Application of sigmoidal transformations to weakly singular and near-singular boundary element integrals

Accurate numerical determination of line integrals is fundamental to reliab le implementation of the boundary element method. For a source point distan t from a particular element, standard Gaussian quadrature is adequate, as w ell as being the technique of choice. However, when the integrals are weakl y singular or nearly singular (source point near the element) this techniqu e is no longer adequate. Here ace-ordinate transformation technique, based on sigmoidal transformati ons, is introduced to evaluate weakly singular and near-singular integrals. A sigmoidal transformation has the effect of clustering the integration po ints towards the endpoints of the interval of integration. The degree of cl ustering is:governed by the order of the transformation. Comparison of this new method with existing co-ordinate transformation tech niques shows that more accurate evaluation of these integrals can be obtain ed. Based on observations of several integrals considered, guidelines are s uggested for the order of the sigmoidal transformations. Copyright (C) 1999 John Wiley & Sons, Ltd.