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|
.. _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 <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex50.c.html#line1>`__
- `the source code <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex50.c.html#line21>`__
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 <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex2.c.html#line13>`__
- `the source
code <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex2.c.html#line36>`__
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 <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/snes/tutorials/ex19.c.html#line19>`__
- `main program source
code <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/snes/tutorials/ex19.c.html#line94>`__
- `physics source
code <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/snes/tutorials/ex19.c.html#line246>`__
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 <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex11.c.html>`__
- `main program source code <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex11.c.html#line1403>`__
- `source code of physics modules <PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex11.c.html#line186>`__
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
|
