A Systematic Approach for the Development of Weakly--Singular BIEs
Z. D. Han and S. N. Atluri

doi:10.3970/cmes.2007.021.041
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 21, No. 1, pp. 41-52, 2007
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Keywords boundary integration equation, regularization, decomposition.
Abstract Straight-forward systematic derivations of the weakly singular boundary integral equations (BIEs) are presented, following the simple and directly-derived approach by Okada, Rajiyah, and Atluri (1989b) and Han and Atluri (2002). A set of weak-forms and their algebraic combinations have been used to avoid the hyper-singularities, by directly applying the ``intrinsic properties'' of the fundamental solutions. The systematic decomposition of the kernel functions of BIEs is presented for regularizing the BIEs. The present approach is general, and is applied to developing weakly-singular BIEs for solids and acoustics successfully.
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