FDTD Schemes for Maxwell’s Equations with Embedded Perfect Electric Conductors Based on the Correction Function Method

High-Order FDTD Schemes for Maxwell’s Interface Problems with Discontinuous Coefficients and Complex Interfaces Based on the Correction Function Method

“…Following the procedure described in [20] to construct a functional that is a square measure of the error associated with system (2) leads to an ill-posed minimization problem. As in CFM-FDTD strategies for embedded perfect electric conductors [19], we can take advantage of FD approximations at previous time steps using fictitious interface conditions to retrieve a well-posed minimization problem. Fictitious interface conditions are given by n…”

“…Fictitious interfaces are also aligned with the mesh grid to facilitate the computation of space-time interpolants that are needed in the minimization problem. We refer the reader to [19] for more details on the implementation of local patches and fictitious interface conditions.…”

“…The initialization of CFM-FDTD schemes can be difficult because of time integrals involving H * and E * . An initialization strategy has been developed for the Yee scheme and a fourth-order FDTD scheme based on a multistep method [19]. Another approach, which is specific to some applications, consists to assume that electromagnetic fields close to the interface remain unchanged for t ≤ t 0 .…”

“…It is also worth mentioning that high-order CFM-FDTD schemes have been proposed to handle embedded PEC problems [19].…”

“…The work presented here generalizes CFM-FDTD approaches to Maxwell's interface problems with discontinuous coefficients. We consider two FDTD schemes, namely the Yee scheme and a fourth-order staggered FDTD scheme, and correct them following the procedure described in [19]. In addition to scattering of dielectric cylinder problems, we also use problems with a manufactured solution for which complete discontinuous electromagnetic fields are considered to demonstrate the robustness and accuracy of the proposed numerical strategy.…”