## 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 language | English |
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Pages (from-to) | 953-967 |

Number of pages | 15 |

Journal | SIAM Journal of Scientific Computing |

Volume | 19 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 1998 |

## Keywords

- Boundary elements
- SOR