A non-linear transformation applied to boundary layer effect and thin-body effect in BEM for 2D potential problems

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Abstract
The accurate numerical evaluation of nearly singular integrals plays an important role in many engineering applications. In general, these include evaluating the solution near the boundary or treating problems with thin domains, which are respectively named the boundary layer effect and the thin-body effect in the boundary element method. Although many methods of evaluating nearly singular integrals have been developed in recent years with varying degrees of success, questions still remain. In this article, a general non-linear transformation for evaluating nearly singular integrals over curved two-dimensional (2D) boundary elements is employed and applied to treat boundary layer effect and thin-body effect occurring in 2D potential problems. The introduced transformation can remove or damp out the rapid variations of nearly singular kernels and extremely high accuracy of numerical results can be achieved without increasing other computational efforts. Extensive numerical experiments indicate that the proposed transformation will be more efficient, in terms of the necessary integration points and central processing unit-time, compared to previous transformation methods, especially for dealing with thin-body problems.

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