电磁场问题异步并行迭代算法的研究

发布时间：2018-06-25 03:26

本文选题：并行计算 + 线性方程组　；参考：《南京邮电大学》2015年硕士论文

【摘要】：利用数值计算方法求解电磁场问题已经被广泛应用,线性方程组的求解是其中重要的一部分。随着电磁场问题的日益复杂,线性方程组的规模也变得越来越大,串行算法已经不能满足科研工作对计算速度的需求。针对上述情况,本文首先提出了一种基于高斯-赛德尔迭代的异步并行迭代算法。该算法首先对矩阵分块得到多个不同的线性方程组,然后在不同的处理机中计算不同的线性方程组,某个处理机计算完毕后将计算结果发送给其它处理机并接收它们当前的数据,然后再利用接收到的数据求解新的线性方程组。实验结果表明该算法具有更快的计算速度,并将该算法应用到二维静电场的求解之中,证明了该算法的实用性。针对于一些收敛性比较差的线性方程组,本文提出了一种基于值域子空间投影法的异步并行迭代算法。此算法首先对系数矩阵按列分块得到多个不同的投影方程,然后在不同的处理机计算不同的投影方程,处理机计算完毕后将计算结果发送给其它处理机并接收它们当前的数据,然后再利用接收到的数据求解新的投影方程。实验结果表明该算法收敛性比较好,计算速度也比较快,并将该算法应用到电磁散射问题的求解之中,证明了该算法的实用性。
[Abstract]:The numerical method has been widely used to solve electromagnetic problems, and the solution of linear equations is an important part of it. With the increasing complexity of electromagnetic problems, the scale of linear equations has become larger and larger. The serial algorithm can not meet the needs of scientific research for computing speed. In this paper, an asynchronous parallel iterative algorithm based on Gauss-Seidel iteration is proposed. In this algorithm, first of all, the matrix is divided into several different linear equations, and then different linear equations are calculated in different processors. One processor sends the results to other processors and receives their current data, and then uses the received data to solve the new linear equations. The experimental results show that the algorithm has a faster computing speed, and the algorithm is applied to the solution of two-dimensional electrostatic field, which proves the practicability of the algorithm. For some linear equations with poor convergence, an asynchronous parallel iterative algorithm based on the range subspace projection method is proposed in this paper. In this algorithm, several different projection equations are obtained by dividing the coefficient matrix into columns, and then different projection equations are calculated by different processors. After the calculation is finished, the calculation results are sent to other processors and their current data are received. Then the new projection equation is solved by using the received data. The experimental results show that the algorithm has good convergence and fast calculation speed. The algorithm is applied to solve the electromagnetic scattering problem and the practicability of the algorithm is proved.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O441.4

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