Using a hybrid tree structure in the MLFMA in the multi-resolution case

The multilevel fast multipole algorithm (MLFMA) has been used in calculating electromagnetic scatterings from electrically large objects. The octree structure plays an important role in the MLFMA. However, in the multi-resolution case, a single octree structure may produce a larger near-field matrix. In this paper, in order to overcome this shortcoming to a certain extent, a hybrid tree structure scheme is proposed. In this scheme, there are two kinds of bottom-layer cubes with different edge size. With the hybrid tree structure, the memory requirement for the near matrix can be significantly reduced in the multi-resolution case compared with the MLFMA equipped with a single octree structure. Numerical examples are provided to demonstrate the efficiency of the proposed scheme.