A multi-moment scheme for the two dimensional Maxwell's equations

TL;DR

This paper introduces a high-order, explicit numerical scheme for 2D Maxwell's equations that preserves sharp profiles and achieves stability with a CFL number of one, improving accuracy in electromagnetic simulations.

Contribution

It presents a novel multi-moment scheme based on the Poisson formula, combining high-order accuracy and explicit integration for Maxwell's equations.

Findings

Achieves higher order accuracy with explicit scheme

Preserves sharp profiles without smearing

Stable with CFL number equal to one

Abstract

We develop a numerical scheme for solving time-domain Maxwell's equation. The method is motivated by CIP method which uses function values and its derivatives as unknown variables. The proposed scheme is developed by using the Poisson formula for the wave equation. It is fully explicit space and time integration method with higher order accuracy and CFL number being one. The bi-cubic interpolation is used for the solution profile to attain the resolution. It preserves sharp profiles very accurately without any smearing and distortion due to the exact time integration and high resolution approximation. The stability and numerical accuracy are investigated.