Modified Dual-Level Fast Multipole Algorithm For Three-Dimensional Potential Problems

A modified dual-level fast multipole algorithm is constructed for analyzing three-dimensional (3D) potential problems. The core idea of the method is to use a dual-level structure for handling the excessive storage requirement and illconditioning caused by the fully populated interpolation matrix. The algorithm uses the fast multipole method to expedite matrix vector multiplication processes. The boundary element method (BEM) is used as the basic method in the algorithm. The 3D potential model is used as the physical background to illustrate this novel algorithm. The complexity analysis shows that the method has O(N) operations and low memory requirements for a 3D potential model.

Keywords: Boundary element method, Fast multipole method, Modified dual-level algorithm, Three-dimensional potential model.