A ghost-point based second order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering around curved perfect electric conductors with corners

Abstract

We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor (PEC) that impedes the propagation of electromagnetic waves. Our method relies on the level set characterization of the interface and the PDE-based extension technique which allows us to construct fictitious ghost values inside the PEC without scrutinizing the local geometries of its boundaries. As opposed to a locally perturbed body fitting grid used in [1], we promote a much simpler uniform orthogonal grid which necessitates a new approach for the extension technique to work. A novelty of our work is the introduction of what we call guest values which are accurately estimated boundary values deliberately and carefully misplaced near the interface. We stipulate a mild requirement on the accuracy of our ghost values that they need only be locally second-order accurate. Nevertheless, the resulting accuracy of our method is second order thanks to the application of back and forth error correction and compensation, which also relaxes CFL conditions. We demonstrate the effectiveness of our approach with some numerical examples.