A modified non--linear transformation method for evaluating weakly singular boundary element integrals
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Accurate numerical evaluation of boundary integrals is fundamental to producing useful results with the boundary element method. This paper introduces a generalisation of a recently introduced combined method (subtraction of singularity followed by a non-linear transformation), which takes into account the effect of the basis functions. The new method is applied to solve weakly singular integrals which arise in the solution of the two-dimensional Laplace equation. The new method was found, in the cases considered, to be numerically superior to both the combined method and any of the non-linear transformation methods.
Applied Mathematics and Computation
© 2004 Elsevier. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.