Title: Efficient Approaches for Time-Domain Wave Equations with Application to Computational Electromagnetics

Abstract: For engineering or applied sciences, high-order accurate numerical methods are often desirable because they are potentially orders of magnitude more efficient than their low-order counterparts. However, realizing the potential payoff of high-order methods in complex domains, particularly for wave equations, has proven challenging. Here I highlight two aspects of our recent work on high-order accurate methods for the second-order formulation of the governing equations. Part I of the talk presents a numerical approach for dispersive Maxwell's equations built around an efficient 3-level time stepping algorithm. Overlapping grids are used to address geometric complexity, and both second- and fourth-order accurate schemes are presented. Part II presents recent developments for Galerkin Differences (GD). Although GD is fundamentally a finite element approximation based on a Galerkin projection, the underlying GD space is nonstandard and is derived using profitable ideas from the finite difference literature. The resulting schemes possess remarkable properties including nodal superconvergence and the ability to use large CFL-one time steps.

Bio: Dr. Banks received his Ph.D. in applied mathematics from Rensselaer Polytechnic Institute in 2006. Subsequently he completed postdoctoral appointments at Sandia National Laboratories in Albuquerque, New Mexico, and Lawrence Livermore National Laboratory in Livermore, California. In 2010 he was appointed as a staff scientist at LLNL where he remained until moving back to RPI. In January 2015 he was appointed associate professor in the Department of Mathematical Sciences where he holds the Eliza Ricketts Foundation Career Development Chair. Since 2021 he has served on the editorial board of the Journal of Computational Physics. Dr. Banks is interested in computer simulation of time evolving partial differential equations where linear or nonlinear wave phenomena play a central role. His research involves the development and analysis of highly accurate and efficient algorithms for the numerical simulation of physical systems such as high-speed fluid dynamics, solid mechanics, electromagnetics, plasma physics and fluid-structure interaction.