A Modified Helmholtz Equation with Impedance Boundary Conditions (Advances in Applied Mathematics and Mechanics, 2021)
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.