Link to the source code for this example:

Open miscellaneous_ex16 in new tab.


The console output of the program:

***************************************************************
* Running Example miscellaneous_ex16:
*   ./example-opt  
***************************************************************
 
Running /home/jwpeterson/software/libmesh_build/opt_real/examples/miscellaneous/miscellaneous_ex16/.libs/example-opt

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={2}
  supported_nodal_order()=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()=2
   System #0, "Poisson"
    Type "LinearImplicit"
    Variables="u" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" 
    Approximation Orders="SECOND", "THIRD" 
    n_dofs()=961
    n_local_dofs()=961
    max(n_local_dofs())=961
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=961
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 15.2352
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 25
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0
      Number of Node Constraints = 0
   System #1, "Poisson2"
    Type "LinearImplicit"
    Variables="u" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" 
    Approximation Orders="SECOND", "THIRD" 
    n_dofs()=961
    n_local_dofs()=961
    max(n_local_dofs())=961
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=961
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 11.2549
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 21
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0
      Number of Node Constraints = 0

Static condensation reduced problem size to 736

 -----------------------------------------------------------------------------------
| Time:           Tue Jan 21 15:56:14 2025                                          |
| OS:             Linux                                                             |
| HostName:       dell                                                              |
| OS Release:     6.8.0-51-generic                                                  |
| OS Version:     #52~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Mon Dec  9 15:00:52 UTC 2  |
| Machine:        x86_64                                                            |
| Username:       jwpeterson                                                        |
| Configuration:  /home/jwpeterson/software/libmesh-src/configure  'INSTALL=/usr/bin/install -C'|
|  '--enable-everything'                                                            |
|  '--enable-slepc'                                                                 |
|  '--with-metis=PETSc'                                                             |
|  '--with-subdomain-id-bytes=4'                                                    |
|  '--with-boundary-id-bytes=4'                                                     |
|  '--disable-glpk'                                                                 |
|  '--enable-unique-id'                                                             |
|  '--with-unique-id-bytes=4'                                                       |
|  '--enable-hdf5'                                                                  |
|  '--enable-hdf5-required'                                                         |
|  '--with-hdf5=/home/jwpeterson/software/hdf5_dummy'                               |
|  '--with-nlopt-include=/home/jwpeterson/software/libmesh_install/nlopt/include'   |
|  '--with-nlopt-lib=/home/jwpeterson/software/libmesh_install/nlopt/lib'           |
|  '--with-capnproto=/home/jwpeterson/software/libmesh_install/capnp'               |
|  '--enable-capnp-required'                                                        |
|  '--disable-parmetis'                                                             |
|  '--enable-ifem'                                                                  |
|  '--disable-gmv'                                                                  |
|  '--enable-petsc-required'                                                        |
|  '--enable-nanoflann-pointlocator'                                                |
|  '--prefix=/home/jwpeterson/software/libmesh_install/opt_real/libmesh'            |
|  '--with-methods=opt'                                                             |
|  '--enable-shared'                                                                |
|  '--disable-warnings'                                                             |
|  'PETSC_DIR=/home/jwpeterson/software/libmesh_install/opt_real/petsc'             |
|  'SLEPC_DIR=/home/jwpeterson/software/libmesh_install/opt_real/slepc'             |
 -----------------------------------------------------------------------------------
 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.461972, Active time=0.018513                                                  |
 -----------------------------------------------------------------------------------------------------------------
| 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   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DefaultCoupling                                                                                                 |
|   operator()                       450        0.0004      0.000001    0.0004      0.000001    2.03     2.03     |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   build_sparsity()                 2          0.0010      0.000517    0.0016      0.000783    5.58     8.46     |
|   create_dof_constraints()         2          0.0001      0.000041    0.0001      0.000041    0.45     0.45     |
|   distribute_dofs()                2          0.0002      0.000101    0.0008      0.000375    1.09     4.06     |
|   dof_indices()                    1125       0.0005      0.000000    0.0005      0.000000    2.88     2.88     |
|   prepare_send_list()              4          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         2          0.0005      0.000275    0.0005      0.000275    2.97     2.97     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        570        0.0009      0.000002    0.0009      0.000002    4.87     4.87     |
|   init_shape_functions()           122        0.0000      0.000000    0.0000      0.000000    0.24     0.24     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             570        0.0002      0.000000    0.0002      0.000000    1.29     1.29     |
|   compute_face_map()               120        0.0002      0.000002    0.0007      0.000006    1.02     3.67     |
|   init_face_shape_functions()      2          0.0000      0.000006    0.0000      0.000006    0.06     0.06     |
|   init_reference_to_physical_map() 122        0.0004      0.000003    0.0004      0.000003    1.97     1.97     |
|   inverse_map()                    360        0.0005      0.000001    0.0005      0.000001    2.60     2.60     |
|                                                                                                                 |
| Mesh                                                                                                            |
|   find_neighbors()                 1          0.0002      0.000191    0.0002      0.000191    1.03     1.03     |
|   renumber_nodes_and_elem()        2          0.0000      0.000008    0.0000      0.000008    0.09     0.09     |
|                                                                                                                 |
| MeshBase                                                                                                        |
|   prepare_for_use()                1          0.0001      0.000090    0.0003      0.000312    0.49     1.69     |
|                                                                                                                 |
| MeshTools::Generation                                                                                           |
|   build_cube()                     1          0.0003      0.000295    0.0006      0.000607    1.59     3.28     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition_range()         1          0.0000      0.000015    0.0000      0.000015    0.08     0.08     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          3          0.0098      0.003261    0.0108      0.003609    52.84    58.49    |
|                                                                                                                 |
| System                                                                                                          |
|   assemble()                       2          0.0031      0.001558    0.0056      0.002778    16.83    30.01    |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            3466       0.0185                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------

 
***************************************************************
* Done Running Example miscellaneous_ex16:
*   ./example-opt  
***************************************************************