$Z$-Transform Implementation of the CFS-PML for Arbitrary Media

Time-Synchronized Convolutional Perfectly Matched Layer for Improved Absorbing Performance in FDTD

“…The thickness of the PML is 10 Yee cells and the optimum value for σ max is calculated according to [6] σ max = 0.8(m + 1) Z · ∆l (24) where Z is the impedance of the medium, ∆l is the discretization step (l ∈ {x, y, z}) and m = 3 is the order of the polynomial function which is used to scale σ u along the PML [6]. A constant value κ u = 1 is applied along the FDTD.…”

“…This is a result of convolving spatial derivatives that are at half a time step apart from the corresponding fields that are being updated by the FDTD equations. Therefore, CPML rivals other secondorder accurate techniques based on recursive integration [8], bilinear transform [23] and Z-transform [24].…”

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

“…An extension of the CFS-PML for arbitrary media based on a CPML approach is presented in [289] and for dispersive media based on a -transform approach in [304]. Another extension of the PML for general linear media including anisotropic media based on the CPML with multiple convolutional terms is carried out in [305].…”

Distinguishing correct from incorrect PML proposals and a corrected unsplit PML for anisotropic, dispersive media

“…doi:10.1016/j.jcp.2011.01.006 formulate (via complex coordinate-stretching) and validate a corrected unsplit-field uniaxial PML for arbitrary anisotropic, dispersive, and conducting media in the time domain. Although there exist other correct alternatives for PML in anisotropic media [13][14][15][16][18][19][20][21][22][23][24] (including correct split-field proposals [21,13,15] by the same authors as the later incorrect unsplitfield formulation), our unsplit PML formulation has the appeal of a simple correction to previous UPML-like proposals that were correct for isotropic media [25,26,10]. We demonstrate this PML formulation both for a planewave method in frequency domain and for a finite-difference time-domain method (with a free-software implementation [27]).…”

“…Several such proposals employed the split-field approach [20][21][22][23][13][14][15][16] or convolutional approach [18,19,24] to obtain timedomain equations, and split-field PMLs were also derived for homogeneous anisotropic media by directly computing the reflection coefficients at the PML interface [20,14,23]. The transformational-optics approach also leads to a simple uniaxial anisotropic PML medium in the frequency domain [40], and in this paper we point out that the same approach also yields a straightforward time-domain PML for anisotropic and dispersive media, although in time domain a new factorization is required in order to efficiently implement the frequency dependence.…”