An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems

Bermúdez, Alfredo; Hervella-Nieto, L.; Prieto, Andrés; Rodrı́guez, Rodolfo

doi:10.1016/j.jcp.2006.09.018

Cited by 197 publications

(212 citation statements)

References 34 publications

(37 reference statements)

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“…The PML shows great superiority over the classical boundary conditions mentioned above and is widely used in acoustic wave simulations (e.g. Abarbanel and Gottlieb, 1997;Liu and Tao, 1997;Qi and Geers, 1998;Liu, 1999;Katsibas and Antonopoulos, 2002;Diaz and Joly, 2006;Bermúdez et al, 2007) and elastic wave simulations (e.g. Chew and Liu, 1996;Hastings et al, 1996;Collino and Tsogka, 2001;Festa and Nielsen, 2003;Komatitsch and Tromp, 2003;Basu and Chopra, 2004;Appelö and Kreiss, 2006;Komatitsch and Martin, 2007;Yang et al, 2007;Lan et al, 2013).…”

Section: Perfectly Matched Layermentioning

confidence: 99%

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Gao

Song

Zhang

et al. 2017

Exploration Geophysics

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Abstract. Absorbing boundary conditions are necessary in numerical simulation for reducing the artificial reflections from model boundaries. In this paper, we overview the most important and typical absorbing boundary conditions developed throughout history. We first derive the wave equations of similar methods in unified forms; then, we compare their absorbing performance via theoretical analyses and numerical experiments. The Higdon boundary condition is shown to be the best one among the three main absorbing boundary conditions that are based on a one-way wave equation. The Clayton and Engquist boundary is a special case of the Higdon boundary but has difficulty in dealing with the corner points in implementaion. The Reynolds boundary does not have this problem but its absorbing performance is the poorest among these three methods. The sponge boundary has difficulties in determining the optimal parameters in advance and too many layers are required to achieve a good enough absorbing performance. The hybrid absorbing boundary condition (hybrid ABC) has a better absorbing performance than the Higdon boundary does; however, it is still less efficient for absorbing nearly grazing waves since it is based on the one-way wave equation. In contrast, the perfectly matched layer (PML) can perform much better using a few layers. For example, the 10-layer PML would perform well for absorbing most reflected waves except the nearly grazing incident waves. The 20-layer PML is suggested for most practical applications. For nearly grazing incident waves, convolutional PML shows superiority over the PML when the source is close to the boundary for large-scale models. The Higdon boundary and hybrid ABC are preferred when the computational cost is high and high-level absorbing performance is not required, such as migration and migration velocity analyses, since they are not as sensitive to the amplitude errors as the full waveform inversion.

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Section: Perfectly Matched Layermentioning

confidence: 99%

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Gao

Song

Zhang

et al. 2017

Exploration Geophysics

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“…Here, only the most straighforward kind of PML, that is, with constant coefficients, is considered, but the whole reasoning still applies if these coefficients are complex-valued functions of the space variables satisfying the conditions stated below. One might note in passing that optimizing the choice of the absorbing function for a bounded layer, as done in [25] for instance, cannot cure the problem caused by the presence of backward modes, as can be seen from a straightforward extension of the analysis in subsection 3.2 (see remark 1).…”

Section: Perfectly Matched Layersmentioning

confidence: 99%

“…Once these quantities are available, problems (25) and (26) can be discretized, using a conforming finite element space defined over a mesh of the domain Ω L , and subsequently solved, leading to finite element approximations of the quantities u L and w (k) . It should be remarked that the computation of these various numerical approximations is not as costly as one would expect at first.…”

Section: Practical Implementationmentioning

confidence: 99%

“…It should be remarked that the computation of these various numerical approximations is not as costly as one would expect at first. Indeed, the structure of problems (25) and (26) being identical, the algebraic systems associated with their discrete counterparts share the same (sparse) matrix and differ only by their respective right-hand sides. As a consequence, once the former has been factorized, obtaining the approximations merely amounts to a succession of assemblies of the latter, followed by forward and backward substitutions.…”

Section: Practical Implementationmentioning

confidence: 99%

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On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves

Dhia¹,

Chambeyron²,

Legendre³

2014

Wave Motion

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An efficient method to compute the scattering of a guided wave by a localized defect, in an elastic waveguide of infinite extent and bounded cross section, is considered. It relies on the use of perfectly matched layers (PML) to reduce the problem to a bounded portion of the guide, allowing for a classical finite element discretization. The difficulty here comes from the existence of backward propagating modes, which are not correctly handled by the PML. We propose a simple strategy, based on finite-dimensional linear algebra arguments and using the knowledge of the modes, to recover a correct approximation to the solution with a low additional cost compared to the standard PML approach. Numerical experiments are presented in the two-dimensional case involving Rayleigh-Lamb modes.

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“…[19] Recently, Bermúdez et al investigated absorbing functions for time harmonic Helmholtz equations in the Cartesian and cylindrical coordinates under the condition of ignoring reflection caused by FE-discretization and showed the advantages of non-integrable absorbing functions over conventional functions of power series. [20,21] Most of these investigations of optimizing attenuation parameters of PML employed numerical analysis of scattering problems in the two dimensions such as plane or cylindrical wave scattering problems. For tackling optimization problem of PML parameters, plane wave scattering problem is appropriate because required resource of computation is small.…”

Section: Introductionmentioning

confidence: 99%

Perfectly Matched Layer for Finite Element Analysis of Elastic Waves in Solids

Hasegawa¹,

Shimada²

2012

Finite Element Analysis - Applications in Mechanical Engineering

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An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems

Cited by 197 publications

References 34 publications

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

On the use of perfectly matched layers in the presence of long or backward propagating guided elastic waves

Perfectly Matched Layer for Finite Element Analysis of Elastic Waves in Solids

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