發(fā)布時(shí)間：2018-06-25 03:26

  本文選題：并行計(jì)算 + 線性方程組　； 參考：《南京郵電大學(xué)》2015年碩士論文

【摘要】：利用數(shù)值計(jì)算方法求解電磁場(chǎng)問題已經(jīng)被廣泛應(yīng)用,線性方程組的求解是其中重要的一部分。隨著電磁場(chǎng)問題的日益復(fù)雜,線性方程組的規(guī)模也變得越來越大,串行算法已經(jīng)不能滿足科研工作對(duì)計(jì)算速度的需求。針對(duì)上述情況,本文首先提出了一種基于高斯-賽德爾迭代的異步并行迭代算法。該算法首先對(duì)矩陣分塊得到多個(gè)不同的線性方程組,然后在不同的處理機(jī)中計(jì)算不同的線性方程組,某個(gè)處理機(jī)計(jì)算完畢后將計(jì)算結(jié)果發(fā)送給其它處理機(jī)并接收它們當(dāng)前的數(shù)據(jù),然后再利用接收到的數(shù)據(jù)求解新的線性方程組。實(shí)驗(yàn)結(jié)果表明該算法具有更快的計(jì)算速度,并將該算法應(yīng)用到二維靜電場(chǎng)的求解之中,證明了該算法的實(shí)用性。針對(duì)于一些收斂性比較差的線性方程組,本文提出了一種基于值域子空間投影法的異步并行迭代算法。此算法首先對(duì)系數(shù)矩陣按列分塊得到多個(gè)不同的投影方程,然后在不同的處理機(jī)計(jì)算不同的投影方程,處理機(jī)計(jì)算完畢后將計(jì)算結(jié)果發(fā)送給其它處理機(jī)并接收它們當(dāng)前的數(shù)據(jù),然后再利用接收到的數(shù)據(jù)求解新的投影方程。實(shí)驗(yàn)結(jié)果表明該算法收斂性比較好,計(jì)算速度也比較快,并將該算法應(yīng)用到電磁散射問題的求解之中,證明了該算法的實(shí)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.
【學(xué)位授予單位】：南京郵電大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O441.4

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 蘇仰鋒,朱世東;并行多分裂混亂迭代模型[J];復(fù)旦學(xué)報(bào)(自然科學(xué)版);1991年04期

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本文編號(hào)：2064338