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Reflectionless sponge layers as absorbing boundary conditions for the numerical solution of Maxwell equations in rectangular, cylindrical, and spherical coordinates. (English) Zbl 1025.78016
Summary: A scaling argument is used to derive reflectionless sponge layers to absorb outgoing time-harmonic waves in numerical solutions of the three-dimensional elliptic Maxwell equations in rectangular, cylindrical, and spherical coordinates. We also develop our reflectionless sponge layers to absorb outgoing transient waves in numerical solutions of the time-domain Maxwell equations and prove that these absorbing layers are described by cadescribed by causal, strongly well-posed hyperbolic systems. A representative result is given for wave scattering by a compact obstacle to demonstrate the many orders of magnitude improvement offered by our approach over standard techniques for computational domain truncation.
78M25Numerical methods in optics
35Q60PDEs in connection with optics and electromagnetic theory
65M99Numerical methods for IVP of PDE
78A40Waves and radiation (optics)