Massively parallel adaptive spectral deferred correction in Python

Spectral deferred correction (SDC) methods offer various opportunities for concurrency in the time direction. Recent developments in diagonal preconditioners have enabled small scale parallelism with particularly high parallel efficiency by solving for all stages simultaneously. We combine this with spectral methods in space, which can be parallelized easily via distributed Fourier transforms to obtain massively parallel schemes. By using GPUs, we arrive at implementations that efficiently cater to modern HPC systems at scale. Our implementations form part of pySDC, a Python code that enables rapid prototyping of a wide range of SDC and parallel-in-time related aspects of time integration. We demonstrate excellent strong and weak scaling for multiple PDEs, showcasing the practical capabilities of both the method and the implementation.