## UC Berkeley / Lawrence Berkeley Laboratory

#### High-Order Multigrid-Reduction-In-Time for Linear Hyperbolic PDEs

**Ben Ong, Michigan Technological University**

Multigrid Reduction in Time (MGRIT) uses multigrid reduction techniques to enable temporal parallelism for solving time dependent PDEs. Although MGRIT converges rapidly for diffusion-dominated PDEs, the convergence for advection-dominated PDEs is slow, or even non-convergent. For a two-level scheme with a fine-grid and a coarse grid, it is known that the convergence of MGRIT depends in part on the choice of time-stepping operators on the fine and coarse grid. In this talk, I will give a brief overview to MGRIT, some existing attempts to accelerate convergence for advection-dominated PDEs, and a proposed family of coarse-grid operators to accelerate convergence. This work is a joint effort with Dr. Robert Falgout (Lawrence Livermore National Laboratory).