PETSc comes with a large number of example codes to illustrate usage. Here, we highlight a few, key ones:
- Linear Poisson equation on a 2D grid
- example of linear equation problem
- see also src/ksp/ksp/tutorials
- Nonlinear ODE arising from a time-dependent one dimensional PDE
- example of time-stepping problem
- see also src/ts/tutorials
- Nonlinear PDE on a structured grid
- example of nonlinear PDE
- see also src/snes/tutorials
- Linear Stokes-type PDE on a structured grid
- Nonlinear time dependent PDE on Unstructured Grid
Several examples are also included that represent the interoperability with other numerical software packages in the xSDK Toolkit. These packages can be automatically installed by PETSc by configuring with --download-trilinos, --download-hypre, and/or --download-superlu_dist.
- Nonlinear PDE Example using Trilinos preconditioner ML
- Nonlinear PDE Example using BoomerAMG from HYPRE
- Linear Equation Example using direct solver SuperLU_DIST
Example 1: Linear Poisson equation on a 2D grid
WHAT THIS EXAMPLE DEMONSTRATES:
- Using command line options
- Using Linear Solvers
- Handling a simple structured grid
FURTHER DETAILS:
DO THE FOLLOWING:
- Compile src/ksp/ksp/tutorials/ex50.c
cd petsc/src/ksp/ksp/tutorials make ex50 - Run a 1 processor example with a 3x3 mesh and view the matrix assembled
mpiexec -n 1 ./ex50 -da_grid_x 4 -da_grid_y 4 -mat_view [Expected output] - Run with a 120x120 mesh on 4 processors using superlu_dist and view the solver options used
mpiexec -n 4 ./ex50 -da_grid_x 120 -da_grid_y 120 -pc_type lu -pc_factor_mat_solver_type superlu_dist -ksp_monitor -ksp_view [Expected output] - Run with a 1025x1025 grid using multigrid solver on 4 processors with 9 multigrid levels
mpiexec -n 4 ./ex50 -da_grid_x 1025 -da_grid_y 1025 -pc_type mg -pc_mg_levels 9 -ksp_monitor [Expected output]
Example 2: Nonlinear ODE arising from a time-dependent one dimensional PDE
WHAT THIS EXAMPLE DEMONSTRATES:
- Using command line options
- Handling a simple structured grid
- Using the ODE integrator
- Using call-back functions
FURTHER DETAILS:
DO THE FOLLOWING:
- Compile src/ts/tutorials/ex2.c
cd petsc/src/ts/tutorials make ex2 - Run a 1 processor example on the default grid with all the default solver options
mpiexec -n 1 ./ex2 -ts_max_steps 10 -ts_monitor [Expected output] - Run with the same options on 4 processors plus monitor convergence of the nonlinear and linear solvers
mpiexec -n 4 ./ex2 -ts_max_steps 10 -ts_monitor -snes_monitor -ksp_monitor [Expected output] - Run with the same options on 4 processors with 128 grid points
mpiexec -n 16 ./ex2 -ts_max_steps 10 -ts_monitor -M 128 [Expected output]
Example 3: Nonlinear PDE on a structured grid
WHAT THIS EXAMPLE DEMONSTRATES:
- Handling a 2d structured grid
- Using the nonlinear solvers
- Changing the default linear solver
FURTHER DETAILS:
DO THE FOLLOWING:
- Compile src/snes/tutorials/ex19.c
cd petsc/src/snes/tutorials/ make ex19 - Run a 4 processor example with 5 levels of grid refinement, monitor the convergence of the nonlinear and linear solver
and examine the exact solver used
mpiexec -n 4 ./ex19 -da_refine 5 -snes_monitor -ksp_monitor -snes_view [Expected output] - Run with the same options but use geometric multigrid as the linear solver
mpiexec -n 4 ./ex19 -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type mg [Expected output]Note this requires many fewer iterations than the default solver - Run with the same options but use algebraic multigrid (hypre's BoomerAMG) as the linear solver
mpiexec -n 4 ./ex19 -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type hypre [Expected output]Note this requires many fewer iterations than the default solver but requires more linear solver iterations than geometric multigrid. - Run with the same options but use the ML preconditioner from Trilinos
mpiexec -n 4 ./ex19 -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type ml [Expected output] - Run on 1 processor with the default linear solver and profile the run
mpiexec -n 1 ./ex19 -da_refine 5 -log_view [Expected output]Search for the line beginning with SNESSolve, the fourth column gives the time for the nonlinear solve. - Run on 1 processor with the geometric multigrid linear solver and profile the run
mpiexec -n 1 ./ex19 -da_refine 5 -log_view -pc_type mg [Expected output]Compare the runtime for SNESSolve to the case with the default solver - Run on 4 processors with the default linear solver and profile the run
mpiexec -n 4 ./ex19 -da_refine 5 -log_view [Expected output]Compare the runtime for SNESSolve to the 1 processor case with the default solver. What is the speedup? - Run on 4 processors with the geometric multigrid linear solver and profile the run
mpiexec -n 4 ./ex19 -da_refine 5 -log_view -pc_type mg [Expected output]Compare the runtime for SNESSolve to the 1 processor case with multigrid. What is the speedup? Why is the speedup for multigrid lower than the speedup for the default solver?
Example 4: Linear Stokes-type PDE on a structured grid
WHAT THIS EXAMPLE DEMONSTRATES:
- Handling a 3d structured grid
- Controlling linear solver options
- Selecting composible preconditioners
- Solving a Stokes problem
- Adding your own problem specific visualization
FURTHER DETAILS:
DO THE FOLLOWING:
- Compile src/ksp/ksp/tutorials/ex42.c
cd petsc/src/ksp/ksp/tutorials make ex42 - Solve with the default solver
mpiexec -n 4 ./ex42 -stokes_ksp_monitor [Expected output]Note the poor convergence for even a very small problem - Solve with a solver appropriate for Stoke's problems -stokes_pc_type fieldsplit -stokes_pc_fieldsplit_type schur
mpiexec -n 4 ./ex42 -stokes_ksp_monitor -stokes_pc_type fieldsplit -stokes_pc_fieldsplit_type schur [Expected output] - Solve with a finer mesh
mpiexec -n 4 ./ex42 -mx 20 -stokes_ksp_monitor -stokes_pc_type fieldsplit -stokes_pc_fieldsplit_type schur [Expected output]Repeat with-mx 40
and/or more MPI ranks.
Example 5: Nonlinear time dependent PDE on Unstructured Grid
WHAT THIS EXAMPLE DEMONSTRATES:
- Changing the default ODE integrator
- Handling unstructured grids
- Registering your own interchangeable physics and algorithm modules
FURTHER DETAILS:
DO THE FOLLOWING:
- Compile src/ts/tutorials/ex11.c
cd petsc/src/ts/tutorials make ex11 - Run simple advection through a tiny hybrid mesh
mpiexec -n 1 ./ex11 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo [Expected output] - Run simple advection through a small mesh with a Rosenbrock-W solver
mpiexec -n 1 ./ex11 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw [Expected output] - Run simple advection through a larger quadrilateral mesh of an annulus with least squares reconstruction and no limiting, monitoring the error
mpiexec -n 4 ./ex11 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -monitor Error -advect_sol_type bump -petscfv_type leastsquares -petsclimiter_type sin [Expected output]Compare turning to the error after turning off reconstruction. - Run shallow water on the larger mesh with least squares reconstruction and minmod limiting, monitoring water Height (integral is conserved) and Energy (not conserved)
mpiexec -n 4 ./ex11 -f ${PETSC_DIR}/share/petsc/datafiles/meshes/annulus-20.exo -physics sw -monitor Height,Energy -petscfv_type leastsquares -petsclimiter_type minmod [Expected output]