Electromagnetic cavity Helmholtz equation

Existence and uniqueness Finite element method a b s t r a c t Here considered is the mathematical analysis and numerical computation of the electro-magnetic wave scattering by multiple cavities embedded in an infinite ground plane. Above the ground plane the space is filled with a homogeneous medium, while the interi-ors of the cavities are filled with inhomogeneous media characterized by variable permit-tivities. By introducing a new transparent boundary condition on the cavity apertures, the multiple cavity scattering problem is reduced to a boundary value problem of the two-dimensional Helmholtz equation imposed in the separated interior domains of the cavities. The existence and uniqueness of the weak solution for the model problem is achieved via a variational approach. A block Gauss–Seidel iterative method is introduced to solve the cou-pled system of the multiple cavity scattering problem, where only a single cavity scattering problem is required to be solved at each iteration. Numerical examples demonstrate the efficiency and accuracy of the proposed method. Published by Elsevier Inc. 1