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Computational Geosciences : Volume 21

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Evaluation concepts to compare observed and simulated deposition areas of mass movements

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Nearly perfectly matched layer boundary conditions for operator upscaling of the acoustic wave equation

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A least squares approach for efficient and reliable short-term versus long-term optimization

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Sketching the temperature history of geological samples: analyses of diffusion profiles using multilayer perceptrons

Bayesian model selection for complex geological structures using polynomial chaos proxy

History matching of dual continuum reservoirs—preserving consistency with the fracture model

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Nearly perfectly matched layer boundary conditions for operator upscaling of the acoustic wave equation

Content Provider	Springer Nature Link
Author	Minkoff, Susan E. Lai, Chen
Copyright Year	2017
Abstract	Acoustic imaging and sensor modeling are processes that require repeated solution of the acoustic wave equation. Solution of the wave equation can be computationally expensive and memory intensive for large simulation domains. One scheme for speeding up solution of the wave equation is the operator-based upscaling method. The algorithm proceeds in two steps. First, the wave equation is solved for fine grid unknowns internal to coarse blocks assuming the coarse blocks do not need to communicate with neighboring blocks in parallel. Second, these fine grid solutions are used to form a new problem which is solved on the coarse grid. Accurate and efficient wave propagation schemes also must avoid artificial reflections off of the computational domain edges. One popular method for preventing artificial reflections is the nearly perfectly matched layer (NPML) method. In this paper, we discuss applying NPML to operator upscaling for the wave equation. We show that although we only apply NPML to the first step of this two step algorithm (directly affecting the fine grid unknowns only), we still see a significant reduction of reflections back into the domain. We describe three numerical experiments (one homogeneous medium experiment and two heterogeneous media examples) in which we validate that the solution of the wave equation exponentially decays in the NPML regions. Numerical experiments of acoustic wave propagation in two dimensions with a reasonable absorbing layer thickness resulted in a maximum pressure reflection of 3–8%. While the coarse grid acceleration is not explicitly damped in our algorithm, the tight coupling between the two steps of the algorithm results in only 0.1–1% of acceleration reflecting back into the computational domain.
Ending Page	372
Page Count	14
Starting Page	359
File Format	PDF
ISSN	14200597
e-ISSN	15731499
Journal	Computational Geosciences
Issue Number	3
Volume Number	21
Language	English
Publisher	Springer International Publishing
Publisher Date	2017-01-28
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Wave equation Nearly perfectly matched layers Acoustic wave propagation Earth Sciences Hydrogeology Absorbing boundary conditions Geotechnical Engineering & Applied Earth Sciences Mathematical Modeling and Industrial Mathematics Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Upscaling Finite difference methods Soil Science & Conservation
Content Type	Text
Resource Type	Article
Subject	Computers in Earth Sciences Computational Theory and Mathematics Computer Science Applications Computational Mathematics

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