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論文名稱 Title |
加速區域分解法之實作
Implementation of an Accelerated Domain Decomposition Iterative Procedure |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
20 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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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 |
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統計 Statistics |
本論文已被瀏覽 5693 次,被下載 1772 次 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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