The MLFMA Equipped with a Hybrid Tree Structure for the Multiscale EM Scattering

Abstract

We present an efficient strategy for reducing the memory requirement for the near-field matrix in the multilevel fast multipole algorithm (MLFMA) for solving multiscale electromagnetic (EM) scattering problems. A multiscale problem can obviously lower the storage efficiency of the MLFMA for the near-field matrix. This paper focuses on overcoming this shortcoming to a certain extent. A hybrid tree structure for the MLFMA that possesses two kinds of bottom-layer boxes with different edge sizes will be built to significantly reduce the memory requirement for the near-field matrix in the multiscale case compared with the singletree-structure technique. Several numerical examples are provided to demonstrate the efficiency of the proposed scheme in the multiscale EM scattering.

A Novel Broadband Multilevel Fast Multipole Algorithm With Incomplete-Leaf Tree Structures for Multiscale Electromagnetic Problems

“…In fact, a direct extension of the adaptive FMM would be less accurate compared with the proposed IL-MLFMA and it would yield problems when parallelization is concerned, as briefly explained in Section III. We note that the concept of using a simple hybrid tree structure for a multiscale problem was proposed in [23] with only two different box sizes at the leaf level.…”

Broadband multilevel fast multipole algorithm for large-scale problems with nonuniform discretizations

“…In addition, various broadband MLFMA implementations, which effectively combine low-frequency and high-frequency techniques for efficient and stable computations of interactions in different electromagnetic regimes, have been developed [15]- [25]. On the other hand, algorithmic routines, such as efficiently organizing near-field and far-field interactions, especially on nonuniform discretizations that arise in multiscale structures, have not been considered in sufficient depth [26]. In fact, without a multiscale construction of tree structures, broadband solvers may not provide accurate and/or efficient solutions that benefit from the true power of MLFMA.…”