEstimator::find_squared_element_error(), libMesh::ParsedFEMFunction< T >::init_context(), libMesh::DGFEMContext::neighbor_side_fe_reinit(), and libMesh::GenericProjector< FFunctor, GFunctor, FValue, ProjectionAction >::operator()().

239  { return this->_fe_map->get_xyz(); }
libMesh::FEAbstract::_fe_map
std::unique_ptr< FEMap > _fe_map
Definition: fe_abstract.h:525

◆ increment_constructor_count()

void libMesh::ReferenceCounter::increment_constructor_count ( const std::string &  name)
inlineprotectedinherited

Increments the construction counter. Should be called in the constructor of any derived class that will be reference counted.

Definition at line 181 of file reference_counter.h.

References libMesh::ReferenceCounter::_counts, libMesh::Quality::name(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< RBParametrized >::ReferenceCountedObject().

182 {
183  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
184  std::pair<unsigned int, unsigned int> & p = _counts[name];
185 
186  p.first++;
187 }
libMesh::Quality::name
std::string name(const ElemQuality q)
Definition: elem_quality.C:42
libMesh::Threads::spin_mtx
spin_mutex spin_mtx
Definition: threads.C:29

◆ increment_destructor_count()

void libMesh::ReferenceCounter::increment_destructor_count ( const std::string &  name)
inlineprotectedinherited

Increments the destruction counter. Should be called in the destructor of any derived class that will be reference counted.

Definition at line 194 of file reference_counter.h.

References libMesh::ReferenceCounter::_counts, libMesh::Quality::name(), and libMesh::Threads::spin_mtx.

Referenced by libMesh::ReferenceCountedObject< RBParametrized >::~ReferenceCountedObject().

195 {
196  Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
197  std::pair<unsigned int, unsigned int> & p = _counts[name];
198 
199  p.second++;
200 }
libMesh::Quality::name
std::string name(const ElemQuality q)
Definition: elem_quality.C:42
libMesh::Threads::spin_mtx
spin_mutex spin_mtx
Definition: threads.C:29

◆ init_base_shape_functions()

template<typename OutputType>
virtual void libMesh::FEGenericBase< OutputType >::init_base_shape_functions ( const std::vector< Point > &  qp,
const Elem *  e 
)
protectedpure virtual

Initialize the data fields for the base of an an infinite element. Implement this in the derived class FE<Dim,T>.

Implemented in libMesh::InfFE< Dim, T_radial, T_map >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, and libMesh::FE< Dim, LAGRANGE_VEC >.

◆ is_hierarchic()

virtual bool libMesh::FEAbstract::is_hierarchic ( ) const
pure virtualinherited
Returns
true if the finite element's higher order shape functions are hierarchic

Implemented in libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >, libMesh::FE< Dim, L2_HIERARCHIC >, libMesh::FE< Dim, LAGRANGE_VEC >, libMesh::FE< Dim, T >, libMesh::FE< 2, SUBDIVISION >, libMesh::FE< Dim, HIERARCHIC >, libMesh::FE< Dim, SCALAR >, libMesh::FE< Dim, L2_LAGRANGE >, libMesh::FE< Dim, NEDELEC_ONE >, libMesh::FE< Dim, HERMITE >, libMesh::FE< Dim, CLOUGH >, libMesh::FE< Dim, MONOMIAL >, libMesh::FE< Dim, XYZ >, libMesh::FE< Dim, LAGRANGE >,