Optimization of parallel method of moments based on KNL many-core processors
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摘要: 基于Intel第二代Xeon Phi代号为Knights Landing（KNL）众核处理器平台，利用MPI+OpenMP混合编程策略对并行矩量法（Method of Moments，MoM）进行了优化.利用OpenMP编程技术和KNL的计算资源，提高了CPU（Center Processing Unit）使用率；线程的引入，大幅度减少了矩阵填充过程中进程间的冗余积分；为发挥KNL的512位矢量宽度优势，通过向量化优化进一步提高了循环结构的执行效率；对计算密集型、CPU利用率高的矩阵求解过程，通过引入的OpenMP编程策略，减少了MPI（Message Passing Interface）通信时间，加速了求解.数值结果表明，通过在KNL众核处理器平台上的优化，可以极大地提升矩量法计算复杂电磁问题的效率.
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关键词:
- 众核处理器 /
- MPI+OpenMP /
- 并行矩量法 /
- 向量化
Abstract: The parallel method of moments (MoM) is successfully optimized using the MPI+OpenMP hybrid programming strategy, based on the second-generation Intel Xeon Phi many-core processor platform, codenamed Knights Landing (KNL). Using OpenMP programming technology, the utilization rate of the CPU (Center Processing Unit) is increased, and the computing resources of KNL are fully utilized. The introduction of threads substantially reduces the inter-process redundant integrals in the filling matrix process. In order to give full play to the advantage of KNL's 512-bit vector width, the efficiency of the loop structure is further enhanced through vector optimization. For the matrix solution process, which typically requires intensive computation and high CPU utilization, MPI (Message Passing Interface) communication time is reduced and the solution process is accelerated by introducing an OpenMP programming strategy. Numerical results show that the efficiency of solving complex electromagnetic problems by parallel MoM is greatly improved through optimization on the KNL many-core processor platform.-
Key words:
- many-core processor /
- MPI+OpenMP /
- parallel method of moments (MoM) /
- vectorization
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图 4 矩阵填充MPI+OpenMP优化伪代码
Fig. 4 Pseudo-code of optimization using MPI+OpenMP for the filling matrix
表 1 矩阵填充向量化优化结果
Tab. 1 Results of vector optimization for the filling matrix
进程网格 矩阵填充/s 矩阵填充效率提升/% 优化前 8$\times $8 766.94 — 向量化优化 8$\times $8 681.87 11.09 
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表 2 矩阵填充过程积分次数测试
Tab. 2 Integral numbers of the filling matrix
进程数目 进程网格 线程数目 总积分次数 冗余次数 冗余比例/% 串行 1 1 1 1529435664 0 0 优化前 64 8$\times $8 1 5129137924 3599702260 70.18 优化后 2 1$\times$2 128/32 2293527768 764092104 33.32 4 2$\times $2 64/16 3439353316 1909917652 55.53 8 2$\times $4 32/8 4069270002 2539834338 62.41 16 4$\times $4 16/4 4814555769 3285120105 68.23 注:线程数目一列中, $m/n$表示矩阵填充和矩阵求解在每个节点分别开启$m$和$n$个OpenMP线程.
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表 3 运行时间对比
Tab. 3 Comparison of running time
进程网格 线程数目 矩阵填充/s 矩阵求解/s 总时间/s 总加速倍数 优化前 8$\times $8 1 766.94 255.27 1022.21 — 优化后 1$\times$2 128/32 230.20 285.76 515.96 1.98 2$\times$2 64/16 131.91 258.49 390.40 2.62 2$\times$4 32/8 153.16 261.16 414.32 2.47 4$\times$4 16/4 177.24 259.23 436.47 2.34 注:线程数目一列中, $m/n$表示矩阵填充和矩阵求解在每个节点分别开启$m$和$n$个OpenMP线程.
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表 4 矩阵填充过程积分次数测试
Tab. 4 Integral numbers of the filling matrix
进程数目 进程网格 线程数目 总积分次数 冗余次数 冗余比例/% 串行 1 1 1 22937708304 0 0 优化前 512 16$\times $32 1 87453385158 64515676854 73.77 优化后 8 2$\times$4 256/64 61178300578 38240592274 62.51 16 4$\times $4 128/32 71538061156 48600352852 67.94 32 4$\times $8 64/16 76226472670 53288764355 69.91 64 8$\times $8 32/8 81222150025 58284441721 71.76 128 8$\times $16 16/4 84157313530 61219605226 72.74 注:线程数目一列中, $m/n$表示矩阵填充和矩阵求解在每个节点分别开启$m$和$n$个OpenMP线程.
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表 5 运行时间对比
Tab. 5 Comparison of running time
进程网格 线程数目 矩阵填充/s 矩阵求解/s 总时间/s 总加速倍数 优化前 16$\times $32 1 7977.94 3079.69 11057.63 - - 优化后 2$\times$4 256/64 1124.01 3261.46 4385.46 2.52 4$\times $4 128/32 715.20 3231.76 3946.96 2.80 4$\times $8 64/16 601.36 2449.08 3050.44 3.62 8$\times $8 32/8 810.63 2947.81 3758.44 2.94 8$\times $16 16/4 1243.13 3081.21 4324.35 2.56 注:线程数目一列中, $m/n$表示矩阵填充和矩阵求解在每个节点分别开启$m$和$n$个OpenMP线程.
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