.. _handson: ================================== Tutorials, by Mathematical Problem ================================== TODO: Add link to Python example here .. _handson_example_1: Linear elliptic PDE on a 2D grid -------------------------------- WHAT THIS EXAMPLE DEMONSTRATES: - Using command line options - Using Linear Solvers - Handling a simple structured grid FURTHER DETAILS: - `Mathematical description of the problem `__ - `the source code `__ DO THE FOLLOWING: - Compile ``src/ksp/ksp/tutorials/ex50.c`` .. code-block:: console \$ cd petsc/src/ksp/ksp/tutorials \$ make ex50 - Run a 1 processor example with a 3x3 mesh and view the matrix assembled .. code-block:: console \$ mpiexec -n 1 ./ex50 -da_grid_x 4 -da_grid_y 4 -mat_view Expected output: .. literalinclude:: /../src/ksp/ksp/tutorials/output/ex50_tut_1.out :language: none - Run with a 120x120 mesh on 4 processors using superlu_dist and view the solver options used .. code-block:: console \$ 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: .. literalinclude:: /../src/ksp/ksp/tutorials/output/ex50_tut_2.out :language: none - Run with a 1025x1025 grid using multigrid solver on 4 processors with 9 multigrid levels .. code-block:: console \$ mpiexec -n 4 ./ex50 -da_grid_x 1025 -da_grid_y 1025 -pc_type mg -pc_mg_levels 9 -ksp_monitor Expected output: .. literalinclude:: /../src/ksp/ksp/tutorials/output/ex50_tut_3.out :language: none .. _handson_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: - `Mathematical description of the problem `__ - `the source code `__ DO THE FOLLOWING: - Compile ``src/ts/tutorials/ex2.c`` .. code-block:: console \$ cd petsc/src/ts/tutorials \$ make ex2 - Run a 1 processor example on the default grid with all the default solver options .. code-block:: console \$ mpiexec -n 1 ./ex2 -ts_max_steps 10 -ts_monitor Expected output: .. literalinclude:: /../src/ts/tutorials/output/ex2_tut_1.out :language: none - Run with the same options on 4 processors plus monitor convergence of the nonlinear and linear solvers .. code-block:: console \$ mpiexec -n 4 ./ex2 -ts_max_steps 10 -ts_monitor -snes_monitor -ksp_monitor Expected output: .. literalinclude:: /../src/ts/tutorials/output/ex2_tut_2.out :language: none - Run with the same options on 4 processors with 128 grid points .. code-block:: console \$ mpiexec -n 16 ./ex2 -ts_max_steps 10 -ts_monitor -M 128 Expected output: .. literalinclude:: /../src/ts/tutorials/output/ex2_tut_3.out :language: none .. _handson_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: - `Mathematical description of the problem `__ - `main program source code `__ - `physics source code `__ DO THE FOLLOWING: - Compile ``src/snes/tutorials/ex19.c`` .. code-block:: console \$ 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 .. code-block:: console \$ mpiexec -n 4 ./ex19 -da_refine 5 -snes_monitor -ksp_monitor -snes_view Expected output: .. literalinclude:: /../src/snes/tutorials/output/ex19_tut_1.out :language: none - Run with the same options but use geometric multigrid as the linear solver .. code-block:: console \$ mpiexec -n 4 ./ex19 -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type mg Expected output: .. literalinclude:: /../src/snes/tutorials/output/ex19_tut_2.out :language: none 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 .. code-block:: console \$ mpiexec -n 4 ./ex19 -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type hypre Expected output: .. literalinclude:: /../src/snes/tutorials/output/ex19_tut_3.out :language: none 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 .. code-block:: console \$ mpiexec -n 4 ./ex19 -da_refine 5 -snes_monitor -ksp_monitor -snes_view -pc_type ml Expected output: .. literalinclude:: /../src/snes/tutorials/output/ex19_tut_8.out :language: none - Run on 1 processor with the default linear solver and profile the run .. code-block:: console \$ mpiexec -n 1 ./ex19 -da_refine 5 -log_view Expected output: .. literalinclude:: /../src/snes/tutorials/output/ex19_tut_4.out :language: none 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 .. code-block:: console \$ mpiexec -n 1 ./ex19 -da_refine 5 -log_view -pc_type mg Expected output: .. literalinclude:: /../src/snes/tutorials/output/ex19_tut_5.out :language: none 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 .. code-block:: console \$ mpiexec -n 4 ./ex19 -da_refine 5 -log_view Expected output: .. literalinclude:: /../src/snes/tutorials/output/ex19_tut_6.out :language: none 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 .. code-block:: console \$ mpiexec -n 4 ./ex19 -da_refine 5 -log_view -pc_type mg Expected output: .. literalinclude:: /../src/snes/tutorials/output/ex19_tut_7.out :language: none 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? .. _handson_example_4: 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: - `Mathematical description of the problem `__ - `main program source code `__ - `source code of physics modules `__ DO THE FOLLOWING: - Compile ``src/ts/tutorials/ex11.c`` .. code-block:: console \$ cd petsc/src/ts/tutorials \$ make ex11 - Run simple advection through a tiny hybrid mesh .. code-block:: console \$ mpiexec -n 1 ./ex11 -f \${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo Expected output: .. literalinclude:: /../src/ts/tutorials/output/ex11_tut_1.out :language: none - Run simple advection through a small mesh with a Rosenbrock-W solver .. code-block:: console \$ mpiexec -n 1 ./ex11 -f \${PETSC_DIR}/share/petsc/datafiles/meshes/sevenside.exo -ts_type rosw Expected output: .. literalinclude:: /../src/ts/tutorials/output/ex11_tut_2.out :language: none - Run simple advection through a larger quadrilateral mesh of an annulus with least squares reconstruction and no limiting, monitoring the error .. code-block:: console \$ 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: .. literalinclude:: /../src/ts/tutorials/output/ex11_tut_3.out :language: none 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) .. code-block:: console \$ 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: .. literalinclude:: /../src/ts/tutorials/output/ex11_tut_4.out :language: none