A Hierarchical Partitioning Strategy for an Efficient Parallelization of the Multilevel Fast Multipole Algorithm

Abstract

Cataloged from PDF version of article.We present a novel hierarchical partitioning strategy\ud for the efficient parallelization of the multilevel fast multipole algorithm\ud (MLFMA) on distributed-memory architectures to solve\ud large-scale problems in electromagnetics. Unlike previous parallelization\ud techniques, the tree structure of MLFMA is distributed\ud among processors by partitioning both clusters and samples\ud of fields at each level. Due to the improved load-balancing, the\ud hierarchical strategy offers a higher parallelization efficiency than\ud previous approaches, especially when the number of processors\ud is large. We demonstrate the improved efficiency on scattering\ud problems discretized with millions of unknowns. In addition, we\ud present the effectiveness of our algorithm by solving very large\ud scattering problems involving a conducting sphere of radius 210\ud wavelengths and a complicated real-life target with a maximum\ud dimension of 880 wavelengths. Both of the objects are discretized\ud with more than 200 million unknowns

Mlfma-FFT Parallel Algorithm for the Solution of Large-Scale Problems in Electromagnetics

“…However, it is known that it suffers from bad parallel scaling on distributed memory computers. The difficulties faced in successfully parallelizing it in computer clusters have been widely discussed by many research groups [8,10,14,15]. Considering the favorable MLFMA features in shared-memory computers, and taking into account the high scalability behavior of the FMM-FFT in distributed computers while maintaining a low numerical complexity, a proper combination of both techniques seems to be a good alternative to take a step further after the works of [19] and [22].…”

“…For all these reasons, in last years the well-known Method of Moments [1] made way for acceleration techniques as the Fast Multipole Method (FMM) [2] and its multilevel version, the MLFMA [3,4]. In fact, the attention of many recent studies is concentrated on the improvement of the MLFMA parallelization over shared, distributed and mixed memory computers [5][6][7][8][9][10][11][12][13][14][15].…”

Hierarchical parallelisation strategy for multilevel fast multipole algorithm in computational electromagnetics

“…Simple parallelisation strategies usually fail to provide efficient solutions because of the communication among the processors and the unavoidable duplication of some of the computations over multiple processors [9]. In this Letter, we present a hierarchical strategy for the efficient parallelisation of MLFMA.…”

“…This strategy works efficiently for lower levels involving many clusters. For higher levels, however, it is difficult to distribute small numbers of clusters among the processors without duplication [9]. In addition, dense communications among the processors during the translations become significant for higher levels since large amounts of data are transferred, which reduces the efficiency of the parallelisation significantly [6,9].…”

“…For higher levels, however, it is difficult to distribute small numbers of clusters among the processors without duplication [9]. In addition, dense communications among the processors during the translations become significant for higher levels since large amounts of data are transferred, which reduces the efficiency of the parallelisation significantly [6,9]. To improve the parallelisation efficiency, a hybrid partitioning approach is introduced in [6], where different strategies are applied for lower and higher levels of the tree structure.…”