A numerical method for volume integral equations based on the wave-number domain formulation

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The advantage of the volume integral equation is in that it is possible to clarify the relationship between fluctuations of the wave field and radiation of waves. It is necessary, however, to hadle a dense and large size matrix to solve the volume integral equation in the case that the region for the fluctuation of the wave field spreads to a wider area. In this paper, a numerical method is proposed to obtain a sparse matrix for the volume integral integral equation. The formulation employed here is based on the wavenumber domain solution together with usage of the Haar scaling functions. The usage of the unitarity of the Fourier transform in terms of the Haar scaling functions reveals that the integral equation is transformed into a linear algebraic equation with a sparse matrix. Numerical calculations are carried out to verify the present forrnuluation.

Original languageEnglish
Pages (from-to)132-142
Number of pages11
JournalDoboku Gakkai Ronbunshuu A
Issue number1
Publication statusPublished - 1 Dec 2006



  • Acoustic wave field
  • Ilaar scaling function
  • Sparse matrix
  • Uni-tarity of fourier transform
  • Volume integral equation
  • Wavenumber domain formulation

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