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題名 | Application and Comparison of Conjugate-Gradient-Like Methods to Ground Water Mounding Using Domain Transformation Technique=地下水補注丘問題數值處理方法之比較 |
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作者 | 蔡存孝; | 書刊名 | 農業工程學報 |
卷期 | 40:3 1994.09[民83.09] |
頁次 | 頁103-111 |
分類號 | 443.67 |
關鍵詞 | 地下水丘; 有限差分; 區域變換; 共軛導數; 共軛餘數; Ground water mounding; Finite difference; Domain transformation; Conjugate gradient; Conjugate residual; |
語文 | 英文(English) |
中文摘要 | 本文應用九種疊代方案處理地下水補注引起地下水丘問題之線性聯立方程。地下水丘估算應用區域變換及疊代法預測地下水面位置,由於這兩種方法的應用需要大量的計算,使用POINT SOR便顯得不足。因此考慮應用共軛導數之類似方法。在這些方法中共軛餘數法及其沿生的方法可應用於解非對稱係數之線性聯立方程。對此距陣之preconditioning 的處理更大大改善解非對稱係數之線性聯立方程之收斂速度。由計算之結果顥示,以Choleski factorization為解非對稱線性聯立方程之最佳方法。 |
英文摘要 | Nine schemes including point SOR and conjugate-gradient-like methods for solving systems of linear equations were applied to simulate ground water mounding. The simulation of the ground water mounding used the domain transform techniques and an iteration algorithm to estimate the location of the water table. Since a lot of computations are required, the point SOR is not appropriate for the simulation. The conjugate-gradient-like methods are thus considered. Among them, the conjugate residual method and its extensions are found appropriate for solving systems of linear equations when the coefficients matrix is not symmetric. The process of preconditioning for coefficient matrix of the system of linear equations showed a great improvement on the convergence speed. Results of the simulation indicated that preconditioned generalized conjugate residual method with the incomplete Choleski factorization is the most efficient method for solving systems of linear equations when the coefficients matrices are not symmetric. |
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