Title: **Parallel-in-Time Solution of Systems of Linear and Nonlinear Hyperbolic PDEs**

Abstract: The 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. This has worked well for parabolic equations, but parallel-in-time methods for advection-dominated hyperbolic problems have proven difficult to develop. In previous work, we demonstrated the effectiveness of a modified semi-Lagrangian coarse-grid operator for speeding up the parallel solution of high-order discretizations of variable-wave-speed linear advection problems in both 1D and 2D. We have also recently extended this technique for solving nonlinear hyperbolic conservation laws, including the inviscid Burgers and Buckley-Leverett equations. In this talk, we will present further developments for solving linear and nonlinear systems of hyperbolic PDEs such as the acoustic equations, shallow water equations, and Euler equations.

*Joint work with: Hans De Sterck, Oliver A. Krzysik, and Jacob B. Schroder*

The talk will take place **Thursday Sep. 5, 3:30pm** in room **213 MLH **(MacLean Hall).