| 摘要 | 第4-5页 |
| Abstract | 第5-6页 |
| Chapter 1 Introduction | 第7-14页 |
| Chapter 2 Splitting preconditioners for saddle point problems | 第14-20页 |
| §2.1 Background | 第14-15页 |
| §2.2 Convergence analysis of the stationary scheme | 第15-20页 |
| Chapter 3 Splitting preconditioners for generalized saddle point problems | 第20-29页 |
| §3.1 Background | 第20页 |
| §3.2 The splitting preconditioners for generalized saddle point problems | 第20-22页 |
| §3.3 Convergence analysis of the stationary scheme | 第22-28页 |
| §3.4 Practical implementation of the splitting preconditioners | 第28-29页 |
| Chapter 4 Splitting preconditioners for double saddle point problems | 第29-37页 |
| §4.1 The splitting preconditioners for double saddle point problems | 第29-30页 |
| §4.2 Convergence analysis of the stationary scheme | 第30-36页 |
| §4.3 Practical implementation of the splitting preconditioners | 第36-37页 |
| Chapter 5 Numerical experiments | 第37-49页 |
| §5.1 Numerical experiments for generalized saddle point problems | 第37-42页 |
| 5.1.1 The eigenvalue distribution of the Preconditioned matrix | 第37-39页 |
| 5.1.2 The iteration numbers corresponding to the different parameters | 第39-40页 |
| 5.1.3 The comparison of the different splitting preconditioners | 第40-42页 |
| §5.2 Numerical experiments for double saddle point problems | 第42-49页 |
| 5.2.1 The eigenvalue distribution of the preconditioned matrix | 第42-45页 |
| 5.2.2 The iteration numbers corresponding to the different parameters | 第45-46页 |
| 5.2.3 The comparison of the different splitting preconditioners | 第46-49页 |
| Chapter 6 Conclusions and discussions | 第49-50页 |
| Bibliography | 第50-55页 |
| 致谢 | 第55页 |
