A novel semi-analytic algorithm for evaluation of nearly singular integrals in boundary element analysis

A novel semi-analytic method is proposed to evaluate various nearly singular integrals accurately. Different from the traditional semi-analytical method, the Taylor expansion for shape functions, Jacobian, and so on in our method is based on the nearest point from a source point to an integral element rather than the projection point from the source point to the integral element. Therefore, it can more accurately approximate the distance from the source point to Gaussian integration points. Then, approximate expressions for the integrand functions of two-dimensional potential problems are derived. The effectiveness of the proposed method is verified by evaluating the calculation accuracy of physical quantities at points in different geometric models, and comparing it with the traditional semi-analytical method and distance transform method.