基于MPI的并行分布式高斯消元算法设计和评估

MPI-based Parallel Algorithm Design and Evaluation for Gaussian Elimination

为了满足电磁仿真数值计算日益增高的速度和精度的需求,针对单机内存需求和计算负荷需求都比较大的矛盾,提出基于分布式并行机群环境的并行计算划分和并行存储划分的算法设计思想,并且给出了基于行列循环数据划分的并行计算算法描述。在此基础上进行了实验验证,用MPI+FORTRAN和MPI+C编程实现了对大矩阵求逆的分布式高斯消元,并进行了性能评估和实验验证,在国内外超级计算中心平台上的实验结果表明所完成的工作对于系统的电磁仿真计算具有应用价值,该算法和代码实现可应用于电磁仿真计算的矩量法MOM(Method of Mom)中。

To address the problem of the conflicting requirements between memory need and computation payload of one single computer used for increasingly fast and precise EM numerical computation simulation, a novel parallel data distribution and computation partition based on matrix＇s row/column-cycle array division was proposed. The new data distribution scheme could be used in distribution cluster environment and the Computation partition algorithm was proposed and described. First, a novel scheme was proposed based on MPI （Message Passing Interface） distributed parallel computation environment because MPI-based computation platform could be used to implement the computation and storage partition at the same time for the computation of the inverse of large dense matrix used in MOM （Method of Moment） electromagnetic simulation. Then the implementation and performance evaluation of the algorithm using MPI＋FORTARN and MPI＋ C programming were given out. Finally the effectiveness （correctness and speedup） of the proposed scheme was tested and verified using both TACC system in university of Texas at Austin in USA and HPC system in NPU China. The codes and results can be applied to EM data simulation in subsurface detection.