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題 名 | An Optimal AFAC Algorithm for Nonsymmetric and Indefinite Elliptic Finite Element Problems=關於非對稱及非正定橢圓型有限元問題的一個最不同步快速可調整的複合網格法 |
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作 者 | 程宣仁; | 書刊名 | Proceedings of the National Science Council : Part A, Physical Science and Engineering |
卷 期 | 21:5 1997.09[民86.09] |
頁 次 | 頁379-388 |
分類號 | 319.711 |
關鍵詞 | 非對稱; 非正定橢圓型; 有限元問題; 不同步快速; 複合網格法; Schwarz methods; GMRES method; Elliptic regularity; Extension theorem; Nonsymmetric and indefinite elliptic problems; Finite elements; |
語 文 | 英文(English) |
中文摘要 | 我們針對一些來自於定義在複合網格上的非對稱及非正定的橢圓型有限元問題所 產生大而稀疏的線性系統考慮一求解方法-一不同步快速可調整的複合網格法;此方法被設 計用來解決一些其解具有奇異點的橢圓型邊界值問題;應用此方法好處為在求解的過程中我 們僅需求解一些在均勻網格上的子問題,而不需求解原來複雜的大問題;我們證明在一般的 假設下,此方法之收斂速度與網格分割加細的次數及所有各層次網格的大小等參數均無關; 關於收斂速度此方法與標準的多重網格法的主要差別,在於為了得到均勻的收斂速度界值, 我們不需像在多重網格法中加入一些關於網格大小的限制;此工作推廣了我們先前關於對稱 及正定橢圓型問題的工作。 |
英文摘要 | We consider an AFAC (Asynchronous fast adaptive composite) algorithm for large sparse linear systems of equations which arise from second-order nonsymmetric and indefinite elliptic finite element problems defined on composite meshes. The AFAC method was designed for elliptic boundary value problems with some solution singularities. The benefit of applying AFAC is that we only need to solve some subproblems on uniform meshes rather than solve the original complicated problem. We prove that the rate of convergence is independent of all mesh size parameters and the number of refinement levels under some general assumptions. The main difference between the AFAC method and the standard multigrid method with regard to the convergence rate is that unlike multigrid methods no restrictions are placed on mesh sizes for the AFAC in order to get a uniform convergence bound. This work generalizes our previous work on symmetric and positive definite elliptic problems. |
本系統中英文摘要資訊取自各篇刊載內容。