2025.05.29 Colloquia Seminars
| Speaker |
Prof. Hans De Sterck, University of Waterloo |
| Title |
Multigrid Parallel-in-Time Methods for Nonlinear Hyperbolic PDE Systems |
| Time |
2025.07.31 10:30-11:30 |
| Venue |
N202 |
| Abstract |
Sequential time-stepping using only spatial parallelism is becoming a computational bottleneck because the world's largest parallel computers now have millions of parallel processor cores due to stagnating processor speeds. In this context, parallelization in time can provide additional concurrency leading to further speedups. Parallel-in-time methods have been demonstrated to work well for parabolic PDEs, but remain a challenge for hyperbolic PDEs. In this talk, we present new developments for the multigrid reduction-in-time (MGRIT) parallel-in-time method that solve nonlinear hyperbolic PDEs and hyperbolic systems in a small number of iterations with convergence factor independent of mesh resolution. Crucial ingredients include modified semi-Lagrangian coarse-grid operators, careful linearization strategies, and characteristic block preconditioners for systems. Results are presented for linear advection and linear acoustic systems, and for the nonlinear Burgers equation, shallow water equations and compressible Euler equations with shocks. |
| Affiliation |
Hans De Sterck is a Professor of Computational and Applied Mathematics in the Department of Applied Mathematics at the University of Waterloo, and is currently serving as the Chair of the department.
He did his Ph.D. research at the University of Leuven, Belgium, and the National Center for Atmospheric Research, USA. After postdocs at the von Karman Institute and CU Boulder, he joined the University of Waterloo in 2004. Between 2015 and 2018, he worked at the School of Mathematical Sciences of Monash University in Melbourne, Australia. He served as the Director of Waterloo's Centre for Computational Mathematics from 2020 to 2023.
Prof. De Sterck's area of research is numerical methods for computational science and data science. In particular, he has worked on numerical methods for PDEs and numerical linear algebra, including multigrid methods. More recently he has worked on convergence acceleration methods for optimization, with applications to tensor decomposition and problems in machine learning. He is a SIAM Fellow. He was an invited speaker at the 2019 ICIAM conference, and is a recipient of the 2015 ICPADS Best Paper Award, the 2012 Ontario Early Researcher Award, and the 1999 UCAR Outstanding Publication Award.
Prof. De Sterck is the Editor-in-Chief of the SIAM Journal on Scientific Computing. He is a member of the SIAM Council and a Council representative to the SIAM Board. He co-chaired the 2015 SIAM Conference on Computational Science and Engineering and served as the chair of SIAM's Activity Group on Computational Science and Engineering in 2017-2018, and as the inaugural Chair of SIAM's Activity Group on Data Science in 2021. | |
