Auxiliary differential equation formulation: an efficient implementation of the perfectly matched layer

Ramadan, Omar

doi:10.1109/lmwc.2003.808706

Cited by 66 publications

(37 citation statements)

References 6 publications

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“…The amount of the auxiliary variables in the PML regions is presented in Table 1. As seen from Table 1, the proposed PML formulations require 12W 2 +2LW+2MW auxiliary variables less than those in [11] and [13]. In consequence, the proposed PML formulations save the memory storage and the computational time as compared with those in [11] and [13].…”

Section: The Implementation Of the Sc-pml In Two Dimensional Casementioning

confidence: 97%

“…both σ x ≠0 and σ y ≠0 are chosen, as shown in Fig. 1), transforming (11) into the Z-domain by means of the method used in Section 2.1, we have where b y ¼ 1 1 þ Δtσ y 2" 0 ð Þ À Á and a y ¼ b y 1 À Δtσ y 2" 0 ð Þ À Á . Multiplying both sides of (14) by 1 À a x z À1 ð Þ ð 1 À a y z À1 Þ 1 À z À1 ð Þand rearranging, as the method used in [15], we obtain…”

Section: The Implementation Of the Sc-pml In Two Dimensional Casementioning

confidence: 99%

“…In order to perform a comparison among the proposed PML formulations and those in [11] and [13] in terms of the amount of the auxiliary variables, we assume an FDTD computational domain of L×M cells with a W-cell thick PML used on each one of the sides of the domain, as shown in Fig. 1.…”

Section: The Implementation Of the Sc-pml In Two Dimensional Casementioning

confidence: 99%

“…In [7], split-field formulations of the Stretched Coordinate PML (SC-PML) [8], combined with the nonlinear FDTD formulations using Ztransforms [9], were presented to truncate Kerr and Raman nonlinear FDTD domains. In [10], alternative unsplit-field Auxiliary Differential Equation (ADE) PML formulations [11], which were based on the ADE method and the SC-PML, were introduced to truncate one dimensional Lorentz dispersive and Kerr and Raman nonlinear FDTD lattices. In [12], unsplit-field Z-transform PML formulations [13], based on the Z-transform theory [14] and the SC-PML, were presented to terminate one dimensional nonlinear dispersive FDTD lattices.…”

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confidence: 99%

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Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the Z-Transform Method

Li¹,

Dai

Wan

2007

Int J Infrared Milli Waves

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Based on the Z-transform method, a simple, efficient and unsplit-field implementation of the Stretched Coordinate Perfectly Matched Layer (SC-PML) is proposed for truncating the nonlinear dispersive Finite Difference Time Domain (FDTD) lattices. In addition, the nonlinear FDTD formulations using the Z-transform method are reformulated with the advantage of a simple derivative process. The proposed algorithm is validated through two numerical examples carried out in one dimensional and two dimensional domains which include Lorentz dispersion as well as Kerr and Raman nonlinearities.

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Section: The Implementation Of the Sc-pml In Two Dimensional Casementioning

confidence: 97%

Section: The Implementation Of the Sc-pml In Two Dimensional Casementioning

confidence: 99%

Section: The Implementation Of the Sc-pml In Two Dimensional Casementioning

confidence: 99%

mentioning

confidence: 99%

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Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the Z-Transform Method

Li¹,

Dai

Wan

2007

Int J Infrared Milli Waves

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“…In addition, traditional PML adopts a nonphysical splitting of wave equations, which have been proven to be weakly well-posed. Convolutional PML (Roden and Gedney, 2000) and auxiliary differential equation perfectly matched layer (ADE-PML) (Ramadan, 2003;Zhang and Shen, 2010) are proposed to solve this problem.…”

Section: Introductionmentioning

confidence: 99%

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations

Gao¹,

Zhang²,

Yao³

2015

The Journal of the Acoustical Society of America

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The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

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A perfectly matched layer formulation based on auxiliary differential equations for truncating radial point interpolation method meshless domains

Oliveira

Brandão

Sousa

2018

Int J Numerical Modelling

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An auxiliary‐differential equation perfectly matched layer formulation is developed for the first time for truncating radial point interpolation method meshless domains. Absorption parameters are optimized, producing maximum relative reflection error of −84.14 dB when 10 layers are used. The developed formulation is also validated by calculating the radar cross section of a metallic cylindrical scatterer, which has a known analytical solution.

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Auxiliary differential equation formulation: an efficient implementation of the perfectly matched layer

Cited by 66 publications

References 6 publications

Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the Z-Transform Method

Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the Z-Transform Method

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations

A perfectly matched layer formulation based on auxiliary differential equations for truncating radial point interpolation method meshless domains

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