Abstract

An extension to quadrilateral elements of the fully numerical method DIRECTFN, originally developed for the evaluation of 4-D singular integrals over triangular elements arising in Galerkin surface integral equation formulations, is presented. More specifically, a series of coordinate transformations together with integral re-orderings are applied in order to regularize the associate singular kernels in the case of coincident observation and source elements. The final expressions can be easily computed to machine precision by means of simple Gaussian quadrature rules, while the overall efficiency can be further improved by a judicious choice of the integration order of the resulting four 1-D integrals.

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