Step-7: pySDC with external libraries

pySDC can be used with external libraries, in particular for spatial discretization, parallelization and solving of linear and/or nonlinear systems. In the following, we show a few examples of pySDC + X.

• Part A: pySDC and FEniCS. Finite elements in space, with and without inverting the mass matrix.

• Part B: mpi4py-fft for parallel Fourier transforms. The nonlinear Schrödinger equation with SDC, MLSDC and PFASST.

• Part C: Time-parallel pySDC with space-parallel PETSc. Space and time communicators, split by coloring.

• Part D: pySDC and PyTorch. A tensor data type, and a network trained at the collocation nodes; torch_heat.py holds the data type, the heat equation using it and the network.

• Part E: pySDC and Firedrake. The heat equation of Part A, in Firedrake, serial, parallel across the nodes, or on three levels.

• Part F: pySDC and Gusto. pySDC as a time discretization for Gusto, in the Williamson 5 test case; F_2_plot_pySDC_with_Gusto_result.py plots its results.

• Part G: pySDC on GPUs. A heat equation in finite differences with SDC, MLSDC and PFASST, all of it on the device.

Each part is a Python script in jupytext “percent” format: run it with python (or mpirun) in an environment with the library it needs, or read it on the website. Parts A, B, D, F and G also open as notebooks in Jupyter; C and E read their process layout from the command line and only run as scripts. None of them runs in the browser or in the environment the website is built in; where the CI produces results, the pages show them.