MC 6460 and Zoom (For Zoom Link please contactÌýddelreyfernandez@uwaterloo.ca)Ìý
Ìý
Speaker
Oliver Krzysik, University of À¶Ý®ÊÓƵ
Title
Parallel multigrid-in-time for hyperbolic PDEs
Abstract
Traditionally, time-dependentÌýpartial differential equationsÌý(PDEs) areÌýsimulated via the procedure of sequential time-stepping. However, theyÌýmay also be simulated in a parallel-in-time fashion. To date, manyÌýsuccessful parallel-in-time strategies have been developed,Ìýparticularly for diffusion-dominated PDE problems. On the other hand,Ìýthere has been much less success in this area for hyperbolic problems.Ìý
We discuss solving hyperbolic PDEs using the iterative, multilevelÌýparallel-in-time method known as multigrid reduction-in-time (MGRIT).ÌýThe key to an efficient MGRIT solver is using a coarse-grid problemÌýthat is less expensive to solve than the underlying fine-grid problemÌýwhile also serving as a close approximation to it. We discuss theÌýdevelopment of coarse-grid problems based on semi-LagrangianÌýdiscretizations. These coarse-grid problems result in dramaticallyÌýimproved MGRIT solvers compared to existing approaches for hyperbolicÌýPDEs. Examples will be shown for both linear and nonlinear scalar PDEs,Ìýand for linear PDE systems.