Solving 3D electromagnetic scattering and radiation by local multilevel fast multipole algorithm

As the fastest integral equation solver up to now, multilevel fast multipole algorithm (MLFMA) has been applied successfully to solve electromagnetic scattering and radiation from 3D electrically large object. But for very large scale problems, the storage and CPU time required in MLFMA are still expensive. In this paper, a local multilevel fast multipole algorithm (LMLFMA) is proposed to further speed up the efficiency of MLFMA in conjugate gradient (CG) iteration. In the LMLFMA, only the local interactions between the subscatters are taken into account. And, the interaction regions in iteration are varying adaptively with iterative current density. With decrease of iterative error, iterative current density tends to real one, the interaction regions required are diminishing. When the iterative error is less than a critical iteration error, only the interaction between nearby regions at the finest level is considered. Numerical results show that the LMLFMA has good accuracy, and much better efficiency than traditional MLFMA.