| Abstract (In English) | 第1-10页 |
| Abstract (In Chinese) | 第10-14页 |
| Chapter 1 The Local Grid Refinement Method for Semiconductor Device Problems | 第14-48页 |
| ·Introduction | 第14-17页 |
| ·A Finite Difference Scheme for One-dimensional Semiconductor Device Problem on Grids with Local Refinement in Time and Space | 第17-26页 |
| ·Construction of the finite difference scheme | 第18-19页 |
| ·Error analysis | 第19-23页 |
| ·Schemes on grids with local refinement in time and space | 第23-24页 |
| ·Numerical results | 第24-26页 |
| ·A Finite Difference Scheme for Two-dimensional Semiconductor Device Problem on Grids with Local Refinement in Time and Space | 第26-36页 |
| ·Construction of the finite difference scheme | 第26-28页 |
| ·Error analysis | 第28-33页 |
| ·Schemes on grids with local refinement in time and space | 第33-35页 |
| ·Numerical results | 第35-36页 |
| ·A Finite Difference Scheme for Three-dimensional Semiconductor Device Problem on Grids with Local Refinement in Time and Space | 第36-48页 |
| ·Construction of the finite difference scheme | 第36-39页 |
| ·Error analysis | 第39-44页 |
| ·Schemes on grids with local refinement in time and space | 第44-46页 |
| ·Numerical results | 第46-48页 |
| Chapter 2 Finite Difference Schemes on Triangular Cell-centered Grids with Local Refinement | 第48-80页 |
| ·Introduction | 第48-49页 |
| ·Finite Difference Schemes on Triangular Cell-centered Composite Grids for Convection-diffusion Problem | 第49-63页 |
| ·Finite difference schemes on triangular cell-centered grids with local refinement | 第49-52页 |
| ·Formulation of the discrete problems | 第52-56页 |
| ·Error analysis | 第56-60页 |
| ·Numerical results | 第60-63页 |
| ·Finite Difference Schemes on Triangular Cell-centered Composite Grids for Parabolic Problem | 第63-80页 |
| ·Finite difference schemes on triangular cell-centered grids with local refinement in time and space | 第63-67页 |
| ·The stability of finite difference schemes | 第67-72页 |
| ·Convergence analysis | 第72-80页 |
| Chapter 3 Application of Local Grid Refinement Technique | 第80-90页 |
| ·3D-three Phase Times Profile Control Mathematical Model | 第80-85页 |
| ·The times profile control mathematical model | 第80-81页 |
| ·The finite difference scheme and the application of local refinement technique | 第81-85页 |
| ·Practical Application | 第85-90页 |
| ·The geologic model | 第85-86页 |
| ·Numerical simulation | 第86-90页 |
| Bibliography | 第90-94页 |
| Acknowledgement | 第94-95页 |
| List of Publications | 第95-96页 |
| Curriculum Vitae | 第96-97页 |
| 学位论文评阅及答辩情况表 | 第97页 |
