The evaluation of nearly singular integrals in the direct regularized boundary element method

The numerical analysis of boundary layer effect is one of the major concerned problems in boundary element method (BEM). The accuracy of this problem depends on the precision of the evaluation of the nearly singular integrals. In the boundary element analysis with direct formulation, the hyper-singular integral will arise from the potential derivative boundary integral equations (BIEs). Thus the nearly strong singular and hyper-singular integrals need to be calculated when the interior points are very close to the boundary. For nearly hyper-singular integrals, it is thought, generally, more difficult to calculate. In this paper, a general nonlinear transformation is adopted and applied to calculating the potential and its derivative at the interior points very close to the boundary. Numerical examples demonstrate that the present algorithm is efficient and can overcome the boundary layer effect successfully even when the interior points are very close to the boundary.