(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` ```console $ cd petsc/src/ksp/ksp/tutorials $ make ex50 ``` - Run a 1 processor example with a 3x3 mesh and view the matrix assembled ```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 ```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 ```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` ```console $ cd petsc/src/ts/tutorials $ make ex2 ``` - Run a 1 processor example on the default grid with all the default solver options ```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 ```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 ```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` ```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 ```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 ```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 ```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 ```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 ```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 ```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 ```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 ```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` ```console $ cd petsc/src/ts/tutorials $ make ex11 ``` - Run simple advection through a tiny hybrid mesh ```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 ```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 ```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) ```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 ```