The Hermite-Taylor Correction Function Method for Embedded Boundary and Maxwell's Interface Problems
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We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order m in each Cartesian coordinate. This makes the development of a systematic approach to enforce boundary and interface conditions difficult. Here we use the correction function method to update the numerical solution where the Hermite-Taylor method cannot be applied directly. The proposed high-order method offers a flexible systematic approach to handle embedded boundary and interface problems, including problems with discontinuous solutions at the interface. This method is also easily adaptable to other first order hyperbolic systems.
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