A Fast Boundary Integral Solution for the Acoustic Response of Three-Dimensional Axi-Symmetric Scatterers

Gerard T. Schuster*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations


A Boundary Integral Equation (BIE) method is presented which efficiently computes the harmonic acoustic response of axi-symmetric structures. The key idea is that the BIE's are Fourier transformed via FFT's in the azimuthal variable; this reduces the azimuthal periodic convolutions to simple multiplications. The original three-dimensional problem is transformed into a series of M decoupled two-dimensional problems, where M is the number of azimuthal Fourier components. If N is the number of nodal points along the semi-perimeter of a scatterer, then the harmonic response can be computed with just O(N3M) algebraic operations. This is far less expensive than solving the original problem which requires O(N6) algebraic operations per frequency. Moreover, the active memory requirement is reduced from O(N4) to O(N2) complex words, and the algorithm is ideally suited to a parallel computer. Examples are given where less than three minutes were required by a Gould computer (4 MIPs) to compute the harmonic response of a scatterer four wavelengths in dimension.

Original languageEnglish (US)
Title of host publicationHandbook of Geophysical Exploration
Subtitle of host publicationSeismic Exploration
Number of pages27
StatePublished - Jan 1 1989
Externally publishedYes

Publication series

NameHandbook of Geophysical Exploration: Seismic Exploration
ISSN (Print)0950-1401

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Geophysics
  • Geology


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