Design Sensitivity Analysis of Steady-State Acoustic Problems using Boundary Integral Equation Formulation

Matsumoto, Toshiro; Tanaka, Masataka; Yamada, Yasunaga

doi:10.1299/jsmec1993.38.9

Cited by 13 publications

(4 citation statements)

References 5 publications

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“…Discretizing eqn (9), collecting the equations for all the collocation points and expressing them in matrix forms result in the following form of linear algebraic equations:…”

Section: Cbem Formulations For Acoustic State Analysismentioning

confidence: 99%

3-D acoustic shape sensitivity analysis using the fast multipole boundary element method

Zheng¹,

Matsumoto²,

Takahashi³

et al. 2010

Boundary Elements and Other Mesh Reduction Methods XXXII

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The fast multipole boundary element method (FMBEM), based on the BurtonMiller formulation for 3-D acoustic sensitivity analysis, is presented in this paper in order to overcome the difficulties in the shape sensitivity analyses using the boundary element method based on the direct differentiation method.The Burton-Miller formulation, which is a linear combination of the conventional boundary integral equation (CBIE) and its normal derivative (NDBIE), is applied to circumvent the difficulty caused by the so-called fictitious eigenfrequencies. The fast multipole method (FMM) is also employed to improve the overall computational efficiency. The sensitivity boundary integral equations of hypersingular type are obtained by the direct differentiation method. The correctness and validity of the method are demonstrated through some numerical results, from which the effectiveness of the present method is shown for 3-D acoustic shape sensitivity analyses.

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“…Discretizing eqn (9), collecting the equations for all the collocation points and expressing them in matrix forms result in the following form of linear algebraic equations:…”

Section: Cbem Formulations For Acoustic State Analysismentioning

confidence: 99%

3-D acoustic shape sensitivity analysis using the fast multipole boundary element method

Zheng¹,

Matsumoto²,

Takahashi³

et al. 2010

Boundary Elements and Other Mesh Reduction Methods XXXII

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show abstract

“…Too large or too small a step length will affect the results of the calculation, and the stability is difficult to be guaranteed in the actual calculation. Compared with FDM, the direct differentiation method (DDM) [43][44][45] uses chain differentiation rules to get the gradient value for the objective function on the basis of intermediate gradient values. The DDM is easy to understand and highly stable, so this method is widely used for sensitivity analysis.…”

Section: Introductionmentioning

confidence: 99%

Topology Optimization of Sound-Absorbing Materials for Two-Dimensional Acoustic Problems Using Isogeometric Boundary Element Method

Liu¹,

Zhao²,

Shen³

2023

Computer Modeling in Engineering &Amp; Sciences

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In this work, an acoustic topology optimization method for structural surface design covered by porous materials is proposed. The analysis of acoustic problems is performed using the isogeometric boundary element method. Taking the element density of porous materials as the design variable, the volume of porous materials as the constraint, and the minimum sound pressure or maximum scattered sound power as the design goal, the topology optimization is carried out by solid isotropic material with penalization (SIMP) method. To get a limpid 0-1 distribution, a smoothing Heaviside-like function is proposed. To obtain the gradient value of the objective function, a sensitivity analysis method based on the adjoint variable method (AVM) is proposed. To find the optimal solution, the optimization problems are solved by the method of moving asymptotes (MMA) based on gradient information. Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems. Furthermore, the optimal distribution of sound-absorbing materials is highly frequency-dependent and usually needs to be performed within a frequency band.

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“…The gradient is related to a variation of the objective function, and consists of the sensitivities of the boundary and internal quantities. To calculate these sensitivities, direct differentiation method [3][4][5] and adjoint variable method [6,7] has been proposed. When using BEM, the direct differentiation method uses an additional boundary integral equation obtained by differentiating the original boundary integral equation with respect to an arbitrary shape design variable.…”

Section: Introductionmentioning

confidence: 99%

A shape sensitivity analysis approach based on the boundary element method

Matsumoto¹,

Takahashi²,

Shibata³

et al. 2011

Boundary Elements and Other Mesh Reduction Methods XXXIII

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A revised shape design sensitivity formulation is presented for elastostatic problems based on the adjoint method and the boundary element method. The objective function is assumed as a functional consisting of the boundary quantities and those given at some finite number of points in the domain of the solid. The gradient of the objective function is derived and an adjoint state is introduced so that the unknown sensitivity coefficients of the displacement and traction on the boundary and in the domain are eliminated from the gradient expression. Since the original boundary value problem and the adjoint problem are governed by the same differential equations and the boundary condition types, and also the derived sensitivity formulation is expressed with only the boundary integrals and the quantities at some discrete points in the domain, the boundary element method can be used as the effective computational tool. Also, the recent development of the fast-multipole boundary element method enables a large-scale shape optimization analysis of complicated structures. The validity of the derived formulation is tested through some numerical example problems.

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Design Sensitivity Analysis of Steady-State Acoustic Problems using Boundary Integral Equation Formulation

Cited by 13 publications

References 5 publications

3-D acoustic shape sensitivity analysis using the fast multipole boundary element method

3-D acoustic shape sensitivity analysis using the fast multipole boundary element method

Topology Optimization of Sound-Absorbing Materials for Two-Dimensional Acoustic Problems Using Isogeometric Boundary Element Method

A shape sensitivity analysis approach based on the boundary element method

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