Link to the source code for this example:
Open systems_of_equations_ex3 in new tab.
The console output of the program:
***************************************************************
* Running Example systems_of_equations_ex3:
* example-opt
***************************************************************
Mesh Information:
elem_dimensions()={2}
spatial_dimension()=2
n_nodes()=1681
n_local_nodes()=1681
n_elem()=400
n_local_elem()=400
n_active_elem()=400
n_subdomains()=1
n_partitions()=1
n_processors()=1
n_threads()=1
processor_id()=0
EquationSystems
n_systems()=1
System #0, "Navier-Stokes"
Type "TransientLinearImplicit"
Variables={ "u" "v" } "p" "alpha"
Finite Element Types="LAGRANGE", "JACOBI_20_00" "LAGRANGE", "JACOBI_20_00" "SCALAR", "JACOBI_20_00"
Infinite Element Mapping="CARTESIAN" "CARTESIAN" "CARTESIAN"
Approximation Orders="SECOND", "THIRD" "FIRST", "THIRD" "FIRST", "THIRD"
n_dofs()=3804
n_local_dofs()=3804
n_constrained_dofs()=0
n_local_constrained_dofs()=0
n_vectors()=3
n_matrices()=1
DofMap Sparsity
Average On-Processor Bandwidth <= 40.9611
Average Off-Processor Bandwidth <= 0
Maximum On-Processor Bandwidth <= 3804
Maximum Off-Processor Bandwidth <= 0
DofMap Constraints
Number of DoF Constraints = 0
*** Solving time step 0, time = 0.01 ***
Linear solver converged at step: 51, final residual: 0.000282517 Nonlinear convergence: ||u - u_old|| = 351.27
Linear solver converged at step: 28, final residual: 1.94309e-05 Nonlinear convergence: ||u - u_old|| = 0.669457
Linear solver converged at step: 26, final residual: 9.95896e-08 Nonlinear convergence: ||u - u_old|| = 0.00106343
Linear solver converged at step: 51, final residual: 2.26529e-12 Nonlinear convergence: ||u - u_old|| = 1.31622e-06
Nonlinear solver converged at step 3
*** Solving time step 1, time = 0.02 ***
Linear solver converged at step: 43, final residual: 0.000268558 Nonlinear convergence: ||u - u_old|| = 28.9406
Linear solver converged at step: 22, final residual: 2.0417e-05 Nonlinear convergence: ||u - u_old|| = 0.0406665
Linear solver converged at step: 24, final residual: 1.12851e-07 Nonlinear convergence: ||u - u_old|| = 0.000315505
Nonlinear solver converged at step 2
*** Solving time step 2, time = 0.03 ***
Linear solver converged at step: 37, final residual: 0.000211074 Nonlinear convergence: ||u - u_old|| = 5.51321
Linear solver converged at step: 22, final residual: 1.01234e-05 Nonlinear convergence: ||u - u_old|| = 0.0101518
Linear solver converged at step: 27, final residual: 2.18784e-08 Nonlinear convergence: ||u - u_old|| = 8.18272e-05
Nonlinear solver converged at step 2
*** Solving time step 3, time = 0.04 ***
Linear solver converged at step: 28, final residual: 0.000239353 Nonlinear convergence: ||u - u_old|| = 1.98648
Linear solver converged at step: 18, final residual: 1.38776e-05 Nonlinear convergence: ||u - u_old|| = 0.00606589
Linear solver converged at step: 26, final residual: 3.41727e-08 Nonlinear convergence: ||u - u_old|| = 0.000775948
Nonlinear solver converged at step 2
*** Solving time step 4, time = 0.05 ***
Linear solver converged at step: 23, final residual: 0.000270828 Nonlinear convergence: ||u - u_old|| = 0.903052
Linear solver converged at step: 19, final residual: 2.04306e-05 Nonlinear convergence: ||u - u_old|| = 0.0091482
Linear solver converged at step: 24, final residual: 1.26651e-07 Nonlinear convergence: ||u - u_old|| = 0.000229152
Nonlinear solver converged at step 2
*** Solving time step 5, time = 0.06 ***
Linear solver converged at step: 23, final residual: 0.000286865 Nonlinear convergence: ||u - u_old|| = 0.465778
Linear solver converged at step: 15, final residual: 2.34656e-05 Nonlinear convergence: ||u - u_old|| = 0.00318115
Linear solver converged at step: 22, final residual: 1.43996e-07 Nonlinear convergence: ||u - u_old|| = 0.000212093
Nonlinear solver converged at step 2
*** Solving time step 6, time = 0.07 ***
Linear solver converged at step: 20, final residual: 0.000215688 Nonlinear convergence: ||u - u_old|| = 0.257386
Linear solver converged at step: 18, final residual: 9.85097e-06 Nonlinear convergence: ||u - u_old|| = 0.00379004
Linear solver converged at step: 28, final residual: 1.86885e-08 Nonlinear convergence: ||u - u_old|| = 0.000111296
Nonlinear solver converged at step 2
*** Solving time step 7, time = 0.08 ***
Linear solver converged at step: 16, final residual: 0.000286567 Nonlinear convergence: ||u - u_old|| = 0.147885
Linear solver converged at step: 17, final residual: 1.39735e-05 Nonlinear convergence: ||u - u_old|| = 0.00297817
Linear solver converged at step: 28, final residual: 2.81987e-08 Nonlinear convergence: ||u - u_old|| = 0.000639703
Nonlinear solver converged at step 2
*** Solving time step 8, time = 0.09 ***
Linear solver converged at step: 12, final residual: 0.000267583 Nonlinear convergence: ||u - u_old|| = 0.0836533
Linear solver converged at step: 16, final residual: 1.73457e-05 Nonlinear convergence: ||u - u_old|| = 0.0149353
Linear solver converged at step: 26, final residual: 4.4267e-08 Nonlinear convergence: ||u - u_old|| = 0.00101631
Linear solver converged at step: 57, final residual: 3.90603e-13 Nonlinear convergence: ||u - u_old|| = 1.21151e-06
Nonlinear solver converged at step 3
*** Solving time step 9, time = 0.1 ***
Linear solver converged at step: 11, final residual: 0.000222815 Nonlinear convergence: ||u - u_old|| = 0.0505091
Linear solver converged at step: 16, final residual: 1.39453e-05 Nonlinear convergence: ||u - u_old|| = 0.0133655
Linear solver converged at step: 26, final residual: 4.68354e-08 Nonlinear convergence: ||u - u_old|| = 0.000730003
Nonlinear solver converged at step 2
*** Solving time step 10, time = 0.11 ***
Linear solver converged at step: 10, final residual: 0.000233755 Nonlinear convergence: ||u - u_old|| = 0.0312662
Linear solver converged at step: 16, final residual: 1.53343e-05 Nonlinear convergence: ||u - u_old|| = 0.0114697
Linear solver converged at step: 25, final residual: 4.78201e-08 Nonlinear convergence: ||u - u_old|| = 0.000618281
Nonlinear solver converged at step 2
*** Solving time step 11, time = 0.12 ***
Linear solver converged at step: 10, final residual: 0.000145843 Nonlinear convergence: ||u - u_old|| = 0.0205185
Linear solver converged at step: 18, final residual: 5.65679e-06 Nonlinear convergence: ||u - u_old|| = 0.00791788
Linear solver converged at step: 27, final residual: 9.42197e-09 Nonlinear convergence: ||u - u_old|| = 9.26946e-05
Nonlinear solver converged at step 2
*** Solving time step 12, time = 0.13 ***
Linear solver converged at step: 9, final residual: 0.000232166 Nonlinear convergence: ||u - u_old|| = 0.0134885
Linear solver converged at step: 16, final residual: 1.09545e-05 Nonlinear convergence: ||u - u_old|| = 0.00714973
Linear solver converged at step: 22, final residual: 3.6354e-08 Nonlinear convergence: ||u - u_old|| = 0.000139754
Nonlinear solver converged at step 2
*** Solving time step 13, time = 0.14 ***
Linear solver converged at step: 8, final residual: 0.000251508 Nonlinear convergence: ||u - u_old|| = 0.00867291
Linear solver converged at step: 15, final residual: 1.80725e-05 Nonlinear convergence: ||u - u_old|| = 0.00586875
Linear solver converged at step: 23, final residual: 8.55045e-08 Nonlinear convergence: ||u - u_old|| = 0.000295444
Nonlinear solver converged at step 2
*** Solving time step 14, time = 0.15 ***
Linear solver converged at step: 7, final residual: 0.000278419 Nonlinear convergence: ||u - u_old|| = 0.00370556
Linear solver converged at step: 14, final residual: 1.8148e-05 Nonlinear convergence: ||u - u_old|| = 0.00335723
Linear solver converged at step: 25, final residual: 1.01115e-07 Nonlinear convergence: ||u - u_old|| = 0.000572797
Nonlinear solver converged at step 2
-------------------------------------------------------------------------------------------------------------------
| Time: Wed Apr 13 09:57:41 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= ' |
-------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------
| Systems Example 3 Performance: Alive time=1.08079, Active time=1.02321 |
------------------------------------------------------------------------------------------------------------
| 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 |
|------------------------------------------------------------------------------------------------------------|
| |
| linear solve 47 1.0232 0.021770 1.0232 0.021770 100.00 100.00 |
------------------------------------------------------------------------------------------------------------
| Totals: 47 1.0232 100.00 |
------------------------------------------------------------------------------------------------------------
-----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=1.0954, Active time=1.05825 |
-----------------------------------------------------------------------------------------------------------------
| 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 |
| SCALAR_dof_indices() 44400 0.0059 0.000000 0.0059 0.000000 0.56 0.56 |
| add_neighbors_to_send_list() 1 0.0003 0.000324 0.0004 0.000393 0.03 0.04 |
| build_sparsity() 1 0.0045 0.004457 0.0049 0.004935 0.42 0.47 |
| create_dof_constraints() 1 0.0001 0.000070 0.0001 0.000070 0.01 0.01 |
| distribute_dofs() 1 0.0003 0.000347 0.0013 0.001346 0.03 0.13 |
| dof_indices() 118400 0.0369 0.000000 0.0465 0.000000 3.49 4.39 |
| prepare_send_list() 2 0.0000 0.000000 0.0000 0.000000 0.00 0.00 |
| reinit() 1 0.0010 0.000998 0.0010 0.000998 0.09 0.09 |
| |
| EquationSystems |
| build_solution_vector() 15 0.0180 0.001201 0.0270 0.001798 1.70 2.55 |
| |
| ExodusII_IO |
| write_nodal_data() 15 0.0236 0.001573 0.0236 0.001573 2.23 2.23 |
| |
| FE |
| compute_shape_functions() 37600 0.0537 0.000001 0.0537 0.000001 5.07 5.07 |
| init_shape_functions() 94 0.0004 0.000004 0.0004 0.000004 0.04 0.04 |
| |
| FEMap |
| compute_affine_map() 37600 0.0277 0.000001 0.0277 0.000001 2.62 2.62 |
| init_reference_to_physical_map() 94 0.0009 0.000009 0.0009 0.000009 0.08 0.08 |
| |
| Mesh |
| find_neighbors() 1 0.0007 0.000665 0.0007 0.000665 0.06 0.06 |
| renumber_nodes_and_elem() 2 0.0000 0.000015 0.0000 0.000015 0.00 0.00 |
| |
| MeshOutput |
| write_equation_systems() 15 0.0001 0.000010 0.0507 0.003381 0.01 4.79 |
| |
| MeshTools::Generation |
| build_cube() 1 0.0005 0.000529 0.0005 0.000529 0.05 0.05 |
| |
| Parallel |
| allgather() 1 0.0000 0.000000 0.0000 0.000000 0.00 0.00 |
| |
| Partitioner |
| single_partition() 1 0.0000 0.000032 0.0000 0.000032 0.00 0.00 |
| |
| PetscLinearSolver |
| solve() 47 0.4033 0.008582 0.4033 0.008582 38.11 38.11 |
| |
| System |
| assemble() 47 0.4802 0.010217 0.6169 0.013126 45.38 58.30 |
-----------------------------------------------------------------------------------------------------------------
| Totals: 238340 1.0582 100.00 |
-----------------------------------------------------------------------------------------------------------------
***************************************************************
* Done Running Example systems_of_equations_ex3:
* example-opt
***************************************************************