A Finite Difference Method on Irregular Grids with Local Second Order Ghost Point Extension for Solving Maxwell's Equations Around Curved PEC Objects

TL;DR

This paper introduces a novel finite difference approach combining BFECC and level set methods on irregular grids to accurately simulate electromagnetic waves around curved PEC objects, achieving higher order accuracy.

Contribution

The paper presents a PDE-based local second order ghost cell extension technique integrated with BFECC and level set methods for improved electromagnetic simulation near complex boundaries.

Findings

Achieves higher order accuracy at curved PEC boundaries.

Validates the method through numerical experiments.

Allows larger CFL numbers while maintaining accuracy.

Abstract

A new finite difference method on irregular, locally perturbed rectangular grids has been developed for solving electromagnetic waves around curved perfect electric conductors (PEC). This method incorporates the back and forth error compensation and correction method (BFECC) and level set method to achieve convenience and higher order of accuracy at complicated PEC boundaries. A PDE-based local second order ghost cell extension technique is developed based on the level set framework in order to compute the boundary value to first order accuracy (cumulatively), and then BFECC is applied to further improve the accuracy while increasing the CFL number. Numerical experiments are conducted to validate the properties of the method.