Direct evaluation of double singular integrals and new free terms in 2D (symmetric) Galerkin BEM

Abstract : In this paper a new general algorithm is developed for the direct evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular integrals are treated as a whole, that is, not as inner integrals followed by outer ones. Therefore, when applied to the symmetric Galerkin BEM, the proposed technique is strictly symmetry preserving. Moreover, a careful analysis of the limiting process is performed which shows that some new free terms may arise.
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Marc Bonnet, Massimo Guiggiani. Direct evaluation of double singular integrals and new free terms in 2D (symmetric) Galerkin BEM. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2003, 192, pp.2565-2596. ⟨10.1016/S0045-7825(03)00286-X⟩. ⟨hal-00092398⟩

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