Analysis of Multiscale Problems Using the MLFMA With the Assistance of the FFT-Based Method

A new method for analysis of multiscale problems using the multilevel fast multipole algorithm (MLFMA) is proposed. In this method, the MLFMA bears the main part of the computation at the macro level, while some FFT-based method is responsible for the computation on the subregion with finer meshes. With this strategy, a reasonable balance between the computational efficiency and storage efficiency can be achieved in the case when the local regions with tiny geometry features are relatively centralized. The new method has been compared with several existing methods, including the hybrid method of the MLFMA and LF-FIPWA, the MLFMA equipped with the hybrid tree structure (HTS), and the MLFMA with the near-matrix compression, such as the ID-MLFMA and the MLFMA-ACA. Numerical examples are provided to demonstrate the correctness and efficiency of the proposed method.