**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Tuesday, December 14, 2021 1:00 PM EST

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca

Jacob Schroder, University of New Mexico Department of Mathematics and Statistics

Parallel-in-Time with Multigrid: Method, Theory, and Applications

The need for parallel-in-time algorithms is currently being driven by the rapidly changing nature of computer architectures. Future speedups will come through ever increasing numbers of processors (cores), but not faster clock speeds, which are stagnant. Previously, increasing clock-speeds compensated for traditional sequential time stepping algorithms when the problem size increased. However, this is no longer the case, leading to the sequential time integration bottleneck and the need to parallelize in time. In this talk, we examine an optimal-scaling parallel time integration method, multigrid reduction in time (MGRIT). MGRIT applies multigrid to the time dimension by solving the (non)linear systems that arise when solving for multiple time steps simultaneously. The result is a versatile approach that is nonintrusive and wraps existing time evolution codes. MGRIT allows for various time discretizations (e.g., Runge-Kutta and multistep) and for adaptive refinement/coarsening in time and space. Nonlinear problems are handled through full approximation storage (FAS) multigrid. Some recent theoretical results, as well as practical results for a variety of problems will be presented, e.g., nonlinear diffusion, powergrid systems, advection, and compressible Navier-Stokes. Additionally, a novel application of time-parallelism to deep learning is presented, where the layer dimension of deep neural networks is explicitly parallelized by an MGRIT method.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.