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題名 | Application of High-Order Least-Squares Finite-Element Method for Second-Order Partial Differential Equations=高階最小平方有限元素法在二階偏微分方程式之應用 |
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作 者 | 梁興杰; 施仁傑; 洪振益; | 書刊名 | 中國機械工程學刊 |
卷期 | 19:5 1998.10[民87.10] |
頁次 | 頁457-463 |
分類號 | 446 |
關鍵詞 | 高階最小平方有限元素法; 二階偏微分方程式; P-version; Least-squares minimization; Iterative methods; Sparse matrix computations; |
語文 | 英文(English) |
中文摘要 | 本篇旨在研究高階最小平方有限元素法在二階偏微分方程式之應用。由於該方法 所推導得到的離散方程組具有對稱與正定的特性。許多迭代求解方法,諸如共軛梯度法、一 般最小殘餘法、準最小殘餘法,及其它迭代方法都在此研究中用來求解,並比較各方法之優 缺點及效能。我們以其解含有大梯度變化之線性及非線性二階偏微分方程式為例,以驗證該 方法之特性。 |
英文摘要 | A p-version based least-squares finite-element method (LSFEM) is presented for general second-order partial differential equations. The resulting system of equations of the formulation is symmetric and positive-definite. Various preconditioned iterative solvers, such as, conjugate gradient (CG), generalized minimum residual (GMRES), quasi-minimum residual (QMR) methods and their variants were used to solve the algebraic system of equations and their performance were compared. The method was applied to both linear and non-linear partial differential equations which encounter the sharp gradient solution. |
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