# Link to the source code for this example:

Open fem_system_ex4 in new tab.

# The console output of the program:

```***************************************************************
* Running Example fem_system_ex4:
*   example-opt
***************************************************************

Mesh Information:
elem_dimensions()={1, 2}
spatial_dimension()=2
n_nodes()=1107
n_local_nodes()=1107
n_elem()=280
n_local_elem()=280
n_active_elem()=280
n_subdomains()=2
n_partitions()=1
n_processors()=1
processor_id()=0

EquationSystems
n_systems()=1
System #0, "Heat"
Type "Implicit"
Variables="T"
Finite Element Types="LAGRANGE", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN"
Approximation Orders="FIRST", "THIRD"
n_dofs()=294
n_local_dofs()=294
n_constrained_dofs()=47
n_local_constrained_dofs()=47
n_vectors()=1
n_matrices()=1
DofMap Sparsity
Average  On-Processor Bandwidth <= 8.29932
Average Off-Processor Bandwidth <= 0
Maximum  On-Processor Bandwidth <= 9
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 47
Average DoF Constraint Length= 0

Assembling the System
*** Warning, This code is deprecated, and likely to be removed in future library versions! ../../../include/libmesh/libmesh_common.h, line 497, compiled Apr 12 2016 at 12:26:03 ***
Nonlinear Residual: 0.44101
Linear solve starting, tolerance 0.00044101
Linear solve finished, step 6, residual 0.000218566
Trying full Newton step
Current Residual: 0.000263619
Nonlinear step: |du|/|u| = 1, |du| = 9.07515
Assembling the System
Nonlinear Residual: 0.000263619
Linear solve starting, tolerance 2.63619e-07
Linear solve finished, step 13, residual 2.19057e-11
Trying full Newton step
Current Residual: 3.02183e-11
Nonlinear solver converged, step 1, residual reduction 6.85205e-11 < 1e-07
Nonlinear solver relative step size 4.50166e-05 > 1e-07
Refined mesh to 533 active elements and 476 active dofs.
Assembling the System
Nonlinear Residual: 0.226674
Linear solve starting, tolerance 0.000226674
Linear solve finished, step 11, residual 4.68492e-06
Trying full Newton step
Current Residual: 9.0083e-06
Nonlinear step: |du|/|u| = 0.0026867, |du| = 0.0430946
Assembling the System
Nonlinear Residual: 9.0083e-06
Linear solve starting, tolerance 9.0083e-09
Linear solve finished, step 22, residual 1.16731e-14
Trying full Newton step
Current Residual: 4.61342e-14
Nonlinear solver converged, step 1, residual reduction 2.03527e-13 < 1e-07
Nonlinear solver relative step size 6.58778e-07 > 1e-07
Refined mesh to 1049 active elements and 938 active dofs.
Assembling the System
Nonlinear Residual: 0.156385
Linear solve starting, tolerance 0.000156385
Linear solve finished, step 18, residual 2.33773e-06
Trying full Newton step
Current Residual: 3.11137e-06
Nonlinear step: |du|/|u| = 0.00129394, |du| = 0.0284054
Assembling the System
Nonlinear Residual: 3.11137e-06
Linear solve starting, tolerance 3.11137e-09
Linear solve finished, step 33, residual 6.09154e-15
Trying full Newton step
Current Residual: 1.82249e-14
Nonlinear solver converged, step 1, residual reduction 1.16539e-13 < 1e-07
Nonlinear solver relative step size 9.59056e-07 > 1e-07
L2-Error is: 0.000273268

-------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 10:05:56 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                                                                                            |
| 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=0.270901, Active time=0.230553                                                  |
-----------------------------------------------------------------------------------------------------------------
| 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   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| BoundaryInfo                                                                                                    |
|   add_elements()                   1          0.0001      0.000060    0.0001      0.000060    0.03     0.03     |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     3          0.0004      0.000139    0.0004      0.000139    0.18     0.18     |
|   build_constraint_matrix()        7448       0.0026      0.000000    0.0026      0.000000    1.14     1.14     |
|   build_sparsity()                 3          0.0023      0.000751    0.0027      0.000916    0.98     1.19     |
|   cnstrn_elem_mat_vec()            3724       0.0009      0.000000    0.0009      0.000000    0.38     0.38     |
|   constrain_elem_vector()          3724       0.0007      0.000000    0.0007      0.000000    0.31     0.31     |
|   create_dof_constraints()         3          0.0043      0.001445    0.0049      0.001650    1.88     2.15     |
|   distribute_dofs()                3          0.0006      0.000216    0.0035      0.001155    0.28     1.50     |
|   dof_indices()                    33837      0.0061      0.000000    0.0061      0.000000    2.66     2.66     |
|   enforce_constraints_exactly()    14         0.0004      0.000027    0.0004      0.000027    0.17     0.17     |
|   old_dof_indices()                4746       0.0012      0.000000    0.0012      0.000000    0.51     0.51     |
|   prepare_send_list()              4          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         3          0.0028      0.000940    0.0028      0.000940    1.22     1.22     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_solution_vector()          2          0.0016      0.000781    0.0021      0.001046    0.68     0.91     |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               1          0.0029      0.002918    0.0029      0.002918    1.27     1.27     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        20645      0.0091      0.000000    0.0091      0.000000    3.94     3.94     |
|   init_shape_functions()           10318      0.0174      0.000002    0.0174      0.000002    7.54     7.54     |
|   inverse_map()                    48441      0.0243      0.000001    0.0243      0.000001    10.54    10.54    |
|                                                                                                                 |
| FEMSystem                                                                                                       |
|   assembly()                       6          0.0113      0.001889    0.0238      0.003965    4.92     10.32    |
|   assembly(get_residual)           6          0.0100      0.001671    0.0221      0.003686    4.35     9.59     |
|   postprocess()                    3          0.0030      0.001016    0.0078      0.002606    1.32     3.39     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             20645      0.0115      0.000001    0.0115      0.000001    4.99     4.99     |
|   compute_face_map()               5868       0.0056      0.000001    0.0167      0.000003    2.44     7.24     |
|   init_face_shape_functions()      34         0.0000      0.000001    0.0000      0.000001    0.01     0.01     |
|   init_reference_to_physical_map() 10318      0.0205      0.000002    0.0205      0.000002    8.89     8.89     |
|                                                                                                                 |
| GMVIO                                                                                                           |
|   write_nodal_data()               1          0.0126      0.012575    0.0126      0.012575    5.45     5.45     |
|                                                                                                                 |
| GenericProjector                                                                                                |
|   copy_dofs                        522        0.0002      0.000000    0.0012      0.000002    0.10     0.52     |
|   operator()                       2          0.0026      0.001303    0.0761      0.038053    1.13     33.01    |
|   project_edges                    1060       0.0000      0.000000    0.0000      0.000000    0.02     0.02     |
|   project_interior                 1060       0.0001      0.000000    0.0001      0.000000    0.04     0.04     |
|   project_nodes                    1060       0.0018      0.000002    0.0709      0.000067    0.78     30.75    |
|   project_sides                    1060       0.0001      0.000000    0.0001      0.000000    0.03     0.03     |
|                                                                                                                 |
| JumpErrorEstimator                                                                                              |
|   estimate_error()                 2          0.0178      0.008896    0.0524      0.026218    7.72     22.74    |
|                                                                                                                 |
| Mesh                                                                                                            |
|   contract()                       2          0.0000      0.000017    0.0001      0.000044    0.01     0.04     |
|   find_neighbors()                 4          0.0039      0.000968    0.0039      0.000968    1.68     1.68     |
|   renumber_nodes_and_elem()        10         0.0002      0.000021    0.0002      0.000021    0.09     0.09     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         2          0.0000      0.000010    0.0176      0.008804    0.01     7.64     |
|                                                                                                                 |
| MeshRefinement                                                                                                  |
|   _coarsen_elements()              4          0.0000      0.000011    0.0000      0.000011    0.02     0.02     |
|   _refine_elements()               4          0.0035      0.000865    0.0064      0.001606    1.50     2.79     |
|   add_node()                       8916       0.0022      0.000000    0.0022      0.000000    0.97     0.97     |
|   make_coarsening_compatible()     6          0.0004      0.000073    0.0004      0.000073    0.19     0.19     |
|   make_flags_parallel_consistent() 6          0.0002      0.000040    0.0002      0.000040    0.10     0.10     |
|   make_refinement_compatible()     6          0.0001      0.000014    0.0001      0.000014    0.04     0.04     |
|                                                                                                                 |
| MeshTools::Generation                                                                                           |
|   build_cube()                     1          0.0002      0.000214    0.0002      0.000214    0.09     0.09     |
|                                                                                                                 |
| NewtonSolver                                                                                                    |
|   solve()                          3          0.0006      0.000201    0.0503      0.016750    0.26     21.80    |
|                                                                                                                 |
| OldSolutionValue                                                                                                |
|   Number eval_at_node()            4032       0.0003      0.000000    0.0003      0.000000    0.13     0.13     |
|   check_old_context(c)             522        0.0004      0.000001    0.0007      0.000001    0.18     0.32     |
|   check_old_context(c,p)           2908       0.0018      0.000001    0.0037      0.000001    0.76     1.62     |
|   eval_at_point()                  2908       0.0331      0.000011    0.0683      0.000023    14.36    29.61    |
|   eval_old_dofs()                  522        0.0001      0.000000    0.0009      0.000002    0.06     0.41     |
|                                                                                                                 |
| Parallel                                                                                                        |
|   allgather()                      3          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition()               4          0.0001      0.000037    0.0001      0.000037    0.06     0.06     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          6          0.0034      0.000567    0.0034      0.000567    1.48     1.48     |
|                                                                                                                 |
| System                                                                                                          |
|   project_vector(old,new)          2          0.0011      0.000547    0.0778      0.038885    0.47     33.73    |
|                                                                                                                 |
| TopologyMap                                                                                                     |
|   init()                           4          0.0037      0.000933    0.0037      0.000933    1.62     1.62     |
-----------------------------------------------------------------------------------------------------------------
| Totals:                            194442     0.2306                                          100.00            |
-----------------------------------------------------------------------------------------------------------------

***************************************************************
* Done Running Example fem_system_ex4:
*   example-opt
***************************************************************
```