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p4pdes/python/

The codes in Chapters 13 and 14 use Firedrake, a finite element library based on PETSc data types and solvers. Firedrake uses Python and petsc4py.

These codes will remain here and be maintained and supported in the long term.

configure and install Firedrake

To download and install Firedrake please follow the instructions at the download tab on the Firedrake page. It is recommended that you allow Firedrake to download and configure its own copy of PETSc.

After the initial download (of the Firedrake install script) do something like this:

    $ unset PYTHONPATH; unset PETSC_DIR; unset PETSC_ARCH;
    $ python3 firedrake-install

(The reason to unset variables is so that Firedrake does its own PETSc install with its own compatible version of PETSc.)

Firedrake will then proceed to download and install its rather large stack of dependencies. When it is done you may want to set a convenience alias something like this, for later activation of the Firedrake virtual environment:

    $ alias drakeme='unset PETSC_DIR; unset PETSC_ARCH; source ~/firedrake/bin/activate'

getting started with the Poisson example

Do this to run the Poisson solver in Chapter 13, which will also test whether your Firedrake installation is working:

    $ cd p4pdes/python/ch13/
    $ source ~/firedrake/bin/activate      # or use alias: $ drakeme
    (firedrake) $ ./fish.py

When you run a Firedrake program for the first time it will cache various finite element constructions. Thus it will run much faster the second time.

Note that the default mesh is a 3 x 3 regular grid and the default KSP is CG. Finer meshes can be set by either -refine X and/or -mx and -my. Note that using -refine allows geometric multigrid (GMG). PETSc solver options use prefix -s_. Thus for CG+GMG on a fine grid with tight tolerances do something like this:

    (firedrake) $ ./fish.py -refine 8 -s_pc_type mg -s_ksp_monitor -s_ksp_rtol 1.0e-10

To see help do the following:

    (firedrake) $ ./fish.py -fishhelp
    (firedrake) $ ./fish.py -help

The first gives help specific to fish.py. The second gives the usual PETSc type of help, i.e. with all of the many applicable PETSc options. Do

    (firedrake) $ ./fish.py -help |grep STRING

to find specific PETSc options including STRING.

software testing

To test the Firedrake installation you can also do the following in either ch13/ or ch14/:

    (firedrake) $ make test