A Comparison of Space-Time Multigrid and PFASST with applications to Cardiac Electrophysiology

Pietro Benedusi (Universitàdella Swizzera Italiana)

We present a space-time multilevel method that uses a hierarchy of non-nested meshes, created by semi-geometric coarsening. The “grey box” multigrid starts from a single fine spatial mesh and automatically generates space-time coarse meshes of any dimension over complex geometries.

Two model problems are considered: the heat equation with anisotropy and jumping coefficients; the monodomain equation, a non-linear reaction-diffusion model arising from the study of excitable media such as the myocardium.

We analyze the convergence and scaling properties of the proposed solution strategies, focusing on the spectral properties and conditioning of the underlying discrete operators that arise from the tensor space-time finite element discretization.

Strong and weak scaling of the multilevel space-time approach is compared to PFASST (Parallel Full Approximation Scheme in Space and Time), highlighting properties and conceptual and quantitative differences of both approaches.