May the singular integrals in BEM be replaced by Zero?

Steffen Börm, Nico Krzebek, and Stefan A. Sauter

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Submission date: 08. Oct. 2003
Pages: 17
published in: Computer methods in applied mechanics and engineering, 194 (2005) 2-5, p. 383-393 
DOI number (of the published article): 10.1016/j.cma.2004.03.016
Bibtex
MSC-Numbers: 45B05, 65M39
Keywords and phrases: bem, numerical quadrature, singular integrals
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Abstract:

When approximating the singular integrals arising in the boundary element method by quadrature techniques, it is important to keep the quadrature error consistent with the discretization error in order to reach the optimal order of convergence. In classical approaches, this means that the order of the quadrature grows logarithmically in the number of degrees of freedom.

We present a quadrature scheme based on alternative representations of the singular integrands that allows us to use a constant quadrature order without giving up consistency.