Perfectly matched layers for transient elastodynamics of unbounded domains

Basu, Ushnish; Chopra, Anil K.

doi:10.1002/nme.896

Cited by 196 publications

(125 citation statements)

References 38 publications

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“…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). The PML has been further extended to other methods, such as the pseudo-spectral method (Liu, 1998), the finite element method (Collino and Tsogka, 2001), the spectral element method , and the grid method (Xu and Zhang, 2008).…”

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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“…It is valid for transversely isotropic media with a horizontal or vertical symmetry axis; general anisotropy can be accommodated by tapering it such that the medium becomes transversely isotropic on the absorbing boundary ⌫. It is worth mentioning that in recent years a significantly more efficient absorbing condition called the Perfectly Matched Layer (PML) has been introduced [Bérenger, 1994;Collino and Tsogka, 2001], and it has been shown recently that it can be adapted to SEMs Basu and Chopra, 2004;Festa and Vilotte, 2005]. In the near future, this condition could replace classical paraxial equations such as that of Clayton and Engquist [1977] in existing FEM or SEM codes.…”

Section: The Weak Form Of the Seismic Wave Equationmentioning

confidence: 99%

The spectral-element method in seismology

Komatitsch

Tsuboi

Tromp

2005

Geophysical Monograph Series

121

120

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We present the main properties of the spectral-element method, which is well suited for numerical calculations of synthetic seismograms for three-dimensional Earth models. The technique is based upon a weak formulation of the equations of motion and combines the flexibility of a finite-element method with the accuracy of a pseudospectral method. The mesh is composed of hexahedral elements and honors the main discontinuities in the Earth model. The displacement vector is expressed in each element in terms of high-degree Lagrange interpolants, and integrals are computed based upon Gauss-Lobatto-Legendre quadrature, which leads to an exactly diagonal mass matrix and therefore drastically simplifies the algorithm. We use a fluid-solid coupling formulation that does not require iterations at the core-mantle or inner-core boundaries. The method is efficiently implemented on parallel computers with distributed memory based upon a message-passing methodology. We present two large-scale simulations for a realistic three-dimensional Earth model computed on the Japanese Earth Simulator at periods of 5 s and longer.

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“…Later PML was formulated for the elastic wave equation in e.g. [5,6,7]. However, in this approach the solution for the displacements is dependent on computation of the strains in each time step.…”

Section: Introductionmentioning

confidence: 99%