A review of some recent advances in perfectly-matched absorbers for mesh truncation in FEM

Abstract

The author offer a number of observations on some of the results of research concerned with the problem of mesh truncation with perfectly matched layers (PML). The conformal PML design appears to be useful in reducing the white space in the computational domain of the FEM. Analytical solutions have shown that it is possible to locate the PML arbitrarily close to the surface of a convex, electrically-large scatterer. This leads to the conclusion that the conformal PML is very effective for mesh truncation, especially at high frequencies. The PML concept is applicable not only to electromagnetic propagation problems described by the vector wave equation, but also to applications governed by the scalar Helmholtz equation. This, in turn, implies that PML absorbers can be used for acoustic scattering or radiation problems as well. The tensor constitutive parameters of a perfectly-matched anisotropic medium must satisfy the Kramers-Kronig relationships, such that the dynamical system governed by the constitutive relations is causal. A causal PML design ensures a better performance over the entire frequency spectrum. In the past, the perfectly-matched absorbers have been employed in FDTD and FEM applications. However, it seems feasible to use them for FETD mesh truncation as well. A causal/conformal PML design seems to offer an optimal solution to effective mesh truncation over a wider band of frequencies.