有限元概率算法及其高精度分析

Foreward
前言
Chapter 1 Introduction ／ 1
Chapter 2 Brief Introduction of Markov Chain and Nonnegative Matrices ／ 6
Chapter 3 The Methods of Solving Elliptic Boundary Value Problem ／ 12
3.1 Elliptic Boundary Value Prollem and Limit Transfer Matrix Q ／12
3.2 Method of Solving Nonhomogeneous Elliptic Boundary Value Problem ／ 15
3.3 Solving Parabolic Problem ／ 17
3.4 Monte—Carlo Method of Computing Qand S ／19
3.5 M ethods of Fast Approximate to limit M atrices Q and S ／ 22
3.6 Under the Case That P Is Not Nonnegative Matrix／24
3.7 Iterative Method for Finite Element Probability Computing／26
Chapter 4 The Finite Element Probability Computing Method / 28
Chapter 5 High Accuracy Methods of FiniteElement Probability Computing Method / 35
5.1 The Probability Multigrid Method / 35
5.2 The Boundary Thickening Method / 41
5.3 Numerical Experiment / 42
Chapter 6 Rectangular Finite Element Probability Computing Method / 45
6.1 Introduction / 45
6.2 Probability Computing Model and Its Convergence Conditions / 46
6.3 Numerical Experiment / 50
Chapter 7 Dimentional Independence / 52
Chapter 8 The Fast Computing Scheme of the Finite Element Method for the Two Point Boundary Problem / 57
8.1 Model Problem and P'k-type Finite Element Space / 57
8.2 The Probability Computing Scheme / 62
8.3 Numerical Experiment / 65
Chapter 9 Example Analysis / 67
9.1 The Monte-Carlo Method for Three-dimensional Problems / 67
9.2 The Finite Element Monte-Carlo Method of Plate Problems / 69
Chapter 10 The Space Decomposition Method of the Finite Element / 75
10.1 Abstract Problem / 75
10.2 The Domain Decomposition Method and the Structure of Space S0 / 81
10.3 Example / 83
10.4 Probability Computing Method / 85
References / 87