On calculation of sound fields around three dimensional objects by integral equation methods
TL;DR: In this article, the use of integral equation methods in numerical calculations of exterior sound fields around scattering objects was investigated, where the objects investigated are a rigid body with edges and vertices, a rigid plate and an absorbing body.
About: This article is published in Journal of Sound and Vibration.The article was published on 1980-03-08. It has received 209 citations till now. The article focuses on the topics: Integral equation & Electric-field integral equation.
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TL;DR: A versatile, high-order accurate immersed boundary method for solving the LPCE in complex domains by combining the ghost-cell approach with a weighted least-squares error method based on a high- order approximating polynomial.
179 citations
Cites background from "On calculation of sound fields arou..."
...Although sound wave propagation and scattering by a complex geometry can be modeled with a boundary element method (BEM) [8,9], the prediction of flow-induced sound generation requires more direct approach such as the direct computation of compressible conservation equations (see [10,11])....
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01 Jan 2015
TL;DR: In this paper, a contour integral method is used to convert the nonlinear eigenproblems caused by the boundary element method into ordinary eigen-problems, and all fictitious eigenfrequencies corresponding to the related interior problem are observed.
Abstract: This paper is concerned with the fictitious eigenfrequency problem of the boundary integral equation methods when solving exterior acoustic problems. A contour integral method is used to convert the nonlinear eigenproblems caused by the boundary element method into ordinary eigenproblems. Since both real and complex eigenvalues can be extracted by using the contour integral method, it enables us to investigate the fictitious eigenfrequency problem in a new way rather than comparing the accuracy of numerical solutions or the condition numbers of boundary element coefficient matrices. The interior and exterior acoustic fields of a sphere with both Dirichlet and Neumann boundary conditions are taken as numerical examples. The pulsating sphere example is studied and all fictitious eigenfrequencies corresponding to the related interior problem are observed. The reasons are given for the usual absence of many fictitious eigenfrequencies in the literature. Fictitious eigenfrequency phenomena of the Kirchhoff‐Helmholtz boundary integral equation, its normal derivative formulation and the Burton‐ Miller formulation are investigated through the eigenvalue analysis. The actual effect of the Burton‐ Miller formulation on fictitious eigenfrequencies is revealed and the optimal choice of the coupling parameter is confirmed.
157 citations
TL;DR: In this paper, a general form of the hypersingular BIE is developed for 3D acoustic wave problems, which contains at most weakly singular integrals, which can be derived by employing certain integral identities involving the static Green's function.
Abstract: The composite boundary integral equation (BIE) formulation, using a linear combination of the conventional BIE and the hypersingular BIE, emerges as the most effective and efficient formula for acoustic wave problems in an exterior medium which is free of the well-known fictitious eigen-frequency difficulty. The crucial part in implementing this formulation is dealing with the hypersingular integrals. Various regularization procedures in the literature give rise, in general, to integrals which are still difficult and/or extremely time consuming to evaluate or are limited to the use of special, usually flat, boundary elements. In this paper, a general form of the hypersingular BIE is developed for 3-D acoustic wave problems, which contains at most weakly singular integrals. This weakly singular form can be derived by employing certain integral identities involving the static Green's function. It is shown that the discretization of this weakly singular form of the hypersingular BIE is straightforward and the same collocation procedures and regular quadrature as that used for conventional BIEs are sufficient to compute all the integrals involved. Computing times are only slightly longer than with conventional BIEs. The C 1 smoothness requirement imposed on the density function for existence of the hypersingular BIEs and the possibility of relaxing this requirement are discussed. Three kinds of boundary elements, having different smoothness features, are employed. Numerical results are given for scattering from a rigid sphere at the fictitious frequencies, for values of wavenumber from π to 5π. In essence, with the methodology in this paper the fictitious eigenfrequency difficulty, long associated with the BIE for exterior problems, should no longer be a troublesome issue.
154 citations
TL;DR: In this paper, an adaptive fast multi-pole boundary element method (FMBEM) based on the Burton-Miller formulation for 3D acoustics is presented in order to solve exterior acoustic wave problems.
Abstract: The high solution costs and non-uniqueness difficulties in the boundary element method (BEM) based on the conventional boundary integral equation (CBIE) formulation are two main weaknesses in the BEM for solving exterior acoustic wave problems. To tackle these two weaknesses, an adaptive fast multi- pole boundary element method (FMBEM) based on the Burton-Miller formulation for 3-D acoustics is presented in this paper. In this adaptive FMBEM, the Burton-Miller formulation using a linear combination oftheCBIEandhypersingularBIE(HBIE)isappliedto overcome the non-uniqueness difficulties. The iterative solver generalized minimal residual (GMRES) and fast multipole method (FMM) are adopted to improve the overallcomputationalefficiency.ThisadaptiveFMBEM for acoustics is an extension of the adaptive FMBEM for 3-D potential problems developed by the authors recently. Several examples on large-scale acoustic radi- ationandscatteringproblemsarepresentedinthispaper which show that the developed adaptive FMBEM can be several times faster than the non-adaptive FMBEM while maintaining the accuracies of the BEM.
141 citations
TL;DR: The boundary element method (BEM) is a powerful tool in computational acoustic analysis as discussed by the authors, and it can be used to complete the development of computational models, which can be found in the Boundary Element Method in Acoustics toolkit.
Abstract: The boundary element method (BEM) is a powerful tool in computational acoustic analysis. The Boundary Element Method in Acoustics serves as an introduction to the BEM and its application to acoustic problems and goes on to complete the development of computational models. Software implementing the methods is available.
122 citations
References
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Book•
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01 Jan 1959
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,815 citations
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01 Oct 1999
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,503 citations
Book•
15 Jan 1970
TL;DR: In this article, an exhaustive study of the scattering properties of acoustically soft and hard bodies and perfect conductors, presented for 15 geometrically simple shapes, is presented.
Abstract: : The book represents an exhaustive study of the scattering properties of acoustically soft and hard bodies and of perfect conductors, presented for 15 geometrically-simple shapes Such shapes are important in their own right and as a basis for synthesizing the radiation and scattering properties of more complex configurations Each shape is treated in a separate chapter whose contents are presented in stylized format for easy reference Emphasis is placed on results in the form of formulae and diagrams Although no detailed derivation are included, an outline of methods in scattering theory is given in the Introduction
1,195 citations
TL;DR: The application of integral equation methods to exterior boundary-value problems for Laplace's equation and for the Helmholtz (or reduced wave) equation is discussed in this article, where it is shown that uniqueness can be restored by deriving a second integral equation and suitably combining it with the first.
Abstract: The application of integral equation methods to exterior boundary-value problems for Laplace’s equation and for the Helmholtz (or reduced wave) equation is discussed. In the latter case the straightforward formulation in terms of a single integral equation may give rise to difficulties of non-uniqueness; it is shown that uniqueness can be restored by deriving a second integral equation and suitably combining it with the first. Finally, an outline is given of methods for transforming the integral operators with strongly singular kernels which occur in the second equation.
1,127 citations