A Hybrid Finite Element-Laplace Transform Method for the Analysis of Transient Electromagnetic Scattering by an Over-Filled Cavity in the Ground Plane (Communications in Computational Physics, 2018)
A hybrid finite element-Laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavityembedded in the infinite ground plane. The algorithm divides the whole scatteringdomain into two, interior and exterior, sub-domains. In the interior sub-domain whichcovers the cavity, the problem is solved via the finite element method. The problem issolved analytically in the exterior sub-domain which slightly overlaps the interior subdomain and extends to the rest of the upper half plane. The use of the Laplace transform leads to an analytical link condition between the overlapping sub-domains. Theanalytical link guides the selection of the overlapping zone and eliminates the needto use the conventional Schwartz iteration. This dramatically improves the efficiencyfor solving transient scattering problems. Numerical solutions are tested favorablyagainst analytical ones for a canonical geometry. The perfect link over the artificialboundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the method. An error analysisis also performed.