FDTD schemes for Maxwell's equations with embedded perfect electric conductors based on the correction function method

TL;DR

This paper introduces correction function method-based staggered FDTD schemes for Maxwell's equations with embedded PEC boundaries, achieving high-order convergence and addressing long-term simulation stability.

Contribution

It develops a novel correction function method for FDTD schemes that effectively handles embedded PEC boundaries with high-order accuracy.

Findings

High-order convergence demonstrated in 2-D simulations.

Effective handling of embedded PEC boundaries.

Stable long-term simulation performance.

Abstract

In this work, we propose staggered FDTD schemes based on the correction function method (CFM) to discretize Maxwell's equations with embedded perfect electric conductor (PEC) boundary conditions. The CFM uses a minimization procedure to compute a correction to a given FD scheme in the vicinity of the embedded boundary to retain its order. The minimization problem associated with CFM approaches is analyzed in the context of Maxwell's equations with embedded boundaries. In order to obtain a well-posed problem, we propose fictitious interface conditions to fulfill the lack of information, namely the surface current and charge density, on the embedded boundary. Fictitious interfaces can induce some issues for long time simulations and therefore the penalization coefficient associated with fictitious interface conditions must be chosen small enough. We introduce CFM-FDTD schemes based on the well-known Yee scheme and a fourth-order staggered FDTD scheme. Long time simulations and convergence studies are performed in 2-D for various geometries of the embedded boundary. CFM-FDTD schemes have shown high-order convergence.