A variable order infinite element for multi-domain boundary element modelling of acoustic radiation and scattering

Cremers, Luc; Fyfe, K.R.; Sas, Paul

doi:10.1016/s0003-682x(99)00029-8

Cited by 10 publications

(8 citation statements)

References 22 publications

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“…It must be noted that Equation (24) can be derived simply by applying a normal derivative operator with respect to Equation (23). Differentiation of the Cauchy principal value should be carried out carefully by using Leibnitz's rule.…”

Section: Dual Boundary Integral Formulationmentioning

confidence: 99%

“…The order of singularity and the symmetry properties for the four kernel functions and the continuous properties of the potentials across the boundary resulting from the four kernel functions are summarized in Table I. The linear algebraic equations discretized from the dual boundary integral equations in Equations (23) and (24) can be expressed as…”

Section: Dual Boundary Integral Formulationmentioning

confidence: 99%

“…The complexity proportional to the conventional BEM is N 2 , but the FEM is N because of its banded coefficient matrix [22]. Multi-domain approach [23] or approximate theories such as the theories of plates and shells have been employed to solve the problem using parallel computers. When the size of the influence matrix by using BEM is so large, its storage and solution may cause problems for desktop computer.…”

Section: Introductionmentioning

confidence: 99%

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Applications of the dual integral formulation in conjunction with fast multipole method to the oblique incident wave problem

Chen

Kao

et al. 2008

Numerical Methods in Fluids

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SUMMARYIn this paper, the dual integral formulation is derived for the modified Helmholtz equation in the propagation of oblique incident wave passing a thin barrier (zero thickness) by employing the concept of fast multipole method (FMM) to accelerate the construction of an influence matrix. By adopting the addition theorem, the four kernels in the dual formulation are expanded into degenerate kernels that separate the field point and the source point. The source point matrices decomposed in the four influence matrices are similar to each other or only to some combinations. There are many zeros or the same influence coefficients in the field point matrices decomposed in the four influence matrices, which can avoid calculating the same terms repeatedly. The separable technique reduces the number of floating-point operations fromwhere N is the number of elements and a is a small constant independent of N . Finally, the FMM is shown to reduce the CPU time and memory requirement, thus enabling us to apply boundary element method (BEM) to solve water scattering problems efficiently. Two-moment FMM formulation was found to be sufficient for convergence in the singular equation. The results are compared well with those of conventional BEM and analytical solutions and show the accuracy and efficiency of the FMM.

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Section: Dual Boundary Integral Formulationmentioning

confidence: 99%

Section: Dual Boundary Integral Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Applications of the dual integral formulation in conjunction with fast multipole method to the oblique incident wave problem

Chen

Kao

et al. 2008

Numerical Methods in Fluids

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“…A recent paper by Cremers et al [83] proposed a multi-domain boundary-element technique utilizing infinite boundary elements. In that approach, it was reported that the irregular frequencies had not been observed.…”

Section: H(co) P(w) = G(w) V/(w)mentioning

confidence: 99%

Developments in structural-acoustic optimization for passive noise control

Marburg

2002

ARCO

161

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Low noise constructions receive more and more attention in highly industrialized countries. Consequently, decrease of noise radiation challenges a growing community of engineers. One of the most efficient techniques for finding quiet structures consists in numerical optimization. Herein, we consider structural-acoustic optimization understood as an (iterative) minimum search of a specified objective (or cost) function by modifying certain design variables. Obviously, a coupled problem must be solved to evaluate the objective function. In this paper, we will start with a review of structural and acoustic analysis techniques using numerical methods like the finite-and/or the boundary-element method. This is followed by a survey of techniques for structural-acoustic coupling. We will then discuss objective functions. Often, the average sound pressure at one or a few points in a frequency interval accounts for the objective function for interior problems, whereas the average sound power is mostly used for external problems. The analysis part will be completed by review of sensitivity analysis and special techniques. We will then discuss applications of structuralacoustic optimization. Starting with a review of related work in pure structural optimization and in pure acoustic optimization, we will categorize the problems of optimization in structural acoustics. A suitable distinction consists in academic and more applied examples. Academic examples include simple structures like beams, rectangular or circular plates and boxes; real industrial applications consider problems like that of a fuselage, bells, loudspeaker diaphragms and components of vehicle structures. Various different types of variables are used as design parameters_ Quite often, locally defined plate or shell thickness or discrete point masses are chosen. Furthermore, all kinds of structural material parameters, beam cross sections, spring characteristics and shell geometry account for suitable design modifications. This is followed by a listing of constraints that have been applied. After that, we will discuss strategies of optimization. Starting with a formulation of the optimization problem we review aspects of multiobjective optimization, approximation concepts and optimization methods in general. In a final chapter, results are categorized and discussed. Very often, quite large decreases of noise radiation have been reported. However, even small gains should be highly appreciated in some cases of certain support conditious, complexity of simulation model and large frequency ranges. Optimization outcomes are categorized with respect to objective functions, optimization methods, variables and groups of problems, the latter with particular focus on industrial applications. More specifically, a close-up look at vehicle panel shell geometry optimization is presented. Review of results is completed with a section on experimental validation of optimization gains. The conclusions bring together a number of open problems in the field.Obviously, the (non-Her...

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“…Finally, the interesting paper by Cremers et al [7] proposes a multi-domain boundary-element technique utilizing infinite boundary elements. The basic intention of the authors was to investigate a substructure technique with infinite subdomains separated by infinite boundary elements.…”

Section: Other Methodsmentioning

confidence: 99%

Treating the Phenomenon of Irregular Frequencies

Marburg¹,

Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods

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Summary. This chapter reviews a number of techniques developed to overcome the wellknown non-uniqueness difficulty in the boundary element method for acoustic radiation and scattering in an exterior domain. The non-uniqueness difficulty occurs at a set of irregular frequencies associated with the eigenfrequencies of the corresponding interior problem. The chapter focuses on the comparison of two commonly used techniques, the CHIEF method and the Burton and Miller method, along with their variations. After briefly revisiting the example of the pulsating sphere, a cat's eye radiation problem is used as a test case for evaluating the effectiveness of different techniques. Numerical results confirm that the Burton and Miller method is a very reliable technique at all frequencies, while the CHIEF method is effective only at low frequencies. One potential drawback of Burton and Miller method is the requirement of the C 1 continuity condition at collocation points, which may rule out the use of any C 0 continuous elements. Modified versions of the Burton and Miller method, which compute the normal-derivative integral equation only at the center of each C 0 element, have been proposed in the past to partially alleviate the strict C 1 requirement. It is still uncertain that any of these modified versions is as theoretically robust as the original Burton and Miller method. Nonetheless, the cat's eye radiation test case demonstrates that a modified version that uses 9-node quadrilateral elements is as effective as the original Burton and Miller method in practical use. The paper is completed by applying the Burton and Miller method to the industrial problem of a radiating diesel engine for which the radiated sound power is evaluated.

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A variable order infinite element for multi-domain boundary element modelling of acoustic radiation and scattering

Cited by 10 publications

References 22 publications

Applications of the dual integral formulation in conjunction with fast multipole method to the oblique incident wave problem

Applications of the dual integral formulation in conjunction with fast multipole method to the oblique incident wave problem

Developments in structural-acoustic optimization for passive noise control

Treating the Phenomenon of Irregular Frequencies

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