A method for multi-frequency calculation of boundary integral equation in acoustics based on series expansion

Wang, Z.; Zhao, Zhanwei; Liu, Z.X.; Huang, Q.

doi:10.1016/j.apacoust.2008.05.005

Cited by 25 publications

(16 citation statements)

References 7 publications

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“…As reported by Wang et al, 25 SECHIEF is efficient in low-and medium-frequency bands since larger expansion degree N is required for high frequencies. ISECHIEF inherits such a drawback but the applicable frequency band can be wider with the help of periodicity of both sine and cosine functions.…”

Section: Wider-frequency-band Application Compared With Sechiefmentioning

confidence: 73%

“…Seen from Eqs. (29) and (30), as indicated by Wang et al, 25 both truncation errors will increase with kr so that a larger degree of series expansion is required to guarantee the approximation accuracy. Thus, both of the data storage space and summation time of expansion terms will increase inevitably, cutting down the accelerating effect of SECHIEF and narrowing it to be applicable in medium-and low-frequency regime and for small-scale structures.…”

Section: Series Expansion Methods Combined With Helmholtz Integral Equmentioning

confidence: 94%

“…Thus, both of the data storage space and summation time of expansion terms will increase inevitably, cutting down the accelerating effect of SECHIEF and narrowing it to be applicable in medium-and low-frequency regime and for small-scale structures. 25 More details about the truncation error will be given in the next sections.…”

Section: Series Expansion Methods Combined With Helmholtz Integral Equmentioning

confidence: 99%

“…Another method for speeding up the multi-frequency computation was the so-called algebraic polynomial or the series expansion method (SEM) initially proposed by Kirkup et al 23 Recently, it has also been employed by Li 24 and Wang et al 25 in acoustic multi-frequency analysis. This approach separates the frequency-dependent terms from the integral kernels by means of the Taylor series expansion of the sine and cosine functions, making the numerical integration independent of frequency.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, this speeding-up technique is only suitable for low and medium frequency band and relatively small-scale structures. 24,25 As in the electromagnetic wave radiation, a complete multiple reciprocity method (CMRM) is proposed to break down the numerical integration into frequency-dependent and frequency-independent portions so as to accelerate the multi-frequency calculation. 26 After that, a pre-corrected FFT algorithm and the CMRM are combined to improve the efficiency of the multi-frequency calculation for both near-and far-field points.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Improved Series Expansion Method to Accelerate the Multi-Frequency Acoustic Radiation Prediction

Zhang

Mao

et al. 2015

J. Comp. Acous.

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Multi-frequency calculation is usually very time-consuming due to the repeated numerical integration for numerous frequencies in acoustic scattering or radiation problems. A series expansion method has been proposed to speed up this process just by taking the frequency-dependent terms out of the integral sign. However, this method, constrained by the number of truncation terms, is only applicable to low and medium frequencies and/or small-size structures. This paper develops an improved series expansion method that can be employed in a wider frequency band and larger-scale problems but with less computing expense. In the present method, the frequency-dependent term kr in the integral kernel is firstly transformed into the range from −π to π due to the periodicity of sine and cosine functions. Afterwards, truncation error would be kept reasonably small while the number of expansion terms would not increase with kr. Test cases of acoustic radiation from a pulsating sphere and a cat's eye structure are conducted and numerical results show significant reduction of computational time but suffering little accuracy loss for multi-frequency problems with this approach.

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Section: Wider-frequency-band Application Compared With Sechiefmentioning

confidence: 73%

Section: Series Expansion Methods Combined With Helmholtz Integral Equmentioning

confidence: 94%

Section: Series Expansion Methods Combined With Helmholtz Integral Equmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Improved Series Expansion Method to Accelerate the Multi-Frequency Acoustic Radiation Prediction

Zhang

Mao

et al. 2015

J. Comp. Acous.

View full text Add to dashboard Cite

show abstract

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Chen,

Zhao,

Lian

et al. 2023

Numerical Meth Engineering

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In this article, an innovative method is proposed for broadband topology optimization of sound‐absorbing materials adhering to the surface of a sound barrier structure. Helmholtz equation for the acoustic problems is solved using the boundary element method, while sensitivities of the objective function with respect to a large number of design variables are calculated via a sensitivity analysis method originated from the adjoint variable method (AVM), and the optimal solution is obtained by the method of moving asymptotes (MMA). Since the traditional single‐frequency topology optimization is frequency dependent, that is, the optimal solution at a certain frequency may not be optimal at other frequencies, broadband topology optimization of sound‐absorbing materials is conducted in this work. To address the problem of tremendous computational cost due to repetitive calculations at each discrete frequency point during broadband optimization, Taylor expansion of the Hankel function is performed to decouple the frequency dependent and independent terms in the BEM equations. For large‐scale problems, a reduced‐order model that retains the essential structures and key properties of the original model is built using the second‐order Arnoldi (SOAR) method. The accuracy and feasibility of the proposed algorithms are finally validated via some two‐dimensional numerical examples.

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Machine learning accelerated MMC-based topology optimization for sound quality enhancement of serialized acoustic structures

Xu,

Zhang,

Yao

et al. 2024

Struct Multidisc Optim

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A method for multi-frequency calculation of boundary integral equation in acoustics based on series expansion

Cited by 25 publications

References 7 publications

An Improved Series Expansion Method to Accelerate the Multi-Frequency Acoustic Radiation Prediction

An Improved Series Expansion Method to Accelerate the Multi-Frequency Acoustic Radiation Prediction

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Machine learning accelerated MMC-based topology optimization for sound quality enhancement of serialized acoustic structures

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