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The use of simple solutions in the regularization of hypersingular boundary integral equations. (English) Zbl 0728.73081
This paper presents the regularization of hypersingular integral equations which are derived from the strongly singular integral representation of the normal derivative of the potential field by approaching the internal point to the boundary and interpreting the strongly singular integrals in the sense of Hadamard finite part. The elimination of the strongly singular integrals is based on the superposition of the potential field considered and the linearly distributed field. Nonconforming linear elements are employed for the numerical implementation. The method can be extended also to elasticity problems. No confrontation is made with another known regularization technique leaving direct evaluation of the strong singularities, too.

74S15 Boundary element methods applied to problems in solid mechanics
65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type
74R99 Fracture and damage
Full Text: DOI
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