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題 名 | Application of a General Index Method to Finite Differences in the Curvilinear Coordinates=曲線座標系下通用指標法於有限差分法之應用 |
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作 者 | 蔡存孝; 朱聖浩; | 書刊名 | 農業工程學報 |
卷 期 | 44:4 1998.12[民87.12] |
頁 次 | 頁91-104 |
分類號 | 443.67 |
關鍵詞 | 地下水丘; 共軛梯度類似法; 指標法; Ground water mounding; Conjugate gradient like method; Index method; |
語 文 | 英文(English) |
中文摘要 | 本研究中,為儲存對稱型及非對稱型超大型矩陣通用指標已被開發,且該法被應 用於有限差分法在曲線座標系下,利用共軛梯度類似法求解偏微分方程。本通用指標法特別 強調有限差分法中整體矩陣的型態。本法之優點計有(1)可應用於解各種控制方程式及邊界 條件,(2)可適用於高降之展開估算,(3)與問題之次元無關,(4)可有效率的解複雜問題及非 對稱型矩陣,(5)可適用於解一般型之超大型矩陣,(6)由於僅儲存非零之矩陣元素,因此, 在最耗時的矩陣相乘步驟顯得非常有效率,(7)適用於現階段已開發之解矩陣方法。本研究 將通用指標法結合共軛梯度類似法應用於二維及三維之地下水丘數值模擬,結果發現該方法 比傳統方法有效率。 |
英文摘要 | A general index method for storing un-symmetric and symmetric, sparse matrices was developed and applied to finite differences in the generalized curvilinear coordinates for solving differential equations using conjugate-gradient-like methods. In this general index method, forming the global matrix for finite differences is emphasized. The advantages of this general index method are (1) adaptable to various governing and boundary conditions, (2)flexible for higher order approximation, (3)independent of problem dimension, (4) efficient for complex problems when global matrix is not symmetric, (5)convenient for general sparse matrices, (6) computationally efficient in the most time consuming procedure of matrix multiplication (since only non-zero terms are stored), and (7)flexible and applicable to any developed matrix solver. In this paper, numerical simulation of two-and three-dimensional ground water mounding were used to illustrate and results were compared, which indicated that the general index method is much more efficient than the traditional numerical procedure of the finite difference method. |
本系統中英文摘要資訊取自各篇刊載內容。