High-order transmission conditions in a domain decomposition method for the time-harmonic Maxwell's equations in inhomogeneous media

Highlights: • New well posed and numerically cheap high order transmission conditions for inhomogeneous media. • Large full matrices arising from the exact radiation condition are compressed via ACA. • Parallelized numerical code. • Very accurate numerical results obtained on electrically large objects involving up to 160 million unknowns with a reasonable numerical complexity. A one-way domain decomposition method (DDM) is considered for the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous penetrable 3-D objects: the computational domain is partitioned into concentric subdomains and an integral representation (IR) of the electromagnetic fields on the outer boundary constitutes an exact radiation condition. The corresponding numerical code is efficiently parallelized and the full IR matrices are compressed in order to expedite the solution of very large problems. Exact and approximate high-order transmission conditions (HOTC) are obtained for the model problem of a multi-layer planar structure. Their application to real world objects is investigated in terms of well-posedness and numerical complexity. New well-posed low complexity HOTCs are proposed that speed up the convergence of the DDM algorithm.