Link to the source code for this example:
Open adaptivity_ex4 in new tab.
The console output of the program:
CXX example_dbg-adaptivity_ex4.o
CXXLD example-dbg
***************************************************************
* Running Example adaptivity_ex4:
* example-opt
***************************************************************
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=36
n_local_dofs()=36
n_constrained_dofs()=0
n_local_constrained_dofs()=0
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 21.7778
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 36
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 0
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=25
n_local_nodes()=25
n_elem()=4
n_local_elem()=4
n_active_elem()=4
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=36
n_local_dofs()=36
n_constrained_dofs()=0
n_local_constrained_dofs()=0
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 21.7778
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 36
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 0
Beginning Solve 0
Linear solver converged at step: 5, final residual: 2.30574e-13
L2-Norm is: 0.384025
H1-Norm is: 1.98976
H2-Norm is: 14.3417
L2-Error is: 0.0335358
H1-Error is: 0.267039
H2-Error is: 3.51162
Refining the mesh...
Mean Error: 4.54516e-13
Error Variance: 5.31276e-26
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=41
n_local_nodes()=41
n_elem()=8
n_local_elem()=8
n_active_elem()=7
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=56
n_local_dofs()=56
n_constrained_dofs()=8
n_local_constrained_dofs()=8
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 27.4286
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 52
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 8
Average DoF Constraint Length= 4
Beginning Solve 1
Linear solver converged at step: 5, final residual: 4.32422e-12
L2-Norm is: 0.385688
H1-Norm is: 1.99188
H2-Norm is: 14.3773
L2-Error is: 0.0312488
H1-Error is: 0.251755
H2-Error is: 3.36347
Refining the mesh...
Mean Error: 0.904773
Error Variance: 0.231378
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=69
n_local_nodes()=69
n_elem()=16
n_local_elem()=16
n_active_elem()=13
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=88
n_local_dofs()=88
n_constrained_dofs()=8
n_local_constrained_dofs()=8
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 28
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 52
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 8
Average DoF Constraint Length= 4
Beginning Solve 2
Linear solver converged at step: 8, final residual: 4.96983e-12
L2-Norm is: 0.39603
H1-Norm is: 2.01114
H2-Norm is: 14.5761
L2-Error is: 0.020273
H1-Error is: 0.166208
H2-Error is: 2.36714
Refining the mesh...
Mean Error: 1.07284
Error Variance: 1.26032
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=125
n_local_nodes()=125
n_elem()=32
n_local_elem()=32
n_active_elem()=25
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=152
n_local_dofs()=152
n_constrained_dofs()=32
n_local_constrained_dofs()=32
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 33.6842
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 60
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 32
Average DoF Constraint Length= 4
Beginning Solve 3
Linear solver converged at step: 12, final residual: 1.95735e-12
L2-Norm is: 0.405284
H1-Norm is: 2.03173
H2-Norm is: 14.7515
L2-Error is: 0.00185729
H1-Error is: 0.0267654
H2-Error is: 0.71977
Refining the mesh...
Mean Error: 0.210827
Error Variance: 0.0183284
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=249
n_local_nodes()=249
n_elem()=68
n_local_elem()=68
n_active_elem()=52
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=292
n_local_dofs()=292
n_constrained_dofs()=72
n_local_constrained_dofs()=72
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 35.4521
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 76
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 72
Average DoF Constraint Length= 4
Beginning Solve 4
Linear solver converged at step: 23, final residual: 2.1448e-12
L2-Norm is: 0.405907
H1-Norm is: 2.03286
H2-Norm is: 14.7613
L2-Error is: 0.00113017
H1-Error is: 0.016604
H2-Error is: 0.482316
Refining the mesh...
Mean Error: 0.108787
Error Variance: 0.00898017
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=485
n_local_nodes()=485
n_elem()=140
n_local_elem()=140
n_active_elem()=106
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=548
n_local_dofs()=548
n_constrained_dofs()=120
n_local_constrained_dofs()=120
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 36.7007
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 68
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 120
Average DoF Constraint Length= 4
Beginning Solve 5
Linear solver converged at step: 37, final residual: 2.04494e-11
L2-Norm is: 0.406259
H1-Norm is: 2.03204
H2-Norm is: 14.7673
L2-Error is: 0.000356962
H1-Error is: 0.00613803
H2-Error is: 0.227619
Refining the mesh...
Mean Error: 0.0264705
Error Variance: 0.00117171
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=957
n_local_nodes()=957
n_elem()=280
n_local_elem()=280
n_active_elem()=211
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=1072
n_local_dofs()=1072
n_constrained_dofs()=304
n_local_constrained_dofs()=304
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 38.4776
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 76
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 304
Average DoF Constraint Length= 4
Beginning Solve 6
Linear solver converged at step: 294, final residual: 8.22354e-11
L2-Norm is: 0.406309
H1-Norm is: 2.03185
H2-Norm is: 14.7684
L2-Error is: 8.72883e-05
H1-Error is: 0.00241104
H2-Error is: 0.13224
Refining the mesh...
Mean Error: 0.0109873
Error Variance: 0.000156803
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=1885
n_local_nodes()=1885
n_elem()=560
n_local_elem()=560
n_active_elem()=421
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Biharmonic"
Type "LinearImplicit"
Variables="u"
Finite Element Types="HERMITE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="THIRD", "THIRD"
n_dofs()=2088
n_local_dofs()=2088
n_constrained_dofs()=616
n_local_constrained_dofs()=616
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 38.9885
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 72
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 616
Average DoF Constraint Length= 4
Beginning Solve 7
Linear solver converged at step: 1000, final residual: 2.62662e-07
L2-Norm is: 0.406333
H1-Norm is: 2.03181
H2-Norm is: 14.7688
L2-Error is: 5.02524e-05
H1-Error is: 0.00140302
H2-Error is: 0.082078
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| Time: Wed Apr 13 09:22:42 2016 |
| OS: Darwin |
| HostName: peterson-laptop.local |
| OS Release: 15.0.0 |
| OS Version: Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64 |
| Machine: x86_64 |
| Username: petejw |
| Configuration: ../configure 'INSTALL=/usr/bin/install -C' |
| '--with-methods=opt dbg' |
| '--prefix=/Users/petejw/projects/libmesh_git/installed' |
| '--enable-perflog' |
| '--enable-tracefiles' |
| '--disable-blocked-storage' |
| '--enable-default-comm-world' |
| '--enable-tecio' |
| '--enable-unique-ptr' |
| '--enable-ifem' |
| 'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu' |
| 'SLEPC_DIR=/opt/petejw/slepc/3.6.1' |
| 'CPPFLAGS= ' |
| 'LIBS= ' |
| 'CPPFLAGS= ' |
| 'LIBS= ' |
| '--disable-netcdf-4' |
| '--disable-testsets' |
| 'CXX=mpicxx' |
| 'CC=mpicc' |
| 'F77=mpif77' |
| 'FC=mpif90' |
| 'CPPFLAGS= ' |
| 'LIBS= ' |
-------------------------------------------------------------------------------------------------------------------
-----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=2.98852, Active time=2.94658 |
-----------------------------------------------------------------------------------------------------------------
| Event nCalls Total Time Avg Time Total Time Avg Time % of Active Time |
| w/o Sub w/o Sub With Sub With Sub w/o S With S |
|-----------------------------------------------------------------------------------------------------------------|
| |
| |
| DofMap |
| add_neighbors_to_send_list() 8 0.0004 0.000049 0.0004 0.000049 0.01 0.01 |
| build_constraint_matrix() 835 0.0027 0.000003 0.0027 0.000003 0.09 0.09 |
| build_sparsity() 8 0.0089 0.001106 0.0093 0.001157 0.30 0.31 |
| cnstrn_elem_mat_vec() 835 0.0046 0.000005 0.0046 0.000005 0.16 0.16 |
| create_dof_constraints() 8 0.0203 0.002532 0.2634 0.032923 0.69 8.94 |
| distribute_dofs() 8 0.0005 0.000061 0.0020 0.000256 0.02 0.07 |
| dof_indices() 9115 0.0034 0.000000 0.0034 0.000000 0.12 0.12 |
| enforce_constraints_exactly() 7 0.0005 0.000065 0.0005 0.000065 0.02 0.02 |
| old_dof_indices() 3617 0.0015 0.000000 0.0015 0.000000 0.05 0.05 |
| prepare_send_list() 9 0.0000 0.000000 0.0000 0.000000 0.00 0.00 |
| reinit() 8 0.0016 0.000195 0.0016 0.000195 0.05 0.05 |
| |
| EquationSystems |
| build_solution_vector() 1 0.0584 0.058436 0.0586 0.058589 1.98 1.99 |
| |
| ErrorVector |
| mean() 14 0.0000 0.000001 0.0000 0.000001 0.00 0.00 |
| variance() 7 0.0000 0.000001 0.0000 0.000001 0.00 0.00 |
| |
| ExodusII_IO |
| write_nodal_data() 1 0.0017 0.001678 0.0017 0.001678 0.06 0.06 |
| |
| FE |
| compute_shape_functions() 12104 0.3042 0.000025 0.3042 0.000025 10.32 10.32 |
| init_shape_functions() 12104 2.0802 0.000172 2.0802 0.000172 70.60 70.60 |
| inverse_map() 31968 0.0210 0.000001 0.0210 0.000001 0.71 0.71 |
| |
| FEMap |
| compute_affine_map() 14507 0.0156 0.000001 0.0156 0.000001 0.53 0.53 |
| compute_face_map() 3134 0.0062 0.000002 0.0158 0.000005 0.21 0.54 |
| init_face_shape_functions() 3134 0.0015 0.000000 0.0015 0.000000 0.05 0.05 |
| init_reference_to_physical_map() 12104 0.0429 0.000004 0.0429 0.000004 1.46 1.46 |
| |
| GenericProjector |
| copy_dofs 279 0.0002 0.000001 0.0008 0.000003 0.01 0.03 |
| operator() 7 0.0018 0.000251 1.1120 0.158863 0.06 37.74 |
| project_edges 556 0.0000 0.000000 0.0000 0.000000 0.00 0.00 |
| project_interior 556 0.0001 0.000000 0.0001 0.000000 0.00 0.00 |
| project_nodes 556 0.0041 0.000007 1.1079 0.001993 0.14 37.60 |
| project_sides 556 0.0006 0.000001 0.0006 0.000001 0.02 0.02 |
| |
| JumpErrorEstimator |
| estimate_error() 7 0.0135 0.001923 1.1196 0.159941 0.46 38.00 |
| |
| Mesh |
| all_second_order() 1 0.0000 0.000036 0.0000 0.000036 0.00 0.00 |
| contract() 7 0.0001 0.000007 0.0001 0.000014 0.00 0.00 |
| find_neighbors() 9 0.0020 0.000219 0.0020 0.000219 0.07 0.07 |
| renumber_nodes_and_elem() 25 0.0001 0.000005 0.0001 0.000005 0.00 0.00 |
| |
| MeshOutput |
| write_equation_systems() 1 0.0000 0.000013 0.0603 0.060281 0.00 2.05 |
| |
| MeshRefinement |
| _coarsen_elements() 14 0.0000 0.000002 0.0000 0.000002 0.00 0.00 |
| _refine_elements() 14 0.0022 0.000157 0.0039 0.000275 0.07 0.13 |
| add_node() 5004 0.0012 0.000000 0.0012 0.000000 0.04 0.04 |
| make_coarsening_compatible() 15 0.0006 0.000039 0.0006 0.000039 0.02 0.02 |
| make_flags_parallel_consistent() 21 0.0003 0.000013 0.0003 0.000013 0.01 0.01 |
| make_refinement_compatible() 15 0.0001 0.000005 0.0001 0.000005 0.00 0.00 |
| |
| MeshTools::Generation |
| build_cube() 1 0.0000 0.000037 0.0000 0.000037 0.00 0.00 |
| |
| OldSolutionValue |
| Gradient eval_at_node() 2224 0.0005 0.000000 0.0005 0.000000 0.02 0.02 |
| Number eval_at_node() 2224 0.0002 0.000000 0.0002 0.000000 0.01 0.01 |
| check_old_context(c) 279 0.0002 0.000001 0.0005 0.000002 0.01 0.02 |
| check_old_context(c,p) 7440 0.0045 0.000001 0.0102 0.000001 0.15 0.35 |
| eval_at_point() 7440 0.1817 0.000024 1.1022 0.000148 6.17 37.40 |
| eval_old_dofs() 279 0.0001 0.000000 0.0006 0.000002 0.00 0.02 |
| |
| Parallel |
| allgather() 8 0.0000 0.000000 0.0000 0.000000 0.00 0.00 |
| |
| Partitioner |
| single_partition() 9 0.0001 0.000009 0.0001 0.000009 0.00 0.00 |
| |
| PetscLinearSolver |
| solve() 8 0.1392 0.017394 0.1392 0.017394 4.72 4.72 |
| |
| System |
| assemble() 8 0.0124 0.001545 0.1201 0.015007 0.42 4.07 |
| project_vector(old,new) 7 0.0013 0.000192 1.1143 0.159188 0.05 37.82 |
| |
| TopologyMap |
| init() 14 0.0037 0.000262 0.0037 0.000262 0.12 0.12 |
-----------------------------------------------------------------------------------------------------------------
| Totals: 131120 2.9466 100.00 |
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***************************************************************
* Done Running Example adaptivity_ex4:
* example-opt
***************************************************************