Detection of the interior resonance errors of surface integral boundary conditions for scattering problems

To solve the scaler Helmholtz equation in an unbounded region using finite element methods (FEM), an outer boundary with a suitable radiation boundary condition must be introduced to truncate the finite element mesh. Integral equations such as the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) are a natural choice for boundary conditions for such open region problems. The numerical solutions of surface integral equation formulations can be corrupted by interior resonance problems. We propose the concept of using the residual error of the discretized form of the integral equation to detect interior resonance problems. The extra computational effort required to calculate the residual error is insignificant. Numerical examples show the ability to detect interior resonance problems using the residual error.