# An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration

A.H.W.M. Kuijpers, G. Verbeek, J.W. Verheij

21 Citaties (Scopus)

### Uittreksel

Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be calculated for every Fourier term. These integrals were formerly treated for each Fourier term separately. In this paper a new method is proposed to calculate these integrals using fast Fourier transform techniques. The advantage of this integration method is that the integrals are simultaneously computed for all Fourier terms in the boundary element formulation. The improved efficiency of the method compared to a Gaussian quadrature based integration algorithm is illustrated by some example calculations. The proposed method is not only usable for acoustic problems in particular, but for Fourier BEM in general. ©1997 Acoustical Society of Americ
Originele taal-2 Engels 1394-1401 Journal of the Acoustical Society of America 102 3 https://doi.org/10.1121/1.420099 Gepubliceerd - 1997

### Vingerafdruk

boundary element method
formulations
acoustics
Fourier series
Acoustics

### Citeer dit

title = "An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration",
abstract = "Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be calculated for every Fourier term. These integrals were formerly treated for each Fourier term separately. In this paper a new method is proposed to calculate these integrals using fast Fourier transform techniques. The advantage of this integration method is that the integrals are simultaneously computed for all Fourier terms in the boundary element formulation. The improved efficiency of the method compared to a Gaussian quadrature based integration algorithm is illustrated by some example calculations. The proposed method is not only usable for acoustic problems in particular, but for Fourier BEM in general. {\circledC}1997 Acoustical Society of Americ",
author = "A.H.W.M. Kuijpers and G. Verbeek and J.W. Verheij",
year = "1997",
doi = "10.1121/1.420099",
language = "English",
volume = "102",
pages = "1394--1401",
journal = "Journal of the Acoustical Society of America",
issn = "0001-4966",
publisher = "Acoustical Society of America",
number = "3",

}

An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration. / Kuijpers, A.H.W.M.; Verbeek, G.; Verheij, J.W.

In: Journal of the Acoustical Society of America, Vol. 102, Nr. 3, 1997, blz. 1394-1401.

TY - JOUR

T1 - An improved acoustic Fourier boundary element method formulation using fast Fourier transform integration

AU - Kuijpers, A.H.W.M.

AU - Verbeek, G.

AU - Verheij, J.W.

PY - 1997

Y1 - 1997

N2 - Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be calculated for every Fourier term. These integrals were formerly treated for each Fourier term separately. In this paper a new method is proposed to calculate these integrals using fast Fourier transform techniques. The advantage of this integration method is that the integrals are simultaneously computed for all Fourier terms in the boundary element formulation. The improved efficiency of the method compared to a Gaussian quadrature based integration algorithm is illustrated by some example calculations. The proposed method is not only usable for acoustic problems in particular, but for Fourier BEM in general. ©1997 Acoustical Society of Americ

AB - Effective use of the Fourier series boundary element method (FBEM) for everyday applications is hindered by the significant numerical problems that have to be overcome for its implementation. In the FBEM formulation for acoustics, some integrals over the angle of revolution arise, which need to be calculated for every Fourier term. These integrals were formerly treated for each Fourier term separately. In this paper a new method is proposed to calculate these integrals using fast Fourier transform techniques. The advantage of this integration method is that the integrals are simultaneously computed for all Fourier terms in the boundary element formulation. The improved efficiency of the method compared to a Gaussian quadrature based integration algorithm is illustrated by some example calculations. The proposed method is not only usable for acoustic problems in particular, but for Fourier BEM in general. ©1997 Acoustical Society of Americ

U2 - 10.1121/1.420099

DO - 10.1121/1.420099

M3 - Article

VL - 102

SP - 1394

EP - 1401

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 3

ER -