A Time-Domain Finite Element Method for Helmholtz Equations

A time-domain finite element method is developed to approximate the electromagnetic fields scattered by a bounded, inhomogeneous two-dimensional cavity embedded in the infinite ground plane. The time-dependent scattering problem is first discretized in time by Newmarkʹs time-stepping scheme. A nonlocal boundary condition on the cavity aperture is constructed to reduce the computational domain to the cavity itself. The variational problems using finite element methods are shown to have unique solutions. Numerical experiments for both TE and TM polarizations demonstrate the accuracy and stability of the method.