SUPERCOMPUTER AWARE APPROACH FOR THE SOLUTION OF CHALLENGING ELECTROMAGNETIC PROBLEMS
SUPERCOMPUTER AWARE APPROACH FOR THE SOLUTION OF CHALLENGING ELECTROMAGNETIC PROBLEMS
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DOI：
10.2528/pier09121007
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发表时间：
2010
影响因子：
6.7
通讯作者：
M. Araújo;J. M. Taboada;F. Obelleiro;Jose Manuel Bertolo;L. Landesa;Javier Rivero;J. Rodríguez
中科院分区：
文献类型：
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作者：
M. Araújo;J. M. Taboada;F. Obelleiro;Jose Manuel Bertolo;L. Landesa;Javier Rivero;J. Rodríguez
对传统快速多极子方法(FMM)的快速傅立叶变换(FFT)进行扩展，降低了矩阵向量积(MVP)的复杂度，并保持了单级FMM的并行缩放倾向，这是一个事实。本文提出了一种高效的FMM-FFT算法嵌套变体的并行策略，减少了对内存的需求。这种并行实现为一个具有超过5亿个未知数的挑战问题提供了解决方案，并在2009年初创造了计算电磁学(CEM)的世界纪录。近年来，与传统的矩量法相比，随着计算成本的降低，快速而有效的电磁场解的发展趋势越来越明显。其中，快速多极子方法(FMM)[1]及其多层形式MLFMA[2，3]构成了这方面最重要的进展之一。这种快速电磁求解器的发展与计算机技术的不断进步是齐头并进的。由于这种同步增长，为了利用现代高性能计算机系统中可用的大量计算资源和能力，克服可用代码可伸缩性的限制成为当务之急。为此，多层快速多极算法的并行化改进[4{13]在过去几年中引起了人们的兴趣。此外，快速傅立叶变换(FMM-FFT)应该被考虑作为大规模并行分布式计算机中有益的fl的替代方案。这种单级FMM的变种是fl在[14]中首次提出的，作为一种应用于几乎大多数平面表面的加速技术。后来，一种并行实现被应用于一般的三维几何[15]。该方法使用快速傅立叶变换来加速翻译阶段，从而大大减少了相对于快速傅立叶变换的矩阵向量积(MVP)时间需求。虽然通常情况下，FMM-FFT在算法上不像MLFMA一样有效，但它的优点是在谱(
Abstract|It is a proven fact that The Fast Fourier Transform(FFT) extension of the conventional Fast Multipole Method (FMM)reduces the matrix vector product (MVP) complexity and preservesthe propensity for parallel scaling of the single level FMM. In thispaper, an e–cient parallel strategy of a nested variation of the FMM-FFT algorithm that reduces the memory requirements is presented.The solution provided by this parallel implementation for a challengingproblem with more than 0.5 billion unknowns has constituted the worldrecord in computational electromagnetics (CEM) at the beginning of2009.1. INTRODUCTIONRecent years have seen an increasing efiort in the development of fastand e–cient electromagnetic solutions with a reduced computationalcost regarding the conventional Method of Moments. Among others,the Fast Multipole Method (FMM) [1] and its multilevel version, theMLFMA [2,3] have constituted one of the most important advances inthat context.This development of fast electromagnetic solvers has gone handin hand with the constant advances in computer technology. Dueto this simultaneous growth, overcoming the limits in the scalabilityof the available codes became a priority in order to take advantageof the large amount of computational resources and capabilities thatare available in modern High Performance Computer (HPC) systems.For this reason, works focused on the parallelization improvement ofthe Multilevel Fast Multipole Algorithm (MLFMA) [4{13] have gainedinterest in last years.Besides, the FMM-Fast Fourier Transform (FMM-FFT) deservesbe taken into account as an alternative to beneflt from massivelyparallel distributed computers. This variation of the single-level FMMwas flrst proposed in [14] as an acceleration technique applied to almostplanar surfaces. Later on, a parallelized implementation was applied togeneral three-dimensional geometries [15]. The method uses the FFTto speedup the translation stage resulting in a dramatic reduction ofthe matrix-vector product (MVP) time requirement with respect tothe FMM. Although in general the FMM-FFT is not algorithmically ase–cient as the MLFMA, it has the advantage of preserving the naturalparallel scaling propensity of the single-level FMM in the spectral (