High-order Absorbing Boundary Conditions for anisotropic and convective wave equations

Bécache, Éliane; Givoli, Dan; Hagstrom, Thomas

doi:10.1016/j.jcp.2009.10.012

Cited by 72 publications

(96 citation statements)

References 41 publications

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“…As a result, this scheme can be easily used up to any desired order m. Moreover, the computational cost only increases linearly with m (Givoli and Neta, 2003;Givoli, 2004). Corner compatibility conditions are derived for high-order radiation boundary conditions using auxiliary variable equations (Hagstrom and Warburton, 2004;Bécache et al, 2010).…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Gao

Song

Zhang

et al. 2017

Exploration Geophysics

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“…In particular, they provide a characterization of different types of anisotropy by involving slowness curves. In the same time, slowness curves have been introduced in [4] to construct ABCs for anisotropic acoustic equations.…”

Section: Slowness Curvesmentioning

confidence: 99%

Absorbing Boundary Conditions for 2D Tilted Transverse Isotropic elastic media

Barucq

Boillot

Calandra³

et al. 2014

ESAIM: ProcS

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Abstract. This work deals with the construction of a low-order absorbing boundary condition (ABC) for 2D elliptic TTI media, preserving the system stability. The construction is based on comparing and then connecting the slowness curves for isotropic and elliptic TTI waves. Numerical experiments illustrate the performance of the new ABC. They are performed by integrating the ABC in a DG formulation of Elastodynamics. When applied in a TTI medium, the new ABC performs well with the same level of accuracy than the standard isotropic ABC set in an isotropic medium. The condition demonstrates also a good robustness when applied for large times of simulation.Résumé. Ce travail porte sur la construction d'une condition aux limites absorbante (CLA) pour les milieux TTI elliptiques, préservant la stabilité du système. La mise en oeuvre repose sur la comparaison puis la mise en relation des courbes de lenteurs pour les ondes isotropes et TTI elliptiques. Des expériences numériques illustrent la performance de ces nouvelles CLA. Elles sont réalisées en intégrant la CLA dans une formulation de type Galerkin discontinue pour l'Élastodynamique. Pour un milieu TTI, la nouvelle CLA est efficace avec le même niveau de précision que la CLA isotrope standard pour un milieu isotrope. On observe aussi que la condition est robuste en temps long.

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“…The area of ABC's has been the subject of massive research, see for example [8,12,10,16,2], where the approach in [16,2] yields local boundary conditions that can be made arbitrarily accurate. When it comes to the implementation of exact NRBC's it is, for special geometries, possible to localize the boundary conditions in time while still keeping them exact.…”

Section: Introductionmentioning

confidence: 99%

Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability

Eriksson

Nordström

2016

Found Comput Math

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Exact non-reflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that well-posedness is a fundamental property of the non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, energy stability follows automatically. The stability in combination with the high order accuracy results in a reliable, efficient and accurate method. The theory is supported by numerical simulations.

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High-order Absorbing Boundary Conditions for anisotropic and convective wave equations

Cited by 72 publications

References 41 publications

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Absorbing Boundary Conditions for 2D Tilted Transverse Isotropic elastic media

Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability

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