pySDC: A Parallel Framework for Spectral Deferred Corrections

The parallel full approximation scheme in space and time (PFASST) allows to integrate multiple time-steps simultaneously. Based on iterative spectral deferred corrections (SDC) methods, PFASST uses a space-time hierarchy with various coarsening strategies to maximize parallel efficiency. In numerous studies, this approach has been used on up to 448K cores and coupled to space-parallel solvers which use finite differences, spectral methods or even particles for discretization in space. However, since the integration of SDC or PFASST into an existing application code is not straightforward and the potential gain is typically uncertain, we have developed the Python prototyping framework pySDC. It allows to rapidly test new ideas and to implement first toy problems more easily. It also provides interfaces to the finite element library FEniCS and the PETSc toolkit. In this talk, we describe the structure of the code and show different examples to highlight various aspects of the implementation, the capabilities and its usage. Moreover, this code sparked the development of a C++-based PFASST implementation, making use of the DUNE framework. The dune-PFASST module specifically targets finite element simulations and is used for reaction-diffusion examples. We will thus also discuss the transition from pySDC to dune-PFASST and show first numerical results