基于国产众核超级计算机的6×105核并行矩量法

为实现电磁计算的安全可靠和自主可控,该文基于“天河二号”国产众核超级计算机平台,开展大规模并行矩量法(MoM)的开发工作。为减轻大规模并行计算时计算机集群的通信压力以及加速矩量法积分方程求解,通过分析矩量法电场积分方程离散生成的矩阵具有对角占优特性,提出一种新型LU分解算法,即对角块矩阵选主元LU分解(BDPLU)算法,该算法减少了panel列分解的计算量,更重要的是,完全消除了选主元过程的MPI通信开销。利用BDPLU算法,并行矩量法突破了6×105 CPU核并行规模,这是目前在国产超级计算平台上实现的最大规模的并行矩量法计算,其矩阵求解并行效率可达51.95%。数值结果表明,并行矩量法可准确高效地在国产超级计算平台上解决大规模电磁问题。

Parallel MoM Using the Six Hundred Thousand Cores on Domestically-made and Many-core Supercomputer

In order to realize safety, reliability and self-control of electromagnetic computing, the large-scale parallel MoM is studied based on domestically-made many-core supercomputer platform named " Tianhe-2”. A new LU decomposition algorithm named Block Diagonal matrix Pivoting LU decomposition (BDPLU) algorithm, is proposed by analyzing the diagonally dominant characteristics of the matrix generated through dispersing electric field integral equation of MoM, for the purpose of communication pressure reduction to computer cluster and solution acceleration to MoM integral equation during large-scale parallel computation. The BDPLU algorithm reduces the amount of calculation in the process of panel factorization. More importantly, the algorithm completely eliminates MPI communication when pivoting. Using BDPLU algorithm, the maximum number of CPU cores break through 6×105 CPU cores, which is the largest scale of parallel MoM computation in domestically-made and many-core supercomputing platform at present, and the parallel efficiency of solving matrix can reach 51.95%. Numerical results show that parallel MoM can accurately and efficiently solve large-scale electromagnetic field problems on domestic supercomputing platform.