A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems

Hagstrom, Thomas; Warburton, Tim

doi:10.1016/j.wavemoti.2003.12.007

Cited by 162 publications

(165 citation statements)

References 14 publications

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“…Similar to the implementation in Reference [24], since the contribution is frequency independent, the degrees-of-freedom interior to the corner absorbing region can be condensed out, thus reducing the number of degrees-of-freedom. (This idea is also similar to the suggestion in Reference [31]. )…”

Section: Extension To Corner Regionssupporting

confidence: 90%

“…These approaches formulate the corner absorbers by deriving corner compatibility conditions, which are necessary to ensure the regularity of the solution of the problem when the data are smooth. More recently, Vacus [30] and Hagstrom and Warburton [31] also describe procedures for deriving corner compatibility conditions. All these approaches require special implementations and are limited to orthogonal corners.…”

Section: Extension To Corner Regionsmentioning

confidence: 99%

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Continued fraction absorbing boundary conditions for convex polygonal domains

Guddati

Lim

2005

Numerical Meth Engineering

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SUMMARYContinued fraction absorbing boundary conditions (CFABCs) are highly effective boundary conditions for modelling wave absorption into unbounded domains. They are based on rational approximation of the exact dispersion relationship and were originally developed for straight computational boundaries. In this paper, CFABCs are extended to the more general case of polygonal computational domains. The key to the current development is the surprising link found between the CFABCs and the complex co-ordinate stretching of perfectly matched layers (PMLs). This link facilitates the extension of CFABCs to oblique corners and, thus, to polygonal domains. It is shown that the proposed CFABCs are easy to implement, expected to perform better than PMLs, and are effective for general polygonal computational domains. In addition to the derivation of CFABCs, a novel explicit time-stepping scheme is developed for efficient numerical implementation. Numerical examples presented in the paper illustrate that effective absorption is attained with a negligible increase in the computational cost for the interior domain. Although this paper focuses on wave propagation, its theoretical development can be easily extended to the more general class of problems where the governing differential equation is second order in space with constant coefficients.

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Section: Extension To Corner Regionssupporting

confidence: 90%

Section: Extension To Corner Regionsmentioning

confidence: 99%

Continued fraction absorbing boundary conditions for convex polygonal domains

Guddati

Lim

2005

Numerical Meth Engineering

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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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“…As simple as the case is, it allows for a thorough validation through the exact solution. We use 950 elements and an high-order local boundary condition [4]. A snapshot of E z is shown in Fig.…”

Section: The Discontinuous Galerkin Methodsmentioning

confidence: 99%

High-Order Discontinuous Galerkin Methods for Computational Electromagnetics and Uncertainty Quantification

Hesthaven

Warburton

Chauvière

et al. 2010

Scientific Computing in Electrical Engineering SCEE 2008

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We discuss the basics of discontinuous Galerkin methods (DG) for CEM as an alternative of emerging importance to the widely used FDTD. The benefits of DG methods include geometric flexibility, high-order accuracy, explicit timeadvancement, and very high parallel performance for large scale applications. The performance of the scheme shall be illustrated by several examples. As an example of particular interest, we further explore efficient probabilistic ways of dealing with uncertainty and uncertainty quantification in electromagnetics applications. Whereas the discussion often draws on scattering applications, the techniques are applicable to general problems in CEM.

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A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems

Cited by 162 publications

References 14 publications

Continued fraction absorbing boundary conditions for convex polygonal domains

Continued fraction absorbing boundary conditions for convex polygonal domains

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

High-Order Discontinuous Galerkin Methods for Computational Electromagnetics and Uncertainty Quantification

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