pySDC 4.1

A Python implementation of spectral deferred correction methods and the likes

The pySDC project is a Python implementation of the spectral deferred correction (SDC) approach and its flavors, esp. the multilevel extension MLSDC and PFASST. It is intended for rapid prototyping and educational purposes. New ideas like e.g. sweepers or predictors can be tested and first toy problems can be easily implemented.

Features

• Variants of SDC: explicit, implicit, IMEX, multi-implicit, Verlet, multi-level, diagonal, multi-step

• Variants of PFASST: virtual parallel or MPI-based parallel, classical of multigrid perspective

• 8 tutorials: from setting up a first collocation problem to SDC, PFASST and advanced topics

• Projects: many documented projects with defined and tested outcomes

• Many different examples, collocation types, data types already implemented

• Works with PETSc through petsc4py , FEniCS and mpi4py-fft

• Continuous integration via Github Actions

• Fully compatible with 3.6 (or higher)

Getting started

The code is hosted on GitHub, see https://github.com/Parallel-in-Time/pySDC, and PyPI, see https://pypi.python.org/pypi/pySDC. Use

pip install pySDC

to get the latest stable release including the core dependencies. Note that this will omit some of the more complex packages not required for the core functionality of pySDC, e.g. mpi4py, fenics and petsc4py (see below). All requirements are listed in the files requirements.txt . To work with the source files, checkout the code from Github and install the dependencies e.g. by using a conda environment and

conda install -c conda-forge --file requirements.txt

To check your installation, run

pytest pySDC/tests

You may need to update your PYTHONPATH by running

export PYTHONPATH=$PYTHONPATH:/path/to/pySDC/root/folder

in particular if you want to run any of the playgrounds, projects or tutorials. All import statements there assume that the pySDC’s base directory is part of PYTHONPATH.

Note: When installing mpi4py, fenics and petsc4py, make sure they use the same MPI installation (e.g. MPICH3). You can achieve this e.g. by

conda install -c conda-forge mpich petsc4py mpi4py fenics

Most of the code is tested automatically using Github Actions, so a working version of the installation process can always be found in the ci_pipeline.yml file.

For many examples, LaTeX is used for the plots, i.e. a decent installation of this is needed in order to run the tests. When using fenics or petsc4py, a C++ compiler is required (although installation may go through at first).

For more details on pySDC, check out http://www.parallel-in-time.org/pySDC.

How to cite

If you use pySDC or parts of it for your work, great! Let us know if we can help you with this. Also, we would greatly appreciate a citation of this paper:

Robert Speck, Algorithm 997: pySDC - Prototyping Spectral Deferred Corrections, ACM Transactions on Mathematical Software (TOMS), Volume 45 Issue 3, August 2019, https://doi.org/10.1145/3310410