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A new version of the weighted averages (WA) algorithm, called generalized WA, is introduced. Generalized WA exhibit a more compact formulation, devoid of iterative and recursive steps, and a wider range of applications. It is more robust, as it provides a unique formulation, valid for real and imaginary parameters. The implementation of the new version is easier and more economical in terms of basic...
The Double Exponential (DE) quadrature rule is modified in order to efficiently integrate the observation domain of the 4-D weakly singular integrals arising in Mixed Potential Integral Equation (MPIE) formulations. Although, the original DE rule already guarantees numerically exact results, it results in poor convergence when compared to widely used interpolatory quadratures like Gauss Legendre (GL),...
In this paper, the direct evaluation method is outlined for the computation of the hypersingular integrals arising in Galerkin surface integral equation formulations. The key feature of the proposed scheme lies on the appropriate regularization of the singular integrand together with the reduction of the dimensionality of the original integral from 4-D to 2-D. The procedure presented herein succeed...
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