A numerical absorbing boundary condition for finite element analysis

Abstract

In this paper we present a novel approach to deriving local boundary conditions that can be employed in conjunction with the Finite Element Method (FEM) to solve electromagnetic scattering and radiation problems. The proposed Numerical Absorbing Boundary Condition (NABC) approach can he applied to both the nodal and the edge-based formulations of the FEM. The key step in the NABC approach is to derive linear relationships that link the values of the field at the boundary grid points or the field along the boundary edges, depending on formulation, to those at the neighboring ones. Derived via a robust SVD-based scheme, these linear relationships are satisfied, to within a certain tolerance, by all of the outgoing wave components. They can thus be used in lieu of the FEM equations employing the usual absorbing boundary conditions for the boundary edges. The present approach not only provides a simple way to derive an accurate boundary condition for mesh truncation at an arbitrary frequency, but also preserves the banded structure of the FEM matrices. Furthermore, the validity of the method is demonstrated at very low frequencies where the conventional absorbing boundary conditions are prone to fail.