Vol. 14, No. 1, 2019

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An adaptive local discrete convolution method for the numerical solution of Maxwell's equations

Boris Lo and Phillip Colella

Vol. 14 (2019), No. 1, 105–119
Abstract

We present a numerical method for solving the free-space Maxwell’s equations in three dimensions using compact convolution kernels on a rectangular grid. We first rewrite Maxwell’s equations as a system of wave equations with auxiliary variables and discretize its solution from the method of spherical means. The algorithm has been extended to be used on a locally refined nested hierarchy of rectangular grids.

Keywords
electromagnetics, Green's function, propagator method, adaptive mesh refinement
Mathematical Subject Classification 2010
Primary: 65M55, 65M80
Secondary: 78-04
Milestones
Received: 29 April 2018
Revised: 4 February 2019
Accepted: 25 March 2019
Published: 26 April 2019
Authors
Boris Lo
Applied Science and Technology
University of California, Berkeley
Berkeley, CA
United States
Lawrence Berkeley National Laboratory
Berkeley, CA
United States
Phillip Colella
Applied Numerical Algorithms Group
Computational Research Division
Lawrence Berkeley National Laboratory
Berkeley, CA
United States