Non-Maxwellian Locally-Conformal PML Absorbers for Finite Element Mesh Truncation

Conformal Perfectly Matched Layer for the Mixed Finite Element Time-Domain Method

“…The conformal PML can be expressed in terms of dispersive and anisotropic constitutive tensors that depend on the local principal radii of curvature of the mesh termination surface [39]. Implementations of the conformal PML have been considered in non-staggered body-fitted FDTD grids [42], [43], frequency-domain finite element simulations [44]- [47], and FETD simulations [48], the latter being restricted to the second-order wave equation FETD formulation.…”

PO‐based characteristic basis finite element method (CBFEM‐PO)—A parallel, iteration‐free domain decomposition algorithm using perfectly matched layers for large‐scale electromagnetic scattering problems

“…(3) is multiplied by a monotonically decreasing exponential function exp[Àf(n)], which is equivalent to the true PML action satisfying an artificial decay inside the PML region. The function f(n) is defined as the same as the one in the complex coordinate variations of the locally-conformal PML method, which can be found in [19,20] in detail. It is worthwhile to mention that the computation of the decaying functions does not pose additional computational burden, because their parameters are already calculated in the initial, matrix construction phase of the algorithm.…”

“…The CBFEM-PO approach subdivides the original computational domain into a number of subdomains, and then constructs three types of CBFs: (i) primary bases arising from the self-interactions in each subdomain; (ii) secondary bases due to the mutual couplings between subdomains; and (iii) bases that are determined from the PO fields by illuminating the object at different incident angles, polarization, and frequency. The first two types of CBFs are generated by employing specially-designed PML regions that are easily implemented via the use of the locally-conformal PML method [19,20].…”

“…Inside the PML region (X PML ), Eq. (1.a) is valid in the same form except that the real coordinates are just replaced by their complex counterparts calculated via a special complex coordinate transformation, which is defined by the locally-conformal PML method [19,20]. A conventional FEM formulation leads to the following sparse global matrix system:…”

Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations

“…However, in this paper we present an analysis of the new ''locally-conformal PML'' approach, which does not need any artificial materials or coordinate system, for mesh truncation in FEM applications (clearly, the method is non-Maxwellian in the context of electromagnetics, since the avoidance of artificial material layers leads to field expressions that do not satisfy Maxwell's equations). Although we have previously introduced the underlying concept of this approach in [19] for the solution of three-dimensional electromagnetic vector wave equation using edge elements, we have dealt with only the far-field performance of this method in terms of the radar cross section (RCS) calculations. It is evident that the smoothing effect of the far-field calculation may result in a reduction in the magnitude of errors present in the near field terms.…”