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

Abstract 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.

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