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研究生:李怡謀
研究生(外文):Yi-mou Li
論文名稱:加速區域分解法之實作
論文名稱(外文):Implementation of an Accelerated Domain Decomposition Iterative Procedure
指導教授:黃杰森
指導教授(外文):Chien-sen Huang
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:20
中文關鍵詞:疊代法加速區域分解實作
外文關鍵詞:domain decompositioniterative procedureimplementation
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  • 被引用被引用:0
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  • 下載下載:8
  • 收藏至我的研究室書目清單書目收藏:0
我們以實作方式驗證加速的區域分解法,在一維切割上,我們已有證明此方法是有效的[4]。我們除了做了一微切割的實作驗證外,我們進一步將我們的程序延伸至二微切割上,但無理論證明。
數值結果顯示變動參數對於一微切割的加速性具有非常好的效果;而在二微切割上,雖然無法得到一個有效的加速方式,但我們還是找到了一個收斂速度不錯的參數序列 。
This paper is concerned about an implementation of an accelerated domain decomposition iterative
procedure. In [4], Douglas and Huang had shown the convergence for one dimensional
partitioning case. This time we make an implementation to show the numerical results, and
further more extend our procedure to two dimensional partitioning case.
Our results show that the parameter sequence do accelerate our iterative procedure. In
one dimensional partitioning case, we have the rule to choose the parameter sequence[4], but
in two dimensional partitioning case, we still have no idea about the rule, but we still try to
find some parameters to make our procedure more e cient. After some tests, we find that
the sequence {0.4, 0.43, 0.45, 0.47, 0.5} works. Though the iteration steps in two dimensional
partitioning are not decreasing, our results show the computation time is almost the same
as which in the two dimensional partitioning case. It means that the parallelized program
could cut down the computation cost.
Chapter 1 Introduction
Chapter 2 Differential Case
Chapter 3 One-Dimensional Partition
Chapter 4 Two-Dimensional Partition
Chapter 5 Numerical Result
Chapter 6 Conclusion Remark
[1] B. Despr´es. M´ethodes de d´ecomposition de domaines pour les probl´emes de propagationd''ondes en r´egime harmonique. Ph.D. thesis, Universit´e Paris IX Dauphine, UserMath´ematiques de la D´ecision, 1991.[2] J. Douglas. Jr., P. J. Paes Leme, J. E. Roberts, and J. Wang. A parallel iterative procedure applicable to the approximate solution of second order partitial differential equation by mixed finite element methods, Numer. Math., 65(1993), pp.95-108.[3] Jim Douglas, Jr. and Paola Pietra.A Description of Some Alternating-Direction Iterative Techniques for Mixed Finite Element Methods.[4] J. Douglas. Jr. and C.-S. Huang, An Accelerated Domain Decomposition Procedure Based on Robin Transimission Condition, BIT 37:3(1997). 678-686.[5] P. L. Lions. On the schwarz alternating method III: a variant for nonoverlapping subdomains, in Domain Decomposition Methods for Partial Dierential Equations, T. F. Chan, R. Glowinski, J. Periaux, and O. B. Widlund, eds., pp. 202-223, SIAM,Philadelphia, PA, 1990.
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