p4pdes

PETSc for Partial Differential Equations is a book on using PETSc and Firedrake to solve partial differential equations by modern numerical methods.

Order a paper copy from SIAM Press, or the e-book from Google Play.

This repository contains the C and Python example programs upon which the book is based.

These example programs will remain here for the long term, and they will be maintained for future versions of PETSc.

C examples

To compile and run the C examples, for Chapters 1 through 12, see the README.md in the c/ directory.

Python/Firedrake examples

Chapters 13 and 14 use Firedrake, a Python finite element library based on PETSc. See the README.md in the python/ directory to run these examples.

March 2025 update on managing 2 PETSc installations:

Running all the codes from the book can be done with two copies of PETSc. One copy is any PETSc installation, to be used for the C codes in Chapters 1--12; this one can be updated to follow any branch of PETSc, for example. The other copy is separate, and configured so that Firedrake works, and which must have the configuration needed by Firedrake.

Note that, as of March 2025, downloading and installing Firedrake, as in the instructions at the Install tab on the Firedrake page, is usually done by building a copy of PETSc from source, using Firedrake's recommended configuration flags, and then installing Firedrake via pip.

To install and manage two PETSc copies I do the following:

  $ git clone -b release https://gitlab.com/petsc/petsc.git petsc

Configure this copy called petsc with any preferred flags supporting your development of C programs (or C and Fortran programs). Almost any configuration will be compatible with building and running the C codes for Chapters 1--12.

2. Follow the instructions at the Install tab on the Firedrake page to install Firedrake. However, when you clone a copy of PETSc, put it in a different location from the above, e.g.

  $ git clone --depth 1 https://github.com/firedrakeproject/petsc.git petsc-firedrake

For the later stages of the Firedrake installation, make sure that PETSC_DIR is set appropriately, to point to petsc-firedrake. For example, in my case I set the environment variables:

   CC=mpicc CXX=mpicxx PETSC_DIR=/home/bueler/petsc-firedrake PETSC_ARCH=arch-firedrake-default HDF5_MPI=ON

Then the pip install ... for Firedrake installation proceeds as before.

3. Finally, I add certain convenience functions to the .bashrc in my home directory:

parse_git_dirty() {
    [[ $(git status 2> /dev/null | tail -n1) != "nothing to commit, working tree clean" ]] && echo "*"
}
parse_git_branch() {
    git branch --no-color 2> /dev/null | sed -e '/^[^*]/d' -e "s/* \(.*\)/[\1$(parse_git_dirty)]/"
}
petscme() {
    export PETSC_DIR=~/petsc;
    export PETSC_ARCH=linux-c-dbg;
    alias mpiexec=$PETSC_DIR/$PETSC_ARCH/bin/mpiexec;
    export PS1='(petsc) \[\033[0;33m\]\w\[\033[0m\]$(parse_git_branch)$ '
}
drakeme() {
    source ~/venv-firedrake/bin/activate
    export CC=mpicc CXX=mpicxx PETSC_DIR=~/petsc-firedrake PETSC_ARCH=arch-firedrake-default HDF5_MPI=ON
}

These posix-compatible Bash functions give me prompts that are informative of what mode I am in, and also what Git branch I am on. For example, here is how I start to work with the C codes in Chapters 1--12:

  ~/p4pdes/c[master]$ petscme
  (petsc) ~/p4pdes/c[master]$ ...

For working with the Firedrake Python codes in Chapters 13--14, I do:

  ~/p4pdes/python[master]$ drakeme
  (firedrake) ~/p4pdes/python[master]$