The use of simple solutions in the regularization of hypersingular boundary integral equations.

*(English)*Zbl 0728.73081This 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.

Reviewer: V.SlĂˇdek (Bratislava)

##### MSC:

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 |

##### Keywords:

strongly singular integral representation; normal derivative; potential field; Nonconforming linear elements; regularization
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\textit{T. J. Rudolphi}, Math. Comput. Modelling 15, No. 3--5, 269--278 (1991; Zbl 0728.73081)

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##### References:

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