Numerical Simulation of 3D Electromagnetic Scattering by Algebraic Fictitious Domain Method
Abstract
New variants of algebraic fictitious domain method are proposed for solution of the 3D~Helmholtz and Maxwell equations in unbounded domains with the Sommerfeld radiation condition at infinity. They are based on: \begin{itemize} \item the use of an infinite uniform Cartesian mesh (maybe, locally fitted to an obstacle) for finite-difference or finite-element approximation; \item nonsymmetric version of fictitious domain method for solution of a resulting mesh system; \item calculation of the partial solution during the iterative process via summation of mesh Green functions with corresponding weights, using a fast algorithm; \item a special way of construction of the approximate mesh Green function satisfying the radiation condition.