Second-order PML: Optimal choice of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>n</mml:mi><mml:mtext>th</mml:mtext></mml:math>-order PML for truncating FDTD domains

Feng, Naixing; Yue, Yongqing; Zhu, Chunhui; Wan, Liangtian; Liu, Qing

doi:10.1016/j.jcp.2015.01.015

Cited by 37 publications

(24 citation statements)

References 47 publications

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“…(21) . It is meaningful to highlight the approximation between modeling results and analytical solutions; accordingly, the relative error 13 is introduced:…”

Section: Resultsmentioning

confidence: 99%

“…Because the second-order FDTD method suffered from anomalous numerical effects arising from numerical dispersion, high-order finite-difference and pseudo-spectral Maxwell solvers were proposed to effectively reduce discretization 12 . However, unfortunately, when the method based on high-order algorithms was implemented in CFS-PML, it was found that high-order PML exhibited absorption performance similar to that of the 2 nd -order PML 13 . Moreover, in contrast with the traditional recursive convolution (RC) method to evaluate recursion, piecewise linear recursive convolution (PLRC) 14 and trapezoidal recursive convolution (TRC) 15 methods were proven to be more accurate, as was the case for high-order PMLs.…”

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confidence: 99%

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Crosswell electromagnetic modeling from impulsive source: Optimization strategy for dispersion suppression in convolutional perfectly matched layer

Fang

Pan

et al. 2016

Sci Rep

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This study applied the finite-difference time-domain (FDTD) method to forward modeling of the low-frequency crosswell electromagnetic (EM) method. Specifically, we implemented impulse sources and convolutional perfectly matched layer (CPML). In the process to strengthen CPML, we observed that some dispersion was induced by the real stretch κ, together with an angular variation of the phase velocity of the transverse electric plane wave; the conclusion was that this dispersion was positively related to the real stretch and was little affected by grid interval. To suppress the dispersion in the CPML, we first derived the analytical solution for the radiation field of the magneto-dipole impulse source in the time domain. Then, a numerical simulation of CPML absorption with high-frequency pulses qualitatively amplified the dispersion laws through wave field snapshots. A numerical simulation using low-frequency pulses suggested an optimal parameter strategy for CPML from the established criteria. Based on its physical nature, the CPML method of simply warping space-time was predicted to be a promising approach to achieve ideal absorption, although it was still difficult to entirely remove the dispersion.

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“…(21) . It is meaningful to highlight the approximation between modeling results and analytical solutions; accordingly, the relative error 13 is introduced:…”

Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Crosswell electromagnetic modeling from impulsive source: Optimization strategy for dispersion suppression in convolutional perfectly matched layer

Fang

Pan

et al. 2016

Sci Rep

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“…Last, it would be interesting to address the issue of performing a detailed accuracy analysis for CFS-UPML to find optimized profiles for the parameters used in the CFS-type coordinate transform function. 56,57 All the developments presented have been integrated into our widely used open-source software package SPECFEM, which can be freely downloaded from the Computational Infrastructure for Geodynamics at www.geodynamics.org. FIG.…”

Section: Figmentioning

confidence: 99%

A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms

Xie

Matzen

Cristini

et al. 2016

The Journal of the Acoustical Society of America

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A time-domain Legendre spectral-element method is described for full-wave simulation of ocean acoustics models, i.e., coupled fluid-solid problems in unbounded or semi-infinite domains, taking into account shear wave propagation in the ocean bottom. The technique can accommodate range-dependent and depth-dependent wave speed and density, as well as steep ocean floor topography. For truncation of the infinite domain, to efficiently absorb outgoing waves, a fluid-solid complex-frequency-shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique. The complex stretching is rigorously taken into account in the derivation of the fluid-solid matching condition inside the absorbing layer, which has never been done before in the time domain. Two implementations are designed: a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high-order time schemes, leading to reduced numerical dispersion and dissipation, a topic of importance, in particular, in long-range ocean acoustics simulations. The method is validated for a two dimensional fluid-solid Pekeris waveguide and for a three dimensional seamount model, which shows that the technique is accurate and numerically long-time stable. Compared with widely used paraxial absorbing boundary conditions, the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves.

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“…15 The unsplit-field implementations with four auxiliary variables are proposed based on the auxiliary differential equation method, the digital signal processing techniques and so on. [17][18][19][20] Since then, higher order PMLs have been extensively researched.…”

Section: Introductionmentioning

confidence: 99%

Performance enhanced absorbing boundary condition for electromagnetic modelling and simulation

Sun

Chi

et al. 2020

Int J Numerical Modelling

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Based upon the higher order (HO) concept and the convolution perfectly matched layer (CPML) formulation, the efficient and tight HO-CPML implementation is proposed for electromagnetic (EM) simulation. The proposed formulation has the advantages of the higher order concept and the CPML in terms of enhancing absorbing performance and improving computational efficiency. Numerical examples including the half-space soil/metal plate structure and the patch antenna radiation model are carried out in the finite-difference time-domain lattice to validate the effectiveness and efficiency. It can be demonstrated that the proposed HO-CPML can further enhance the absorbing performance compared with the CPML and enjoy considerable computational efficiency compared with the other HO-perfectly matched layers (HO-PMLs). Meanwhile, the proposal can terminate arbitrary mediums without changing the update equations in the PML regions.

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Second-order PML: Optimal choice of nth-order PML for truncating FDTD domains

Cited by 37 publications

References 47 publications

Crosswell electromagnetic modeling from impulsive source: Optimization strategy for dispersion suppression in convolutional perfectly matched layer

Crosswell electromagnetic modeling from impulsive source: Optimization strategy for dispersion suppression in convolutional perfectly matched layer

A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms

Performance enhanced absorbing boundary condition for electromagnetic modelling and simulation

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