Title: EM-WaveHoltz: a flexible frequency-domain Maxwell solver built from time-domain solvers

Abstract: Two main challenges to design efficient iterative solvers for the frequency-domain Maxwell equations are the indefinite nature of the underlying system and the high resolution requirements. Scalable parallel frequency-domain Maxwell solvers are highly desired. This talk will introduce the EM-WaveHoltz method which is an extension of the recently developed WaveHoltz method for the Helmholtz equation to the time-harmonic Maxwell equations. Three main advantages of the proposed method are as follows. (1) It always results in a positive definite linear system. (2) Based on the framework of EM-WaveHoltz, it is flexible and simple to build efficient frequency-domain solvers from current scalable time-domain solvers. (3) It is possible to obtain solutions for multiple frequencies in one solve. The formulation of the EM-WaveHoltz and analysis in the continuous setting for the energy conserving case will be discussed. The performance of the proposed method will be demonstrated through numerical experiments.

Bio: Zhichao Peng is currently a postdoc in the department of Mathematics at Michigan State University (MSU). Before joining MSU, Zhichao Peng got his doctoral degree from Rensselaer Polytechnic Institute in 2020, and his BS degree from Peking University in 2015. His research interest mainly lies in efficient, high order and structure preserving numerical methods and reduced order models for kinetic problems, wave equations and electromagnetics, and characteristic and control problems in quantum computing.