Acoustic multiple scattering using recursive algorithms

Amirkulova, Feruza; Norris, Andrew N.

doi:10.1016/j.jcp.2015.07.031

Cited by 15 publications

(22 citation statements)

References 28 publications

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“…Partially for this reason, many early works are mostly restricted to cylindrical and spherical obstacles embedded in homogeneous media, where the modal expansions of the scattered fields play an essential role (cf. [1,2,3,4,5]). We highlight that the reader-friendly monograph by Martin [6] was largely concerned with time-harmonic waves with multiple obstacles and with exact methods including separation of variables, integral equations and T -matrices, but only the last chapter is concerned with some numerics.…”

Section: Introductionmentioning

confidence: 99%

An efficient iterative method for solving multiple scattering in locally inhomogeneous media

Xie

Zhang

Wang

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then apply purely outgoing wave decomposition for the scattering field outside the enclosed region. As a result, the original multiple scattering problem can be decomposed into a finite number of single scattering problems, where each of them communicates with the other scattering problems only through its surrounding artificial boundary. Accordingly, they can be solved in a parallel manner at each iteration. This framework enjoys a great flexibility in using different combinations of iterative algorithms and single scattering problem solvers. The spectral element method seamlessly integrated with the non-reflecting boundary condition and the GMRES iteration is advocated and implemented in this work. The convergence of the proposed method is proved by using the compactness of involved integral operators.Ample numerical examples are presented to show its high accuracy and efficiency. key word: Multiple scattering, inhomogeneous media, iterative method, spectral element method, non-reflecting boundary condition, GMRES iteration arXiv:1908.10527v1 [math.NA]

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Section: Introductionmentioning

confidence: 99%

An efficient iterative method for solving multiple scattering in locally inhomogeneous media

Xie

Zhang

Wang

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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“…In a related approach, [8] uses a combination of double and single-layer potentials for configurations of up to 400 obstacles of size λ. Using T-matrix, [9] 30 studies scattering for up to 2000 obstacles of radius ≤ 1.6λ. More sophisticated methods (coupling BIE with FEM etc.)…”

Section: Introductionmentioning

confidence: 99%

“…Despite the existence of pieces of software for this type of simulation, e.g. the Matlab toolbox µ-diff 55 [19], see also [9] for a review of available packages, we would like to develop a high-performance computing software that can work on clusters 9 . Our codes offer choices of the direct solvers (Mumps, Lapack and Scalapack), and GM-RES (with restart) solvers [20] with various preconditioners.…”

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confidence: 99%

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Numerical robustness of single-layer method with Fourier basis for multiple obstacle acoustic scattering in homogeneous media

et al. 2018

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We investigate efficient methods to simulate the multiple scattering of obstacles in homogeneous media. With a large number of small obstacles on a large domain, optimized pieces of software based on spatial discretization such as Finite Element Method (FEM) or Finite Difference lose their robustness. As an alternative, we work with an integral equation method, which uses singlelayer potentials and truncation of Fourier series to describe the approximate scattered field. In the theoretical part of the paper, we describe in detail the linear systems generated by the method for impenetrable obstacles, accompanied by a well-posedness study. For the numerical performance study, we limit ourselves to the case of circular obstacles. We first compare and validate our codes with the highly optimized FEM-based software Montjoie. Secondly, we investigate the efficiency of different solver types (direct and iterative of type GMRES) in solving the dense linear system generated by the method. We observe the robustness of direct solvers over iterative ones for closely-spaced obstacles, and that of GMRES with Lower-Upper Symmetric Gauss-Seidel and Symmetric Gauss-Seidel preconditioners for far-apart obstacles.

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“…The recent surge of research effort toward the study of wave propagation in phononic crystals has depended upon the speed, efficiency and versatility of phononic bandstructure calculating algorithms. Several techniques can be used to calculate these bandstructures including the plane wave expansion (PWE) method (Sigalas and Economou 1993;Kushwaha et al 1993;Kushwaha et al 1994;Vasseur et al 1994), the multiple scattering method (Kafesaki and Economou 1999;Amirkulova and Norris 2015), the finite difference time domain method (Sigalas et al 2000;Cao et al 2004;Hsieh et al 2006), the finite element (FE) method (Hladky-Hennion and Decarpigny 1991;Veres and Berer 2012) (See Hussein et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Combining Plane Wave Expansion and Variational Techniques for Fast Phononic Computations

Srivastava

2017

J. Eng. Mech.

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In this paper the salient features of the Plane Wave Expansion (PWE) method and the mixed variational technique are combined for the fast eigenvalue computations of arbitrarily complex phononic unit cells. This is done by expanding the material properties in a Fourier expansion, as is the case with PWE. The required matrix elements in the variational scheme are identified as the discrete Fourier transform coefficients of material properties, thus obviating the need for any explicit integration. The process allows us to provide succinct and closed form expressions for all the matrices involved in the mixed variational method. The scheme proposed here preserves both the simplicity of expression which is inherent in the PWE method and the superior convergence properties of the mixed variational scheme. We present numerical results and comment upon the convergence and stability of the current method. We show that the current representation renders the results of the method stable over the entire range of the expansion terms as allowed by the spatial discretization. When compared with a zero order numerical integration scheme, the present method results in greater computational accuracy of all eigenvalues. A higher order numerical integration scheme comes close to the accuracy of the present method but only with significantly more computational expense.

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Acoustic multiple scattering using recursive algorithms

Cited by 15 publications

References 28 publications

An efficient iterative method for solving multiple scattering in locally inhomogeneous media

An efficient iterative method for solving multiple scattering in locally inhomogeneous media

Numerical robustness of single-layer method with Fourier basis for multiple obstacle acoustic scattering in homogeneous media

Combining Plane Wave Expansion and Variational Techniques for Fast Phononic Computations

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