A modified dual-level fast multipole boundary element method for large-scale three-dimensional potential problems

A modified dual-level fast multipole boundary element method is proposed in this article. The core idea of the method is to use a dual-level structure to handle the excessive storage requirement and ill-conditioned problems resulting from the fully-populated interpolation matrix of the boundary element method. On one hand, the fully-populated matrix is transformed to a locally supported sparse matrix on fine mesh. On the other hand, the dual-level structure helps the method to evaluate far-field interactions only by the coarse mesh. This study combines the fast multipole method with the modified dual-level boundary element method to further expedite its matrix vector multiplications process. The complexity analysis shows that the method has O(N) operations and memory requirements in simulation of potential problems. In some specific examples where the obtained interpolation matrices have high condition number (L2-norm), the method is about 75% faster than the original fast multipole boundary element method. In addition, a large-scale potential problem with up to 3 million degree of freedoms is simulated successfully on a single laptop.