Link to the source code for this example:

Open systems_of_equations_ex7 in new tab.


The console output of the program:

***************************************************************
* Running Example systems_of_equations_ex7:
*   example-opt -ksp_type cg -pc_type bjacobi -snes_linesearch_type basic
***************************************************************

 Mesh Information:
  elem_dimensions()={3}
  spatial_dimension()=3
  n_nodes()=525
    n_local_nodes()=525
  n_elem()=40
    n_local_elem()=40
    n_active_elem()=40
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=2
   System #0, "NonlinearElasticity"
    Type "NonlinearImplicit"
    Variables={ "u" "v" "w" }
    Finite Element Types="LAGRANGE", "JACOBI_20_00"
    Infinite Element Mapping="CARTESIAN"
    Approximation Orders="FIRST", "THIRD"
    n_dofs()=297
    n_local_dofs()=297
    n_constrained_dofs()=27
    n_local_constrained_dofs()=27
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 46.0303
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 81
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 27
      Average DoF Constraint Length= 0
   System #1, "StressSystem"
    Type "Explicit"
    Variables={ "sigma_00" "sigma_01" "sigma_02" "sigma_11" "sigma_12" "sigma_22" }
    Finite Element Types="MONOMIAL", "JACOBI_20_00"
    Infinite Element Mapping="CARTESIAN"
    Approximation Orders="CONSTANT", "THIRD"
    n_dofs()=240
    n_local_dofs()=240
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=1
    n_matrices()=0
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 0
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 0
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Performing solve 0, forcing_magnitude: 0.001
  NL step  0, |residual|_2 = 1.140518e-06
  NL step  1, |residual|_2 = 4.284515e-04
  NL step  2, |residual|_2 = 4.701990e-06
  NL step  3, |residual|_2 = 1.256769e-09
  NL step  4, |residual|_2 = 8.494494e-13
System solved at nonlinear iteration 4 , final nonlinear residual norm: 8.494494e-13

Computing stresses...

 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 10:00:15 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=0.165386, Active time=0.154654                                                  |
 -----------------------------------------------------------------------------------------------------------------
| 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()     2          0.0001      0.000047    0.0001      0.000047    0.06     0.06     |
|   build_constraint_matrix()        360        0.0002      0.000001    0.0002      0.000001    0.13     0.13     |
|   build_sparsity()                 1          0.0005      0.000452    0.0005      0.000513    0.29     0.33     |
|   constrain_elem_matrix()          160        0.0002      0.000001    0.0002      0.000001    0.12     0.12     |
|   constrain_elem_vector()          200        0.0001      0.000000    0.0001      0.000000    0.04     0.04     |
|   create_dof_constraints()         2          0.0003      0.000170    0.0004      0.000199    0.22     0.26     |
|   distribute_dofs()                2          0.0001      0.000067    0.0006      0.000287    0.09     0.37     |
|   dof_indices()                    2320       0.0012      0.000001    0.0012      0.000001    0.77     0.77     |
|   enforce_constraints_exactly()    10         0.0001      0.000007    0.0001      0.000007    0.04     0.04     |
|   prepare_send_list()              4          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         2          0.0004      0.000220    0.0004      0.000220    0.29     0.29     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_solution_vector()          1          0.0013      0.001305    0.0016      0.001585    0.84     1.02     |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               1          0.0020      0.001987    0.0020      0.001987    1.28     1.28     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        400        0.0008      0.000002    0.0008      0.000002    0.51     0.51     |
|   init_shape_functions()           10         0.0001      0.000009    0.0001      0.000009    0.06     0.06     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             400        0.0008      0.000002    0.0008      0.000002    0.49     0.49     |
|   init_reference_to_physical_map() 10         0.0005      0.000049    0.0005      0.000049    0.32     0.32     |
|                                                                                                                 |
| Mesh                                                                                                            |
|   find_neighbors()                 1          0.0001      0.000142    0.0001      0.000142    0.09     0.09     |
|   renumber_nodes_and_elem()        2          0.0000      0.000005    0.0000      0.000005    0.01     0.01     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         1          0.0000      0.000031    0.0036      0.003604    0.02     2.33     |
|                                                                                                                 |
| MeshTools::Generation                                                                                           |
|   build_cube()                     1          0.0001      0.000113    0.0001      0.000113    0.07     0.07     |
|                                                                                                                 |
| Parallel                                                                                                        |
|   allgather()                      2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition()               1          0.0000      0.000017    0.0000      0.000017    0.01     0.01     |
|                                                                                                                 |
| PetscNonlinearSolver                                                                                            |
|   jacobian()                       4          0.1367      0.034177    0.1383      0.034569    88.39    89.41    |
|   residual()                       5          0.0035      0.000698    0.0052      0.001045    2.26     3.38     |
|   solve()                          1          0.0052      0.005222    0.1488      0.148756    3.38     96.19    |
|                                                                                                                 |
| System                                                                                                          |
|   solve()                          1          0.0003      0.000331    0.1491      0.149087    0.21     96.40    |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            3904       0.1547                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example systems_of_equations_ex7:
*   example-opt -ksp_type cg -pc_type bjacobi -snes_linesearch_type basic
***************************************************************