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博碩士論文 etd-0715102-143756 詳細資訊
Title page for etd-0715102-143756
論文名稱
Title
加速區域分解法之實作
Implementation of an Accelerated Domain Decomposition Iterative Procedure
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
20
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2002-06-07
繳交日期
Date of Submission
2002-07-15
關鍵字
Keywords
疊代法、加速區域分解、實作
domain decomposition, iterative procedure, implementation
統計
Statistics
本論文已被瀏覽 5693 次,被下載 1772
The thesis/dissertation has been browsed 5693 times, has been downloaded 1772 times.
中文摘要
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 。
Abstract
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.
目次 Table of Contents
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
參考文獻 References
[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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