libMesh::Quality Namespace Reference

Utility functions for computing element quality indicators. More...

Functions
std::string	name (const ElemQuality q)
std::string	describe (const ElemQuality q)
std::vector< ElemQuality >	valid (const ElemType t)

Variables
const unsigned int	num_quals = 16

Detailed Description

Utility functions for computing element quality indicators.

A namespace for quality utility functions.

Author

John W. Peterson

Date

2002

Function Documentation

describe()

std::string libMesh::Quality::describe

(

const ElemQuality

q

)

Returns

A description for a ElemQuality enum

This function returns a string containing a short description of q. Useful for asking the enum what it computes.

Definition at line 130 of file elem_quality.C.

References libMesh::ASPECT_RATIO, libMesh::ASPECT_RATIO_BETA, libMesh::ASPECT_RATIO_GAMMA, libMesh::CONDITION, libMesh::DIAGONAL, libMesh::DISTORTION, libMesh::JACOBIAN, libMesh::MAX_ANGLE, libMesh::MIN_ANGLE, libMesh::SHAPE, libMesh::SHEAR, libMesh::SIZE, libMesh::SKEW, libMesh::STRETCH, libMesh::TAPER, and libMesh::WARP.

{

  std::ostringstream desc;

  switch (q)
    {

    case ASPECT_RATIO:
      desc << "Max edge length ratio\n"
           << "at element center.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Hexes: (1 -> 4)\n"
           << "Quads: (1 -> 4)";
      break;

    case SKEW:
      desc << "Maximum |cos A|, where A\n"
           << "is the angle between edges\n"
           << "at element center.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Hexes: (0 -> 0.5)\n"
           << "Quads: (0 -> 0.5)";
      break;

    case SHEAR:
      desc << "LIBMESH_DIM / K(Js)\n"
           << '\n'
           << "LIBMESH_DIM   = element dimension.\n"
           << "K(Js) = Condition number of \n"
           << "        Jacobian skew matrix.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Hexes(LIBMESH_DIM=3): (0.3 -> 1)\n"
           << "Quads(LIBMESH_DIM=2): (0.3 -> 1)";
      break;

    case SHAPE:
      desc << "LIBMESH_DIM / K(Jw)\n"
           << '\n'
           << "LIBMESH_DIM   = element dimension.\n"
           << "K(Jw) = Condition number of \n"
           << "        weighted Jacobian\n"
           << "        matrix.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Hexes(LIBMESH_DIM=3): (0.3 -> 1)\n"
           << "Tets(LIBMESH_DIM=3): (0.2 -> 1)\n"
           << "Quads(LIBMESH_DIM=2): (0.3 -> 1).";
      break;

    case MAX_ANGLE:
      desc << "Largest included angle.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (90 -> 135)\n"
           << "Triangles: (60 -> 90)";
      break;

    case MIN_ANGLE:
      desc << "Smallest included angle.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (45 -> 90)\n"
           << "Triangles: (30 -> 60)";
      break;

    case CONDITION:
      desc << "Condition number of the\n"
           << "Jacobian matrix.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (1 -> 4)\n"
           << "Hexes: (1 -> 8)\n"
           << "Tris: (1 -> 1.3)\n"
           << "Tets: (1 -> 3)";
      break;

    case DISTORTION:
      desc << "min |J| * A / <A>\n"
           << '\n'
           << "|J| = norm of Jacobian matrix\n"
           << " A  = actual area\n"
           << "<A> = reference area\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (0.6 -> 1), <A>=4\n"
           << "Hexes: (0.6 -> 1), <A>=8\n"
           << "Tris: (0.6 -> 1), <A>=1/2\n"
           << "Tets: (0.6 -> 1), <A>=1/6";
      break;

    case TAPER:
      desc << "Maximum ratio of lengths\n"
           << "derived from opposite edges.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (0.7 -> 1)\n"
           << "Hexes: (0.4 -> 1)";
      break;

    case WARP:
      desc << "cos D\n"
           << '\n'
           << "D = minimum dihedral angle\n"
           << "    formed by diagonals.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (0.9 -> 1)";
      break;

    case STRETCH:
      desc << "Sqrt(3) * L_min / L_max\n"
           << '\n'
           << "L_min = minimum edge length.\n"
           << "L_max = maximum edge length.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (0.25 -> 1)\n"
           << "Hexes: (0.25 -> 1)";
      break;

    case DIAGONAL:
      desc << "D_min / D_max\n"
           << '\n'
           << "D_min = minimum diagonal.\n"
           << "D_max = maximum diagonal.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Hexes: (0.65 -> 1)";
      break;

    case ASPECT_RATIO_BETA:
      desc << "CR / (3 * IR)\n"
           << '\n'
           << "CR = circumsphere radius\n"
           << "IR = inscribed sphere radius\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Tets: (1 -> 3)";
      break;

    case ASPECT_RATIO_GAMMA:
      desc << "S^(3/2) / 8.479670 * V\n"
           << '\n'
           << "S = sum(si*si/6)\n"
           << "si = edge length\n"
           << "V = volume\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Tets: (1 -> 3)";
      break;

    case SIZE:
      desc << "min (|J|, |1/J|)\n"
           << '\n'
           << "|J| = norm of Jacobian matrix.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (0.3 -> 1)\n"
           << "Hexes: (0.5 -> 1)\n"
           << "Tris: (0.25 -> 1)\n"
           << "Tets: (0.2 -> 1)";
      break;

    case JACOBIAN:
      desc << "Minimum Jacobian divided by\n"
           << "the lengths of the LIBMESH_DIM\n"
           << "largest edge vectors.\n"
           << '\n'
           << "LIBMESH_DIM = element dimension.\n"
           << '\n'
           << "Suggested ranges:\n"
           << "Quads: (0.5 -> 1)\n"
           << "Hexes: (0.5 -> 1)\n"
           << "Tris: (0.5 -> 1.155)\n"
           << "Tets: (0.5 -> 1.414)";
      break;

    default:
      desc << "Unknown";
      break;
    }

  return desc.str();
}

name()

std::string libMesh::Quality::name

(

const ElemQuality

q

)

Returns

A descriptive name for a ElemQuality enum

This function returns a string containing some name for q. Useful for asking the enum what its name is. I added this since you may want a simple way to attach a name or description to the ElemQuality enums. It can be removed if it is found to be useless.

Definition at line 42 of file elem_quality.C.

References libMesh::ASPECT_RATIO, libMesh::ASPECT_RATIO_BETA, libMesh::ASPECT_RATIO_GAMMA, libMesh::CONDITION, libMesh::DIAGONAL, libMesh::DISTORTION, libMesh::JACOBIAN, libMesh::MAX_ANGLE, libMesh::MIN_ANGLE, libMesh::SHAPE, libMesh::SHEAR, libMesh::SIZE, libMesh::SKEW, libMesh::STRETCH, libMesh::TAPER, and libMesh::WARP.

Referenced by GETPOT_NAMESPACE::GetPot::_convert_to_type_no_default(), libMesh::EquationSystems::add_system(), libMesh::Factory< Base >::build(), libMesh::cast_ptr(), libMesh::cast_ref(), libMesh::ExodusII_IO_Helper::check_existing_vars(), libMesh::command_line_next(), libMesh::command_line_value(), libMesh::command_line_vector(), libMesh::Utility::complex_filename(), libMesh::ElemCutter::cut_3D(), libMesh::EquationSystems::delete_system(), libMesh::demangle(), DMlibMeshSetUpName_Private(), DMView_libMesh(), libMesh::Factory< Base >::Factory(), libMesh::Parameters::get(), libMesh::BoundaryInfo::get_id_by_name(), libMesh::MeshBase::get_id_by_name(), libMesh::ReferenceCounter::get_info(), libMesh::EquationSystems::get_system(), libMesh::EquationSystems::has_system(), libMesh::Parameters::have_parameter(), libMesh::ReferenceCounter::increment_constructor_count(), libMesh::ReferenceCounter::increment_destructor_count(), libMesh::PetscNonlinearSolver< Number >::init(), libMesh::PetscLinearSolver< T >::init(), libMesh::Parameters::insert(), libMesh::NameBasedIO::is_parallel_file_format(), libMesh::Xdr::open(), GETPOT_NAMESPACE::GetPot::variable::operator=(), libMesh::PetscMatrix< T >::print_matlab(), libMesh::PetscVector< T >::print_matlab(), libMesh::ExodusII_IO_Helper::NamesData::push_back_entry(), libMesh::OFFIO::read(), libMesh::NameBasedIO::read(), libMesh::TetGenIO::read(), libMesh::PltLoader::read(), libMesh::GmshIO::read(), libMesh::GMVIO::read(), libMesh::UnstructuredMesh::read(), libMesh::MatlabIO::read(), libMesh::VTKIO::read(), libMesh::EquationSystems::read(), libMesh::CheckpointIO::read_header(), libMesh::PltLoader::read_header(), libMesh::VariationalMeshSmoother::readmetr(), libMesh::ReferenceCountedObject< RBParametrized >::ReferenceCountedObject(), libMesh::Parameters::remove(), libMesh::Parameters::set(), libMesh::Parameters::Parameter< T >::type(), libMesh::NameBasedIO::write(), libMesh::GmshIO::write(), libMesh::UnstructuredMesh::write(), libMesh::CheckpointIO::write(), libMesh::EnsightIO::write(), libMesh::EquationSystems::write(), libMesh::TecplotIO::write_binary(), libMesh::PltLoader::write_dat(), libMesh::GMVIO::write_discontinuous_gmv(), libMesh::NameBasedIO::write_nodal_data(), libMesh::UCDIO::write_soln(), and libMesh::ReferenceCountedObject< RBParametrized >::~ReferenceCountedObject().

{
  std::string its_name;

  switch (q)
    {

    case ASPECT_RATIO:
      its_name = "Aspect Ratio";
      break;

    case SKEW:
      its_name = "Skew";
      break;

    case SHEAR:
      its_name = "Shear";
      break;

    case SHAPE:
      its_name = "Shape";
      break;

    case MAX_ANGLE:
      its_name = "Maximum Angle";
      break;

    case MIN_ANGLE:
      its_name = "Minimum Angle";
      break;

    case CONDITION:
      its_name = "Condition Number";
      break;

    case DISTORTION:
      its_name = "Distortion";
      break;

    case TAPER:
      its_name = "Taper";
      break;

    case WARP:
      its_name = "Warp";
      break;

    case STRETCH:
      its_name = "Stretch";
      break;

    case DIAGONAL:
      its_name = "Diagonal";
      break;

    case ASPECT_RATIO_BETA:
      its_name = "AR Beta";
      break;

    case ASPECT_RATIO_GAMMA:
      its_name = "AR Gamma";
      break;

    case SIZE:
      its_name = "Size";
      break;

    case JACOBIAN:
      its_name = "Jacobian";
      break;

    default:
      its_name = "Unknown";
      break;
    }

  return its_name;
}

valid()

std::vector< ElemQuality > libMesh::Quality::valid

(

const ElemType

t

)

Returns

The valid ElemQuality metrics for a given ElemType element type.

Returns all valid quality metrics for element type t.

Definition at line 324 of file elem_quality.C.

References libMesh::ASPECT_RATIO, libMesh::ASPECT_RATIO_BETA, libMesh::ASPECT_RATIO_GAMMA, libMesh::CONDITION, libMesh::DIAGONAL, libMesh::DISTORTION, libMesh::EDGE2, libMesh::EDGE3, libMesh::EDGE4, libMesh::HEX20, libMesh::HEX27, libMesh::HEX8, libMesh::INFEDGE2, libMesh::INFHEX16, libMesh::INFHEX18, libMesh::INFHEX8, libMesh::INFPRISM12, libMesh::INFPRISM6, libMesh::INFQUAD4, libMesh::INFQUAD6, libMesh::JACOBIAN, libMesh::MAX_ANGLE, libMesh::MIN_ANGLE, libMesh::PRISM18, libMesh::PRISM6, libMesh::PYRAMID13, libMesh::PYRAMID14, libMesh::PYRAMID5, libMesh::QUAD4, libMesh::QUAD8, libMesh::QUAD9, libMesh::QUADSHELL4, libMesh::QUADSHELL8, libMesh::SHAPE, libMesh::SHEAR, libMesh::SIZE, libMesh::SKEW, libMesh::STRETCH, libMesh::TAPER, libMesh::TET10, libMesh::TET4, libMesh::TRI3, libMesh::TRI6, libMesh::TRISHELL3, and libMesh::WARP.

{
  std::vector<ElemQuality> v;

  switch (t)
    {
    case EDGE2:
    case EDGE3:
    case EDGE4:
      {
        // None yet
        break;
      }

    case TRI3:
    case TRISHELL3:
    case TRI6:
      {
        v.resize(7);
        v[0] = MAX_ANGLE;
        v[1] = MIN_ANGLE;
        v[2] = CONDITION;
        v[3] = JACOBIAN;
        v[4] = SIZE;
        v[5] = SHAPE;
        v[6] = DISTORTION;
        break;
      }

    case QUAD4:
    case QUADSHELL4:
    case QUAD8:
    case QUADSHELL8:
    case QUAD9:
      {
        v.resize(13);
        v[0]  = ASPECT_RATIO;
        v[1]  = SKEW;
        v[2]  = TAPER;
        v[3]  = WARP;
        v[4]  = STRETCH;
        v[5]  = MIN_ANGLE;
        v[6]  = MAX_ANGLE;
        v[7]  = CONDITION;
        v[8]  = JACOBIAN;
        v[9]  = SHEAR;
        v[10] = SHAPE;
        v[11] = SIZE;
        v[12] = DISTORTION;
        break;
      }

    case TET4:
    case TET10:
      {
        v.resize(7);
        v[0]  = ASPECT_RATIO_BETA;
        v[1]  = ASPECT_RATIO_GAMMA;
        v[2]  = CONDITION;
        v[3]  = JACOBIAN;
        v[4]  = SHAPE;
        v[5]  = SIZE;
        v[6]  = DISTORTION;
        break;
      }

    case HEX8:
    case HEX20:
    case HEX27:
      {
        v.resize(11);
        v[0]  = ASPECT_RATIO;
        v[1]  = SKEW;
        v[2]  = SHEAR;
        v[3] = SHAPE;
        v[4]  = CONDITION;
        v[5]  = JACOBIAN;
        v[6]  = DISTORTION;
        v[7]  = TAPER;
        v[8]  = STRETCH;
        v[9]  = DIAGONAL;
        v[10]  = SIZE;
        break;
      }

    case PRISM6:
    case PRISM18:
      {
        // None yet
        break;
      }

    case PYRAMID5:
    case PYRAMID13:
    case PYRAMID14:
      {
        // None yet
        break;
      }



#ifdef LIBMESH_ENABLE_INFINITE_ELEMENTS

    case INFEDGE2:
      {
        // None yet
        break;
      }

    case INFQUAD4:
    case INFQUAD6:
      {
        // None yet
        break;
      }

    case INFHEX8:
    case INFHEX16:
    case INFHEX18:
      {
        // None yet
        break;
      }

    case INFPRISM6:
    case INFPRISM12:
      {
        // None yet
        break;
      }

#endif


    default:
      libmesh_error_msg("Undefined element type!");
    }

  return v;
}

Variable Documentation

num_quals

const unsigned int libMesh::Quality::num_quals = 16

The number of element quality types we have defined. This needs to be updated if you add one.

Definition at line 55 of file elem_quality.h.