臺灣博碩士論文加值系統

在本篇論文中，我們研究將預優化算子運用於二維 Possion 方程和
二維不可壓 Navier-Stokes 方程上，並且在預優化線性系統中使用
不同近代迭代方法解題，觀察預優化算子對迭代方法收斂的影響。

In this paper,we study using preconditioner to solving two dimension
Possion equation or two dimension Navier-Stokes equation .
We use different iterative methods in preconditioning linear system and
observe the effect of convergence with different preconditioner in iterative methods .

1 序論
2 預優化線性系統與預優化算子
2.1 預優化線性系統(PRECONDITIONED LINEAR SYSTEM)
2.2 預優化算子( PRECONDITIONER )
2.2.1 迭代型預優化算子
2.2.2 分解型預優化算子
3 迭代法提要與預優化
3.1 CONJUGATE GRADIENT METHOD ( CG )
3.2 BICONJUGATE GRADIENT METHOD ( BICG )
3.3 CONJUGATE GRADIENT SQUARED METHOD ( CGS )
3.4 BICONJUGATE GRADIENT STABILIZED METHOD (BI-CGSTAB)
3.5 THE GENERALIZED MINIMUM RESIDUAL METHOD (GMRES)
3.6 THE QUASI-MINIMAL RESIDUAL METHOD ( QMR )
3.7 EXITY ANALYSIS OF THE LINEAR SOLVERS
4. Poisson 方程與基本測試
4.1 POISSON 方程與離散化
4.2 各種迭代方法之效果
CG 迭代方法
BiCG 迭代方法
CGS 迭代方法
Bi-CGSTAB 迭代方法
GMRES 迭代方法
QMR 迭代方法
4.3 SSOR 預優化算子鬆弛係數 W 之影響
左預優化與右預優化之比較
5 . Navier-Stokes 方程與應用測試
5.1 不可壓 NAVIER-STOKES 方程
5.2 單邊驅動穴流之結果
6 結論

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Nucleaire, October 1999