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

TL;DR

This paper introduces an adaptive local discrete convolution method for numerically solving three-dimensional Maxwell's equations, utilizing compact kernels and local grid refinement to improve accuracy and efficiency.

Contribution

The paper develops a novel adaptive convolution-based numerical scheme for Maxwell's equations that incorporates local grid refinement and reformulates the equations as wave systems.

Findings

Effective handling of 3D Maxwell's equations with local grid refinement

Utilizes compact convolution kernels for improved numerical stability

Reformulates Maxwell's equations as wave systems for better discretization

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.