A general algorithm for numerical evaluation of nearly singular integrals over high-order geometry elements in 3D BEM

The accurate evaluation of nearly singular boundary integrals is an important issue in BEM. Several techniques have been developed in recent years, with various degree of success, but it should be stressed that the boundary geometry is depicted essentially by using lower-order elements in those approaches. However, a high level of the geometry approximation in BEM is desired in many applications, and the usage of high-order elements can meet this requirement. In this study, we propose a general methodology for computation of the nearly singular integrals with using high-order surface elements in 3D BEM. Using two benchmark solutions for potential problems we demonstrate the high efficiency and the stability of the proposed scheme, even when the internal point is very close to the boundary.