Maxwell equations contain a dielectric coefficient ɛ that describes the particular media. For homogeneous materials the dielectric coefficient is constant. There is a jump in this coefficient across the interface between differing media. This discontinuity can significantly reduce the order of accuracy of the numerical scheme. We present an analysis and implementation of a fourth order accurate algorithm for the solution of Maxwell equations with an interface between two media and so the dielectric coefficient is discontinuous. We approximate the discontinuous function by a continuous one either locally or in the entire domain. We study the one-dimensional system in frequency space. We only consider schemes that can be implemented for multidimensional problems both in the frequency and time domains.
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Kashdan, E., Turkel, E. A High-Order Accurate Method for Frequency Domain Maxwell Equations with Discontinuous Coefficients. J Sci Comput 27, 75–95 (2006). https://doi.org/10.1007/s10915-005-9049-5
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DOI: https://doi.org/10.1007/s10915-005-9049-5