A NUMERICAL ABSORBING BOUNDARY-CONDITION FOR 3D EDGE-BASED FINITE-ELEMENT ANALYSIS OF VERY LOW-FREQUENCY FIELDS

The numerical absorbing boundary condition (NABC) approach in conjunction with the three-dimensional edge-based formulation of the finite-element method (FEM) is applied to the problem of very low frequency (VLF) electromagnetic radiation and scattering. The key step in the NABC approach is to derive linear relationships that link the values of the field along the boundary edges 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. Although the NABC approach provides a simple way to derive an accurate local boundary condition for mesh truncation at an arbitrary frequency, it appears to be the only viable absorbing boundary condition at VLF, because the conventional absorbing boundary conditions are almost as reflecting as perfectly conducting magnetic walls at these frequencies. (C) 1995 John Wiley & Sons, Inc.