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New identities for fundamental solutions and their applications to non-singular boundary element formulations. (English) Zbl 0969.74073
Summary: Based on a general operational approach, we establish two new integral identities for the fundamental solutions of potential and elastostatic problems. Non-singular forms of the conventional boundary integral equations (BIEs) are derived by employing these two identities for fundamental solutions, and by using the two-term subtraction technique. Both the strongly (Cauchy type) and weakly singular integrals existing in the conventional BIEs are removed from the BIE formulation. The existence of non-singular forms of conventional BIEs raises new questions about the smoothness requirement in the boundary element method, since the two-term subtraction requires, theoretically, $$C^1$$ continuity of the density function, rather than the $$C^0$$ continuity as required by the original singular or weakly singular forms of conventional BIEs. Implication of the non-singular BIEs on the smoothness requirement are discussed in this paper.

##### MSC:
 74S15 Boundary element methods applied to problems in solid mechanics 74B05 Classical linear elasticity 31B10 Integral representations, integral operators, integral equations methods in higher dimensions
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