On the implementation of 3D Galerkin boundary integral equations

• Autores: Sylvain Nintcheu Fata, J.J. Gray
• Localización: Engineering analysis with boundary elements, ISSN 0955-7997, Vol. 34, Nº. 1, 2010, págs. 60-65
• Idioma: inglés
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• Resumen

  • In this article, a reverse contribution technique is proposed to accelerate the construction of the dense influence matrices associated with a Galerkin approximation of hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of the preconditioner is implicitly built by employing an incomplete LU factorization. Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate the performance and validity of the proposed techniques.