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In this work, we propose staggered FDTD schemes based on the correctionfunction method (CFM) to discretize Maxwell's equations with embedded perfectelectric conductor (PEC) boundary conditions. The CFM uses a minimizationprocedure to compute a correction to a given FD scheme in the vicinity of theembedded boundary to retain its order. The minimization problem associated withCFM approaches is analyzed in the context of Maxwell's equations with embeddedboundaries. In order to obtain a well-posed problem, we propose fictitiousinterface conditions to fulfill the lack of information, namely the surfacecurrent and charge density, on the embedded boundary. Fictitious interfaces caninduce some issues for long time simulations and therefore the penalizationcoefficient associated with fictitious interface conditions must be chosensmall enough. We introduce CFM-FDTD schemes based on the well-known Yee schemeand a fourth-order staggered FDTD scheme. Long time simulations and convergencestudies are performed in 2-D for various geometries of the embedded boundary.CFM-FDTD schemes have shown high-order convergence.

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