Multigrid methods in space and time for extreme-scale scientific computing

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving systems of equations. They are widely used to solve the sparse spatial systems that arise in these simulations, and they have been shown to scale efficiently on today’s supercomputers. For time-dependent simulations, however, the traditional approach of sequential time stepping is becoming a bottleneck as computer architectures must rely on higher concurrency to increase peak performance (million-way parallelism on previous-generation computers, and billion-way on the new exascale platforms). Parallel-in-time solution approaches have been developed to avoid this bottleneck and provide significant speedups by solving for the full space-time system all at once in parallel. Our multigrid reduction in time (MGRIT) method is a parallel multigrid-in-time solver designed to be as non-intrusive as possible and take advantage of existing simulation codes and techniques, allowing scientists to migrate to a parallel-in-time simulation paradigm more easily.

In this talk, we will discuss the multigrid method, its role in scientific computing, and some of our current research directions. We will also discuss our efforts to develop the MGRIT method and the MGRIT open-source software library XBraid.