From f76653af4997da54a9723c46bf20f4b1735ebb79 Mon Sep 17 00:00:00 2001 From: John Peterson Date: Tue, 31 Oct 2023 11:52:44 -0500 Subject: [PATCH] Add vector_fe_ex6.html --- examples/vector_fe_ex6.html | 751 ++++++++++++++++++++++++++++++++++++ 1 file changed, 751 insertions(+) create mode 100644 examples/vector_fe_ex6.html diff --git a/examples/vector_fe_ex6.html b/examples/vector_fe_ex6.html new file mode 100644 index 00000000..6dff3885 --- /dev/null +++ b/examples/vector_fe_ex6.html @@ -0,0 +1,751 @@ + + + + + libMesh - A C++ Finite Element Library + + + + + + + + +
+ + + + +
+ +

Link to the source code for this example:

+Open vector_fe_ex6 in new tab. + +


The console output of the program:

+
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=TRI6 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={2}
+  spatial_dimension()=2
+  n_nodes()=961
+    n_local_nodes()=961
+  n_elem()=450
+    n_local_elem()=450
+    n_active_elem()=450
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p" "l"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+    Approximation Orders="FIRST" "CONSTANT" "FIRST"
+    n_dofs()=1156
+    n_local_dofs()=1156
+    max(n_local_dofs())=1156
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=1156
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 7.66955
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 1156
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134373
+HDiv semi-norm error is: 0.344042
+HDiv error is: 0.369353
+~~ Scalar field (p) ~~
+L2 error is: 0.0697862
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=TRI6 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=TRI7 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={2}
+  spatial_dimension()=2
+  n_nodes()=1411
+    n_local_nodes()=1411
+  n_elem()=450
+    n_local_elem()=450
+    n_active_elem()=450
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p" "l"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+    Approximation Orders="FIRST" "CONSTANT" "FIRST"
+    n_dofs()=1156
+    n_local_dofs()=1156
+    max(n_local_dofs())=1156
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=1156
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 7.66955
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 1156
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134373
+HDiv semi-norm error is: 0.344042
+HDiv error is: 0.369353
+~~ Scalar field (p) ~~
+L2 error is: 0.0697862
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=TRI7 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=QUAD8 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={2}
+  spatial_dimension()=2
+  n_nodes()=736
+    n_local_nodes()=736
+  n_elem()=225
+    n_local_elem()=225
+    n_active_elem()=225
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p" "l"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+    Approximation Orders="FIRST" "CONSTANT" "FIRST"
+    n_dofs()=706
+    n_local_dofs()=706
+    max(n_local_dofs())=706
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=706
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 9.3711
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 706
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134503
+HDiv semi-norm error is: 0.421249
+HDiv error is: 0.442201
+~~ Scalar field (p) ~~
+L2 error is: 0.0854505
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=QUAD8 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=QUAD9 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={2}
+  spatial_dimension()=2
+  n_nodes()=961
+    n_local_nodes()=961
+  n_elem()=225
+    n_local_elem()=225
+    n_active_elem()=225
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p" "l"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+    Approximation Orders="FIRST" "CONSTANT" "FIRST"
+    n_dofs()=706
+    n_local_dofs()=706
+    max(n_local_dofs())=706
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=706
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 9.3711
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 706
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134503
+HDiv semi-norm error is: 0.421249
+HDiv error is: 0.442201
+~~ Scalar field (p) ~~
+L2 error is: 0.0854505
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=QUAD9 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=3 element_type=TET14 grid_size=6 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={3}
+  spatial_dimension()=3
+  n_nodes()=19045
+    n_local_nodes()=19045
+  n_elem()=5184
+    n_local_elem()=5184
+    n_active_elem()=5184
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p" "l"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+    Approximation Orders="FIRST" "CONSTANT" "FIRST"
+    n_dofs()=15985
+    n_local_dofs()=15985
+    max(n_local_dofs())=15985
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=15985
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 9.48596
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 15985
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.334771
+HDiv semi-norm error is: 0.836328
+HDiv error is: 0.900842
+~~ Scalar field (p) ~~
+L2 error is: 0.113127
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=3 element_type=TET14 grid_size=6 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=3 element_type=HEX27 boundary_condition=neumann
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={3}
+  spatial_dimension()=3
+  n_nodes()=29791
+    n_local_nodes()=29791
+  n_elem()=3375
+    n_local_elem()=3375
+    n_active_elem()=3375
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p" "l"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
+    Approximation Orders="FIRST" "CONSTANT" "FIRST"
+    n_dofs()=14176
+    n_local_dofs()=14176
+    max(n_local_dofs())=14176
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=14176
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 12.9992
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 14176
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.2325
+HDiv semi-norm error is: 0.773177
+HDiv error is: 0.807378
+~~ Scalar field (p) ~~
+L2 error is: 0.104528
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=3 element_type=HEX27 boundary_condition=neumann
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=TRI6 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={2}
+  spatial_dimension()=2
+  n_nodes()=961
+    n_local_nodes()=961
+  n_elem()=450
+    n_local_elem()=450
+    n_active_elem()=450
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+    Approximation Orders="FIRST" "CONSTANT"
+    n_dofs()=1155
+    n_local_dofs()=1155
+    max(n_local_dofs())=1155
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=1155
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 5.67532
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 7
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134279
+HDiv semi-norm error is: 0.344042
+HDiv error is: 0.369318
+~~ Scalar field (p) ~~
+L2 error is: 0.0697398
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=TRI6 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=TRI7 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={2}
+  spatial_dimension()=2
+  n_nodes()=1411
+    n_local_nodes()=1411
+  n_elem()=450
+    n_local_elem()=450
+    n_active_elem()=450
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+    Approximation Orders="FIRST" "CONSTANT"
+    n_dofs()=1155
+    n_local_dofs()=1155
+    max(n_local_dofs())=1155
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=1155
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 5.67532
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 7
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134279
+HDiv semi-norm error is: 0.344042
+HDiv error is: 0.369318
+~~ Scalar field (p) ~~
+L2 error is: 0.0697398
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=TRI7 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=QUAD8 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={2}
+  spatial_dimension()=2
+  n_nodes()=736
+    n_local_nodes()=736
+  n_elem()=225
+    n_local_elem()=225
+    n_active_elem()=225
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+    Approximation Orders="FIRST" "CONSTANT"
+    n_dofs()=705
+    n_local_dofs()=705
+    max(n_local_dofs())=705
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=705
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 7.38298
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 9
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134333
+HDiv semi-norm error is: 0.421249
+HDiv error is: 0.442149
+~~ Scalar field (p) ~~
+L2 error is: 0.0853821
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=QUAD8 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=QUAD9 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={2}
+  spatial_dimension()=2
+  n_nodes()=961
+    n_local_nodes()=961
+  n_elem()=225
+    n_local_elem()=225
+    n_active_elem()=225
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+    Approximation Orders="FIRST" "CONSTANT"
+    n_dofs()=705
+    n_local_dofs()=705
+    max(n_local_dofs())=705
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=705
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 7.38298
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 9
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.134333
+HDiv semi-norm error is: 0.421249
+HDiv error is: 0.442149
+~~ Scalar field (p) ~~
+L2 error is: 0.0853821
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=2 element_type=QUAD9 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=3 element_type=TET14 grid_size=6 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={3}
+  spatial_dimension()=3
+  n_nodes()=19045
+    n_local_nodes()=19045
+  n_elem()=5184
+    n_local_elem()=5184
+    n_active_elem()=5184
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+    Approximation Orders="FIRST" "CONSTANT"
+    n_dofs()=15984
+    n_local_dofs()=15984
+    max(n_local_dofs())=15984
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=15984
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 7.48649
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 9
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.33473
+HDiv semi-norm error is: 0.836328
+HDiv error is: 0.900826
+~~ Scalar field (p) ~~
+L2 error is: 0.113105
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=3 element_type=TET14 grid_size=6 boundary_condition=dirichlet
+***************************************************************
+***************************************************************
+* Running Example vector_fe_ex6:
+*   ./example-opt dim=3 element_type=HEX27 boundary_condition=dirichlet
+***************************************************************
+
+ Mesh Information:
+  elem_dimensions()={3}
+  spatial_dimension()=3
+  n_nodes()=29791
+    n_local_nodes()=29791
+  n_elem()=3375
+    n_local_elem()=3375
+    n_active_elem()=3375
+  n_subdomains()=1
+  n_elemsets()=0
+  n_partitions()=1
+  n_processors()=1
+  n_threads()=1
+  processor_id()=0
+  is_prepared()=true
+  is_replicated()=true
+
+ EquationSystems
+  n_systems()=1
+   System #0, "DivGrad"
+    Type "LinearImplicit"
+    Variables="u" "p"
+    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
+    Approximation Orders="FIRST" "CONSTANT"
+    n_dofs()=14175
+    n_local_dofs()=14175
+    max(n_local_dofs())=14175
+    n_constrained_dofs()=0
+    n_local_constrained_dofs()=0
+    max(local unconstrained dofs)=14175
+    n_vectors()=1
+    n_matrices()=1
+    DofMap Sparsity
+      Average  On-Processor Bandwidth <= 11
+      Average Off-Processor Bandwidth <= 0
+      Maximum  On-Processor Bandwidth <= 13
+      Maximum Off-Processor Bandwidth <= 0
+    DofMap Constraints
+      Number of DoF Constraints = 0
+
+~~ Vector field (u) ~~
+L2 error is: 0.23237
+HDiv semi-norm error is: 0.773177
+HDiv error is: 0.807341
+~~ Scalar field (p) ~~
+L2 error is: 0.104476
+
+***************************************************************
+* Done Running Example vector_fe_ex6:
+*   ./example-opt dim=3 element_type=HEX27 boundary_condition=dirichlet
+***************************************************************
+
+
+ + + + + + + + +