An Adaptive Element Division Algorithm for Accurate Evaluation of Singular and Near Singular Integrals in 3d

Abstract

An adaptive algorithm for evaluation of singular and near singular integrals in 3D is presented. The algorithm is based on successive adaptive/selective subdivisions of the element until a prescribed error criteria is met. For evaluating the integrals in each subdivision, Gauss quadrature is applied. The method is computationally simple, memory efficient and can be applied for both triangular and quadrilateral elements, including the elements with nonplanar and/or curved surfaces. To assess the method, several examples are discussed. It has shown that the algorithm performs well for singular and near-singular integral examples presented in the paper and evaluates the integrals with very high accuracy.