有限元概率算法及其高精度分析PDF电子书下载

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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 Q∞ and S∞ 19

3.5 Methods of Fast Approximate to limit Matrices 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 Finite Element 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 ？0 81

10.3 Example  83

10.4 Probability Computing Method 85

References 87

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