An exact hybrid numerical boundary condition for electromagnetic scattering problems

To solve the scalar Helmholtz equation in an unbounded region using finite element methods (FEM), an outer boundary with a suitable boundary condition must be introduced to truncate the finite element mesh. In the paper, an exact hybrid numerical boundary condition (HNBC), applicable to an absorbing boundary with an arbitrary shape, is proposed. The HNBC is as accurate as surface integral equation methods. In addition, it does not suffer from internal resonance problems when the outer boundary of the mesh is in the vicinity of an interior resonance boundary.