A Modified Helmholtz Equation with Impedance Boundary Conditions

Here considered is the problem of transient electromagnetic scattering fromoverfilled cavities embedded in an impedance ground plane. An artificial boundarycondition is introduced on a semicircle enclosing the cavity that couples thefields from the infinite exterior domain to those fields inside. A Green'sfunction solution is obtained for the exterior domain, while the interior problemis solved using finite element method. Well-posedness of the associated variationalformulation is achieved and convergence and stability of the numerical scheme are confirmed. Numerical experiments show the accuracy and robustness of the method.