Fourth order accurate compact scheme for first-order maxwell's equations

TL;DR

This paper introduces a fourth-order accurate compact numerical scheme for solving time-dependent Maxwell's equations, improving accuracy while maintaining a compact stencil on a Yee grid.

Contribution

The paper presents a novel fourth-order compact scheme for Maxwell's equations that uses elliptic equations and compatible boundary conditions, enhancing computational efficiency and accuracy.

Findings

The scheme achieves fourth-order accuracy in space and time.

It maintains a compact stencil while solving elliptic equations.

Comparative results show improved performance over non-compact schemes.

Abstract

We construct a compact fourth-order scheme, in space and time, for the time-dependent Maxwell's equations given as a first-order system on a staggered (Yee) grid. At each time step, we update the fields by solving positive definite second-order elliptic equations. We face the challenge of finding compatible boundary conditions for these elliptic equations while maintaining a compact stencil. The proposed scheme is compared computationally with a non-compact scheme and data-driven approach.