A ghost-point based second order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering around PEC

TL;DR

This paper introduces a second-order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering problems involving PEC objects, improving computational efficiency and flexibility over previous body-fitted grid methods.

Contribution

The method modifies existing ghost-point techniques to work on uniform grids for complex PEC geometries, using PDE-based extension and error correction to achieve second-order accuracy.

Findings

Achieves second-order accuracy with simplified grid structure.

Reduces CFL restrictions through error correction.

Demonstrates effectiveness with numerical examples.

Abstract

We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor that impedes the propagations of electromagnetic waves. Our method is a modification of the existing approach by Zou and Liu [36], from a locally perturbed body-fitted grid to a uniform orthogonal one for complicated PEC objects. Similar to their work we extrapolate ghost point values by exploiting the level set function of the interface and the PDE-based extension technique, which allows us to circumvent scrutinizing local geometries of the interface. We stipulate a mild requirement on the accuracy of our extrapolation that the ghost values need only be locally second order accurate. Nevertheless the resulting accuracy of our method is second order thanks to the application of back and forth error correction and compensation, which also relaxes CFL conditions. We demonstrate the effectiveness of our approach with some numerical examples.