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-dimension al elliptic Maxwell equations in rectangular, cylindrical, and spherical co ordinates. We also develop our reflectionless sponge layers to absorb outgo ing transient waves in numerical solutions of the time-domain Maxwell equat ions and prove that these absorbing layers are described by causal, strongl y well-posed hyperbolic systems. A representative result is given for wave scattering by a compact obstacle to demonstrate the many orders of magnitud e improvement offered by our approach over standard techniques for computat ional domain truncation.