A binary-tree element subdivision method for evaluation of nearly singular domain integrals with continuous or discontinuous kernel

Abstract

An adaptive and efficient volume element subdivision method using binary tree for evaluation of nearly singular domain integrals with continuous or discontinuous kernel in three-dimensional (3-D) boundary element method (BEM) has been presented. In the Conventional Subdivision Method (CSM) for evaluation of nearly singular integrals, the patches are obtained by simply connecting the source point with each vertex of the element. Thus, the accuracy of the integral obtained with CSM is easily affected by the shape of the element and the location of the source point. In contrast, the proposed Binary-Tree Subdivision Method (BTSM) is more convenient to implement and can guarantee successful patch generation under any circumstances for accurate evaluation of nearly singular domain integrals with continuous or discontinuous kernel. Numerical results for volume elements of arbitrary type with various relative locations of the source point demonstrate robustness, accuracy and efficiency of the proposed method. • The BTSM is proposed for evaluating nearly singular integrals with various kernel. • The BTSM is applicable to different kinds of volume element with arbitrary shape. • The BTSM is more convenient to implement by the single binary-tree data structure. • The BTSM can guarantee the convergence of element subdivision in any situation. • The BTSM possesses better accuracy and efficiency than the conventional method.