| 论文摘要 | 第1-13页 |
| ABSTRACT | 第13-20页 |
| 1 Diagonalization of exterior Dirichlet to Neumann map on general shapes in 2D and 3D | 第20-80页 |
| ·Introduction | 第20-23页 |
| ·The special case of the disc | 第23-26页 |
| ·Approximate solution of DN with the IEM on an exponential mesh | 第26-35页 |
| ·Construction of the exponential mesh | 第26-30页 |
| ·The special case of the disc with the Fourier method | 第30-33页 |
| ·Solving one DN problem | 第33-35页 |
| ·Spherical harmonics | 第35-40页 |
| ·Three dimensional exterior problems of the Laplace equation with the IEM | 第40-47页 |
| ·Construction of the exponential mesh | 第40-41页 |
| ·Construction of the stiffness matrix and the mass matrix | 第41-45页 |
| ·Impact on implementation | 第45-47页 |
| ·Diagonalization with a triangular flow | 第47-56页 |
| ·Principle of the triangular flow method | 第47-54页 |
| ·Solving with a Adaptive time-stepping Runge-Kutta method | 第54-56页 |
| ·Numerical results | 第56-71页 |
| ·Conclusion | 第71-72页 |
| ·Application | 第72-80页 |
| 2 Explicit formulas of the common generalized inverses , perturbation analysis and the iterative computing methods | 第80-102页 |
| ·Introduction | 第80-82页 |
| ·Definition of complementary generalized inverse and its proposition | 第82-90页 |
| ·Perturbation theory of A_(T,S)~(-1) and iterative computing methods | 第90-98页 |
| ·Relationship between A_(T,S)~(-1) and A_(T,S)~(2) | 第98-102页 |
| 3 A note on the generalized Bott-Duffin inverse | 第102-108页 |
| ·Introduction | 第102-103页 |
| ·Main results | 第103-108页 |
| 4 Explicit formulas of the generalized inverse A_(T,S)~(2) and its applications | 第108-118页 |
| ·Introduction | 第108-111页 |
| ·Main results | 第111-118页 |
| 5 Application of explicit formulas of the generalized inverses | 第118-128页 |
| ·The reverse order | 第118-120页 |
| ·Lowner partial order | 第120-123页 |
| ·Continuity | 第123-124页 |
| ·Computing methods for generalized inverse | 第124-128页 |
| Bibliography | 第128-138页 |
| 博士期间发表论文 | 第138-139页 |
| 致谢 | 第139页 |
