Stephanie Friedhoff, Ph.D., KU Leuven, Numerical Analysis and Applied Mathematics Section

Title:
Multigrid reduction techniques for parallel-in-time integration

Abstract:

With current trends in computer architectures leading towards systems with more, but not faster, processors, faster time-to-solution must come from greater parallelism. In this talk, we present an optimal-scaling, true multilevel approach to parallel-in-time integration based on multigrid reduction (MGR) principles. The resulting multigrid-reduction-in-time (MGRIT) algorithm is a non-intrusive approach, which directly uses an existing time propagator and, thus, can easily exploit substantially more computational resources than standard sequential time-stepping. Furthermore, we demonstrate that MGRIT offers excellent strong and weak parallel scaling up to thousands of processors for solving diffusion equations in two and three space dimensions. A complementary semi-algebraic mode analysis methodology will also be presented, which provides a predictive analysis tool for MGRIT and related algorithms on space-time grids.