Abstract
This study investigates the dramatic drop of the numerical accuracy of the boundary element method (BEM) in near-boundary regions, where we encounter “nearly singular” integrals as the field point approaches the boundary source points. In this study, a previously developed nonlinear coordinate transformation technique based on the sinh function is further extended in a more flexible fashion to allow the accurate evaluation of the nearly singular integrals which arise in general three-dimensional (3D) elasticity problems. The implementation of this transformation technique is straightforward and can be applied to any type and order of the fundamental solutions or Green's functions considered. Our numerical experiments verify that the proposed approach can improve the near-boundary solution accuracy of the BEM by several orders of magnitude in terms of the relative errors. The BEM solution is accurate even at the calculation points very close to the boundary with a relative distance of 10−7.
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