A fast multipole method accelerated adaptive background cell-based domain integration method for evaluation of domain integrals in 3D boundary element method

Abstract

A background cell-based domain integration method is proposed in this paper for evaluating domain integrals in 3D problems. The cells are created by an adaptive oct-tree structure based on the information of boundary elements, and no other discretization is needed. Cells that contain boundary elements can be subdivided into smaller sub-cells adaptively to obtain the desired accuracy according to the sizes and levels of the boundary elements. Applying the method directly in the boundary element method is time-consuming since the time complexity is O(NM), where N and M are the numbers of nodes and cells, respectively. The fast multipole method is coupled with the cell-based domain integration method to further accelerate the computational efficiency, and the main formulations are introduced in this paper. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.