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On the parallelization of electrodynamic multilevel fast multipole method on distributed memory computers

机译:在分布式存储器计算机上的电动多级快速多极法的平行化

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In recent years, the Multilevel Fast Multipole Method (MLFMA) has been developed into one of the most powerful techniques for accelerating the iterative solution of integral equations of electromagnetics. It has been shown that the MLFMA reduces the computational complexity of a matrix-vector multiply from O(N/sup 2/) to O(N log N), where N is the number of unknowns. In an attempt to extend the range of problems that can be solved using this technique, we have recently developed an application independent, parallel MLFMA kernel, called ScaleME, for distributed memory computers using MPI. In this paper, we shall discuss the characteristic features which distinguishes it from its static counterpart, such as work required for each level, the size of multipole expansions and interpolation/filtering operations, and their influence in the parallel algorithm design. We shall follow it with a discussion of major issues in the parallelization which are unique to the dynamic MLFMA, such as reducing the memory requirements for translation operators and the reduction of replicated geometric data structures. We shall also briefly discuss the load balancing strategies. Finally, we shall present some representative numerical results from some ScaleME accelerated electromagnetic scattering codes, including a simulation involving 4 million unknowns and that of the radar cross-section computation of a full scale aircraft on a Beowulf class cluster.
机译:近年来,多级快速多极方法(MLFMA)已经开发为加速电磁Intental等方程的迭代解之一的一种最强大的技术之一。已经表明,MLFMA从O(n / sup 2 /)到o(n log n)降低了矩阵矢量的计算复杂度,其中n是未知数的数量。在尝试扩展使用该技术可以解决的问题范围,我们最近开发了一个独立,并行MLFMA内核的应用程序,称为Scaleme,用于使用MPI的分布式存储器计算机。在本文中,我们将讨论将其与静态对应物区分开的特征,例如每个级别所需的工作,多极扩展和插值/过滤操作的工作,以及它们对并行算法设计的影响。我们将讨论对动态MLFMA独有的并行化中的主要问题,例如降低转换运算符的内存要求和复制的几何数据结构的减少。我们还应简要介绍负载平衡策略。最后,我们将介绍一些Scaleme加速电磁散射代码的一些代表性数值结果,包括涉及400万个未知数的模拟,以及Beowulf类集群上全尺度飞机的雷达横截面计算的模拟。

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