Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

Please note that all times are shown in the time zone of the conference. The current conference time is: 10th Dec 2022, 09:28:18am CET

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Session Overview
MS 30a: advanced numerical methods for electromagnetic problems
Monday, 12/July/2021:
4:00pm - 6:00pm

Session Chair: Daniel Appelo
Session Chair: Jeffrey William Banks
Virtual location: Zoom 2

Session Abstract

The primary objective of this minisymposium is to present new developments in theory and algo-

rithms related to discretization of Maxwell’s equations. Engineered electromagnetic materials show

great promise to revolutionize the field of optical design by providing smaller and lighter devices

that consume less power while also being multi-functional and tunable. Numerical algorithms and

simulation tools will play an important role in turning this promise into practical devices. In this

minisymposium we will bring together researchers with the intent to provide a forum for cross fer-

tilization of ideas. The minisymposium will feature both senior and junior researchers.

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4:00pm - 5:00pm

Tutorial: High-Order accurate solution of PDEs using Overture

William Henshaw

Rennselaer Polytechnic Institute, United States of America

Overture is an object-oriented open-source framework for solving PDEs in complex moving geometry using overset grids. This tutorial will give an introduction to Overture, overset grid generation, and solving PDES to high-order accuracy. Examples will be given for simulating high-speed compressible flow, incompressible flow, solid-mechanics, fluid-structure interactions and electromagnetics.

5:00pm - 5:30pm

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

Zhichao Peng, Daniel Appelö

Michigan State University, United States of America

The main challenges to solve the frequency-domain Maxwell equations are: (1) the indefinite nature of the discrete system and (2) the high resolution requirements. We extend the recently developed WaveHoltz iterative method for the Helmholtz equation to the frequency-domain Maxwell equations. Similar to the exact controllability method, the proposed EM-WaveHoltz iterative method converts the frequency-domain problem to a time-domain problem, but unlike the exact controllability method, no adjoint solves are needed. 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 and the basic properties of the EM-WaveHoltz method will be presented, and its performance will be demonstrated through a series of numerical experiments.

5:30pm - 6:00pm

Discontinuous Galerkin Galerkin Differences for the Wave Equation in Second-Order Form

Benjamin Brett Buckner1, Jeffrey Banks2, Thomas Hagstrom3

1Independent Researcher, United States of America; 2Rensselaer Polytechnic Institute, Troy NY, United States of America; 3Southern Methodist University, Dallas TX, United States of America

This talk describes the development of an Interior Penalty Galerkin Difference Method for the second order wave equation. A simple choice of either upwind or centered fluxes leads to energy dissipative or conservative schemes that exhibit nodal superconvergence away from the boundaries of the domain. The use of the Galerkin difference basis functions preclude the need for mesh dependent penalty terms to achieve coercivity for the symmetric method as required with the standard basis. The basic properties of the scheme and numerical examples will be discussed.

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