Analysis of stretched grids as buffer zones in simulations of wave propagation

Kreiss, Gunilla; Krank, Benjamin; Efraimsson, Gunilla

doi:10.1016/j.apnum.2016.04.008

Cited by 12 publications

(10 citation statements)

References 21 publications

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“…A discrete wave equation based on a higher order scheme may require a different discrete Cauchy-Riemann relation. Designing PMLs that are coupled with a real grid stretching [74] may require a different analytic continuation of the wave equation. Another notable property of the current discrete wave equation is that it allows one to investigate the PML dimension by dimension, each of which fortunately admits a straightforward discrete complex extension.…”

Section: Discussionmentioning

confidence: 99%

A reflectionless discrete perfectly matched layer

Chern

2019

Journal of Computational Physics

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Perfectly Matched Layer (PML) is a widely adopted non-reflecting boundary treatment for wave simulations. Reducing numerical reflections from a discretized PML has been a long lasting challenge. This paper presents a new discrete PML for the multi-dimensional scalar wave equation which produces no numerical reflection at all. The reflectionless discrete PML is discovered through a straightforward derivation using Discrete Complex Analysis. The resulting PML takes an easily-implementable finite difference form with compact stencil. In practice, the discrete waves are damped exponentially in the PML, and the error due to domain truncation is maintained at machine zero by a moderately thick PML. The numerical stability of the proposed PML is also demonstrated.

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Section: Discussionmentioning

confidence: 99%

A reflectionless discrete perfectly matched layer

Chern

2019

Journal of Computational Physics

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“…The process iterates until all coefficients are determined as follows. Given 20) and gives a transport equation on α j defined by Πa j = α j Φ as before. This transport equation, with initial data given by g j , uniquely determines a j .…”

Section: Preliminariesmentioning

confidence: 99%

“…We neither summarize, evaluate, nor criticize other strategies. The interested reader can consult [21], [14], [5], [18], [25], [19], [17], [1], [2], [7], [4], [3], [22], [24], [20], listed here in chronological order, to appreciate the variety of interesting ideas and methods.…”

Section: Introductionmentioning

confidence: 99%

Nobody's Perfect; Matched Layers for Heterogeneous Media

Halpern¹,

Métivier²,

Rauch³

et al. 2019

SIAM J. Sci. Comput.

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“…The first approach is the absorbing boundary condition (ABC) [52,4,69,53,29,85,11,64,63,56,66,11,65,14,57,97,28], which is a boundary condition enforced at an artificial boundary such that unwanted reflections from the boundary are significantly minimised. The second approach corresponds to extending the domain to an absorbing layer of finite thickness where the underlying equations are transformed such that waves decay rapidly in the layer [83,7,23,15,102,6,36,41,94,77,99,59,1,73,90,72]. In order for an absorbing layer to be effective the equations must be perfectly matched [35,67,23,15].…”

Section: Introductionmentioning

confidence: 99%

The perfectly matched layer (PML) for hyperbolic wave propagation problems: A review

Duru¹,

Kreiss²

2022

Preprint

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It is well-known that reliable and efficient domain truncation is crucial to accurate numerical solution of most wave propagation problems. The perfectly matched layer (PML) is a method which, when stable, can provide a domain truncation scheme which is convergent with increasing layer width/damping. The difficulties in using the PML are primarily associated with stability, which can be present at the continuous level or be triggered by numerical approximations. The mathematical and numerical analysis of the PML for hyperbolic wave propagation problems has been an area of active research. It is now possible to construct stable and high order accurate numerical wave solvers by augmenting wave equations with the PML and approximating the equations using summation-by-parts finite difference methods, continuous and discontinuous Galerkin finite element methods. In this review we summarise the progress made, from mathematical, numerical and practical perspectives, point out some open problems and set the stage for future work. We also present numerical experiments of model problems corroborating the theoretical analysis, and numerical simulations of real-world wave propagation demonstrating impact. Stable and parallel implementations of the PML in the high performance computing software packages WaveQLab3D and ExaHyPE allow to sufficiently limit the computational domain of seismological problems with only a few grid points/elements around the computational boundaries where the PML is active, thus saving as much as 96% of the required computational resources for a three space dimensional seismological benchmark problem.

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Analysis of stretched grids as buffer zones in simulations of wave propagation

Cited by 12 publications

References 21 publications

A reflectionless discrete perfectly matched layer

A reflectionless discrete perfectly matched layer

Nobody's Perfect; Matched Layers for Heterogeneous Media

The perfectly matched layer (PML) for hyperbolic wave propagation problems: A review

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