Numerical Analysis and Scientific Computing Seminar | Oliver Krzysik, Parallel multigrid-in-time for hyperbolic PDEs

MC 6460 and Zoom (For Zoom Link please contact ddelreyfernandez@uwaterloo.ca) 

Speaker

Oliver Krzysik, University of Waterloo

Title

Parallel multigrid-in-time for hyperbolic PDEs

Abstract

Traditionally, time-dependent partial differential equations (PDEs) are simulated via the procedure of sequential time-stepping. However, they may also be simulated in a parallel-in-time fashion. To date, many successful parallel-in-time strategies have been developed, particularly for diffusion-dominated PDE problems. On the other hand, there has been much less success in this area for hyperbolic problems. 

We discuss solving hyperbolic PDEs using the iterative, multilevel parallel-in-time method known as multigrid reduction-in-time (MGRIT). The key to an efficient MGRIT solver is using a coarse-grid problem that is less expensive to solve than the underlying fine-grid problem while also serving as a close approximation to it. We discuss the development of coarse-grid problems based on semi-Lagrangian discretizations. These coarse-grid problems result in dramatically improved MGRIT solvers compared to existing approaches for hyperbolic PDEs. Examples will be shown for both linear and nonlinear scalar PDEs, and for linear PDE systems.