Back and Forth Error Compensation and Correction Method for Linear Hyperbolic Systems with Application to the Maxwell's equations

TL;DR

This paper extends the BFECC method to linear hyperbolic PDE systems, including Maxwell's equations, achieving higher accuracy and stability on structured and unstructured grids with simpler implementation.

Contribution

The paper introduces new BFECC schemes for Maxwell's equations that operate on a single non-staggered grid, improving accuracy and stability on unstructured grids.

Findings

Achieved second order accuracy for Maxwell's equations

Allowed larger CFL numbers than classical Yee scheme

Demonstrated effectiveness through numerical examples

Abstract

We study the Back and Forth Error Compensation and Correction (BFECC) method for linear hyperbolic PDE systems. The BFECC method has been applied to schemes for advection equations to improve their stability and order of accuracy. Similar results are established in this paper for schemes for linear hyperbolic PDE systems with constant coefficients. We apply the BFECC method to central difference scheme and Lax-Friedrichs scheme for the Maxwell's equations and obtain second order accurate schemes with larger CFL number than the classical Yee scheme. The method is further applied to schemes on non-orthogonal unstructured grids. The new BFECC schemes for the Maxwell's equations operate on a single non-staggered grid and are simple to implement on unstructured grids. Numerical examples are given to demonstrate the effectiveness of the new schemes.