Optimised correction polynomial functions for the Flux Reconstruction method in time-harmonic electromagnetism

Abstract

The Flux Reconstruction (FR) method is classically used in the Computational Fluid Dynamics field. However, its use for the simulation of electromagnetic wave propagation is not as developed yet. Following on from the development of a priori error estimates for the 1D wave equations, we introduce optimisation problems to allow an adaptation of the FR correction polynomial functions to the discretisation parameters. Showing notable accuracy gains in 1D, especially in the preasymptotic regime, we generalise this procedure to the 3D Maxwell’s equations, leading to similar interesting possibilities to reduce the computational cost for a given accuracy.