Adaptive spatial decomposition in fast multipole method

This work presents a new adaptive node-cluster algorithm for fast multipole method. In the algorithm, we use rectangular boxes instead of cubes, subdivide a box based on its shape, and tighten the child boxes at each subdivision step. More importantly, we determine the number of expansion terms in multipole to local translations according to the distance between the two interaction boxes. Our method is tested using benchmark examples for three-dimensional potential problems. The results obtained show that the new algorithm can solve a problem with 100 thousands nodes in about 20 min, and runs nearly three times faster than the standard algorithm. The proposed algorithm is especially suitable for treating slender and shell-like structures.