A generalized SOR method for dense linear systems of boundary element equations

K. Davey, S. Bounds

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper an iterative scheme of first degree is developed for the purpose of solving linear systems of boundary element equations of the form Hx = c where H is a dense square nonsingular matrix. The iterative scheme considered is (D + (ΩH)sl)x(k+1) = (D- (ΩH)u)x(k) + Ωc, where (ΩH)u and (ΩH)sl are defined as the upper triangular and strictly lower triangular terms of ΩH, respectively. The parameter matrix Ω is selected to minimize the Frobenius norm ∥D - (ΩH)u∥F. Mathematical arguments and numerical experiments are presented to show that minimizing ∥D - (ΩH)u∥F provides for faster convergence. Numerical tests are performed for systems of boundary element equations generated by three-dimensional potential and elastostatic problems. Computation times are determined and compared against those for Gaussian elimination and Gauss-Seidel iteration.

Original languageEnglish
Pages (from-to)953-967
Number of pages15
JournalSIAM Journal of Scientific Computing
Volume19
Issue number3
DOIs
Publication statusPublished - May 1998

Keywords

  • Boundary elements
  • SOR

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