Abstract
A simple quadrature rule is proposed for the evaluation of one-dimensional quasi-singular integrals with a complex pole. The technique is based on the concept of synthetic division of two polynomials, as a means of regularizing the quasi-singularity, followed by a quadrature using the roots of shifted Legendre polynomials as fixed abscissas. This procedure is a generalization of the technique proposed in a previous paper for singularities due to a real pole. With this technique, it is even possible to conceive of procedures for the analytical or semi-analytical evaluation of most kinds of integrals that appear in a general boundary element formulation with curved elements.
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