Analysis of a Cartesian PML approximation to acoustic scattering problems in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>

Kim, Seungil; Pasciak, Joseph E.

doi:10.1016/j.jmaa.2010.05.006

Cited by 36 publications

(2 citation statements)

References 30 publications

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“…In the case of infinite media, the nonreflecting condition for wavefield components is applied at the boundaries of region Ω. We used the perfectly matched layer boundary conditions (Hastings et al, 1996;Kim and Pasciak, 2010). However, at a free-surface boundary, one needs to incorporate the following boundary:…”

Section: Acoustic-wave Equation Forward Modeling In Laplace-fourier Dmentioning

confidence: 99%

Embedded boundary methods for modeling 3D finite-difference Laplace-Fourier domain acoustic-wave equation with free-surface topography

et al. 2018

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We have developed embedded boundary methods to handle arbitrarily shaped topography to accurately simulate acoustic seismic wave propagation in the Laplace-Fourier domain. The purpose is to use this method to enhance accurate wave simulation near the surface. Unlike most existing methods such as the ones using curvilinear grids to fit irregular surface topography, we use a regular Cartesian grid system without suffering from the staircasing error that occurs in conventional implementations. In this improved embedded-boundary method, we use the method of images, by imposing ghost nodes above the surface and approximating their acoustic pressures using linear extrapolation, quadratic interpolation, or cubic interpolation, to account for an arbitrarily curved surface. Implementing this method instead of using curvilinear grids near the boundaries greatly reduces the complexity of preprocessing procedures and the computational cost. Furthermore, using numerical examples, we found the accuracy gain and performance of our embedded-boundary methods in comparison with conventional finite-difference implementation of the problem.

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Section: Acoustic-wave Equation Forward Modeling In Laplace-fourier Dmentioning

confidence: 99%

Embedded boundary methods for modeling 3D finite-difference Laplace-Fourier domain acoustic-wave equation with free-surface topography

et al. 2018

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“…In the case of infinite media, the non-reflecting condition for wavefield components is applied at the boundaries of region Ω. We used the perfectly matched layer (PML) boundary conditions (Hastings et al, 1996;Kim and Pasciak, 2010). However, at a free-surface boundary, one needs to incorporate the following boundary: EMBEDDED BOUNDARY METHOD Introduction Special attention to the numerical treatment of the free-surface boundary for topography is deserved because it does not follow naturally from a Cartesian grid.…”

Section: Governing Equationsmentioning

confidence: 99%

Efficient three-dimensional Laplace-Fourier domain acoustic-wave simulations using discontinuous finite-difference meshes with embedded boundaries

AlSalem

Petrov

Newman

et al. 2018

SEG Technical Program Expanded Abstracts 2018

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We develop embedded boundary and discontinuous mesh methods to handle arbirarily shaped topography and accurately simulate acoustic seismic wave propagation in Laplace-Fourier domain. The purpose of the embedded boundary method is to enhance accurate wave simulation near the surface and the discontinuous mesh method is used to achieve considerable savings in both computation time and memory savings relative to fixed mesh schemes.

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An automatic perfectly matched layer for acoustic finite element simulations in convex domains of general shape

Bériot

Modave

2020

Int J Numer Methods Eng

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This article addresses the efficient finite element solution of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers (PMLs). The PML is a popular nonreflecting technique that combines accuracy, computational efficiency, and geometric flexibility. Unfortunately, the effective implementation of the PML for convex domains of general shape is tricky because of the geometric parameters that are required to define the PML medium. In this work, a comprehensive implementation strategy is proposed. This approach, which we call the automatically matched layer (AML) implementation, is versatile and fully automatic for the end-user. With the AML approach, the mesh of the layer is extruded, the required geometric parameters are automatically obtained during the extrusion step, and the practical implementation relies on a simple modification of the Jacobian matrix in the elementwise integrals. The AML implementation is validated and compared with other implementation strategies using numerical benchmarks in two and three dimensions, considering computational domains with regular and nonregular boundaries. A three-dimensional application with a generally shaped domain generated using a convex hull is proposed to illustrate the interest of the AML approach for realistic industrial cases. K E Y W O R D S exterior acoustics, finite element method, Helmholtz equation, perfectly matched layer, wave propagation 1 INTRODUCTION Finite element methods (FEMs) are widely used in academia and industry to simulate acoustic wave propagation phenomena. With these methods, high-frequency oscillatory fields can be represented accurately in realistic settings with complicated geometries thanks to unstructured meshes, curved elements, high-order basis functions and hp-adaptivity. 1 Nevertheless, for many applications occurring in the free space, the computational domain must be truncated, and a specific nonreflecting technique must be used at the artificial boundary of the finite element mesh to represent the outward [Correction added on 6 January 2021, after first online publication: ζ symbols have been corrected to throughout the article.] This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Analysis of a Cartesian PML approximation to acoustic scattering problems in R2

Cited by 36 publications

References 30 publications

Embedded boundary methods for modeling 3D finite-difference Laplace-Fourier domain acoustic-wave equation with free-surface topography

Embedded boundary methods for modeling 3D finite-difference Laplace-Fourier domain acoustic-wave equation with free-surface topography

Efficient three-dimensional Laplace-Fourier domain acoustic-wave simulations using discontinuous finite-difference meshes with embedded boundaries

An automatic perfectly matched layer for acoustic finite element simulations in convex domains of general shape

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