高阶矩量法的超级电磁计算研究

矩量法是广泛使用的高精度电磁数值算法之一。在仿真复杂电磁问题时,该算法需要处理大型复数稠密矩阵方程,这导致其面临内存需求高、计算时间长的问题。与传统基函数相比,本文采用的高阶多项式基函数能够在保证计算精度的前提下大幅度降低未知量,进而降低矩阵阶数。在此基础上,本文设计了基于分块矩阵的高效并行策略,在国内超级计算机平台开展了并行高阶矩量法的超级电磁计算研究,大幅度提升了矩量法的仿真能力。在国产神威蓝光超级计算机上,以机载天线阵列的辐射特性计算为例,对并行规模高达30720 CPU核时的算法性能进行了评估,测试结果表明算法在并行规模扩大20倍以上时仍可获得50%以上的并行效率。在当前排名世界第一的天河2号超级计算机上,以飞机散射特性计算为例,对并行规模高达201600 CPU核时的算法性能进行了评估,测试结果表明算法在并行规模扩大约8倍时可获得50%以上的并行效率。数值仿真结果表明并行高阶矩量法可以在不同架构的超级计算机上高效完成复杂电大目标的精确电磁计算。

Study of Super Electromagnetic Computing for Higher-Order MoM

The method of moments (MoM) is one of the widely used and numerical accurate electromagnetic algorithms. It needs to deal with a large dense complex matrix equation when simulating complex electromagnetic problems, which results in high memory requirements and long computation time. Higherorder basis functions are utilized to significantly reduce the number of unknowns without loss of numerical accuracy and thus reduce the order of matrix compared with traditional basis functions. The parallel strategy is designed based on block partitioning of the matrix, and the super electromagnetic computing of the parallel higher-order MoM is studied with the Chinese supercomputers to greatly improve the capability of MoM. The radiation of an airborne array is used to verify the parallel performance of the algorithm using up to 30720 CPU cores on the Sunway BlueLight Supercomputer. The results show that an efficiency of higher than 50% is achieved when the number of CPU cores increases more than 20 times. The scattering of an airplane is simulated to further test the parallel performance using up to 201600 CPU cores on the Tianhe-2 Supercomputer that is ranked the fastest supercomputer in the world currently. The results show that one can achieve the efficiency of higher than 50% when the number of CPU cores increases about 8 times. Numerical results show that the parallel algorithm is able to efficiently solve complex electromagnetic problems on supercomputers with different architectures.