Time-domain finite-element simulation of three-dimensional scattering and radiation problems using perfectly matched layers

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

“…The perfectly matched layer (PML) in particular has become a very popular absorbing boundary condition because of its efficacy and ease of implementation, and because it preserves the underlying sparsity of the methods. The PML was originally developed for rectangular FDTD grids (Cartesian PML) [22]- [27] and later implemented in rectangular FETD grid terminations [17], [28]- [30].…”

Mixed Finite-Element Time-Domain Method for Transient Maxwell Equations in Doubly Dispersive Media

“…The implementation described here is based on the first-order Maxwell equations and it is a particular case of the double-dispersive anisotropic material modeling discussed above. We refer the reader to [38] for an implementation of the rectangular perfectly matched layer in finite-element time-domain simulations based on the second-order wave equation.…”

“…Given an anisotropic and dispersive interior media with constitutive tensors and , the associated tensors and to achieve reflectionless absorption are given by [39] (36) (37) (38) where , , and are complex stretching variables [37]. For diagonal tensors , , the above simplifies to (39) (40) with , For the 2-D cases considered in the examples that follow, and using conventional stretching variables of the form , and similarly for , the perfectly matched layer tensor elements reduce to (41) (42) (43) If the background material parameters in (41)-(43), i.e., , , and , are modeled by second-order polynomials in , the tensors and can be realized by a fourth-order polynomial .…”

A New 2d Non-Spurious Discontinuous Galerkin Finite Element Time Domain (Dg-Fetd) Method for Maxwell's Equations

“…FETD can be implemented in two ways, one based on the curlcurl second order wave equation [13][14][15][16] and the other based on the first order Maxwell's equations [17][18][19][20]. The former one can use the relatively plenty of research results from frequency domain FEM, such as the choice of basis functions and stability analysis, however, it is difficult to implement the perfectly matched layer (PML) as an absorbing boundary condition.…”