Fast multipole method as an efficient solver for 2D elastic wave surface integral equations

Y. H. Chen, W. C. Chew, S. Zeroug

Research output: Contribution to journalArticlepeer-review


The fast multipole method (FMM) is very efficient in solving integral equations. This paper applies the method to solve large solid-solid boundary integral equations for elastic waves in two dimensions. The scattering problem is first formulated with the boundary element method. FMM is then introduced to expedite the solution process. By using the FMM technique, the number of floating-point operations of the matrix-vector multiplication in a standard conjugate gradient algorithm is reduced from O(N2) to O(N1.5), where N is the number of unknowns. The matrix-filling time and the memory requirement are also of the order N1.5. The computational complexity of the algorithm is further reduced to 0(N4/3) by using a ray propagation technique. Numerical results are given to show the accuracy and efficiency of FMM compared to the boundary element method with dense matrix.

Original languageEnglish (US)
Pages (from-to)495-506
Number of pages12
JournalComputational Mechanics
Issue number6
StatePublished - 1997
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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