Reflectionless sponge layers as absorbing boundary conditions for the numerical solution of Maxwell equations in rectangular, cylindrical, and spherical coordinates

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 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.