An RBF-based method for computational electromagnetics with reduced numerical dispersion

TL;DR

This paper introduces a meshless RBF-based approach for computational electromagnetics that reduces numerical dispersion and anisotropy, improving accuracy over traditional finite difference methods.

Contribution

It proposes a novel meshless RBF interpolation method with hyperviscosity terms, enhancing dispersion properties and convergence in electromagnetic simulations.

Findings

Increased stencil size reduces numerical dispersion.

The method exhibits decreased dispersion anisotropy.

It remains fully explicit and convergent with proper hyperviscosity.

Abstract

The finite difference time domain method is one of the simplest and most popular methods in computational electromagnetics. This work considers two possible ways of generalising it to a meshless setting by employing local radial basis function interpolation. The resulting methods remain fully explicit and are convergent if properly chosen hyperviscosity terms are added to the update equations. We demonstrate that increasing the stencil size of the approximation has a desirable effect on numerical dispersion. Furthermore, our proposed methods can exhibit a decreased dispersion anisotropy compared to the finite difference time domain method.