Perfectly matched layer mesh terminations for nodal-based finite-element methods in electromagnetic scattering

Abstract

The perfectly matched layer (PML) concept introduced by Berenger (1994) is implemented for nodal-based finite-element frequency-domain methods. Starting from a scalar/vector potential framework, anisotropic media-equivalent gauge conditions are developed for both coupled and uncoupled (i.e., direct field) scalar/vector field formulations. The resulting discrete system of equations are shown to be identical for both the anisotropic and stretched coordinate viewpoints of PML mesh termination on node-based finite elements. Reaching this equivalency requires that special attention be paid to the basis/weighting functions used within the PML region, specifically, a material dependency is found to be essential. The alternative but identical stretched coordinate approach provides the perspective needed to realize a scheme for generalizing the PML to non-Cartesian mesh terminations which are more natural in the finite element context. Several benchmark problems and associated numerical results are presented to demonstrate the performance of the PML on node-based finite elements.