High-order non-reflecting boundary scheme for time-dependent waves

Givoli, Dan; Neta, Beny

doi:10.1016/s0021-9991(03)00005-6

Cited by 197 publications

(157 citation statements)

References 61 publications

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“…In contrast to the original formulation of the Higdon conditions, this scheme does not involve any high derivatives beyond the second order by introducing special auxiliary variables. 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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“…Here we apply an NRBC proposed by Higdon [7] on the artificial boundary. A scheme to discretize high-order Higdon NRBCs that was developed by the authors [8][9][10] is refined and used in this paper. To be more precise, Givoli and Neta have developed two different formulations.…”

Section: Introductionmentioning

confidence: 99%

“…To be more precise, Givoli and Neta have developed two different formulations. In [8] the high-derivative (HD) formulation is introduced and in [9] the auxiliary variable (AV) formulation is given. The HD formulation involves quantities in 'inner layers' of the domain, and also in previous time steps.…”

Section: Introductionmentioning

confidence: 99%

Application of high‐order Higdon non‐reflecting boundary conditions to linear shallow water models

Neta

Joolen

Dea

et al. 2007

Commun. Numer. Meth. Engng.

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SUMMARYA shallow water model with linear time-dependent dispersive waves in an unbounded domain is considered. The domain is truncated with artificial boundaries B where a sequence of high-order non-reflecting boundary conditions (NRBCs) proposed by Higdon are applied. Methods devised by Givoli and Neta that afford easy implementation of Higdon NRBCs are refined in order to reduce computational expenses. The new refinement makes the computational effort associated with the boundary treatment quadratic rather than exponential (as in the original scheme) with the order. This allows for implementation of NRBCs of higher orders than previously. A numerical example for a semi-infinite channel truncated on one side is presented. Finite difference schemes are used throughout.

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“…See [5,6] for reviews on the subject. See also Higdon's papers [7,8], Givoli-Neta [9,10] and Neta et al [11].…”

Section: Introductionmentioning

confidence: 99%

High-order non-reflecting boundary conditions for dispersive waves in polar coordinates using spectral elements

Lindquist¹,

Neta²,

Giraldo³

2012

Applied Mathematics and Computation

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High-order non-reflecting boundary scheme for time-dependent waves

Cited by 197 publications

References 61 publications

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

Application of high‐order Higdon non‐reflecting boundary conditions to linear shallow water models

High-order non-reflecting boundary conditions for dispersive waves in polar coordinates using spectral elements

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