MONTE CARLO METHODS FOR ELECTROMAGNETICS: MONTE CARLO METHODS FOR ELECTROMAGNETICS.pdf

2009年新书
Contents
Preface......................................................................................................................xi
Author Biography............................................................................................... xiii
1. Introduction....................................................................................................1
1.1 Why Monte Carlo?...........................................................................................1
1.2 Historical Background....................................................................................2
1.3 Applications of MCMs....................................................................................3
1.4 Review of Electromagnetic Theory..............................................................4
1.4.1 Maxwell’s Equations...........................................................................4
1.4.2 Scalar and Vector Potentials...............................................................5
1.4.3 Boundary Conditions..........................................................................7
References.................................................................................................................8
2. Probability and Statistics........................................................................... 11
2.1 Generation of Random Numbers................................................................ 11
2.2 Statistical Tests of Pseudorandom Numbers............................................. 15
2.2.1 Moments Test..................................................................................... 16
2.2.2 Frequency Test................................................................................... 16
2.3 Generation of Random Variates.................................................................. 18
2.3.1 Inverse Transformation Method...................................................... 18
2.3.2 Rejection Method............................................................................... 19
2.4 Generation of Continuous Random Variates............................................20
2.4.1 Uniform Distribution........................................................................ 21
2.4.2 Exponential Distribution..................................................................22
2.4.3 Normal Distribution.........................................................................23
2.5 Evaluation of Error........................................................................................26
2.6 Summary........................................................................................................ 31
References............................................................................................................... 31
Problems..................................................................................................................33
3. Finite Difference Method..........................................................................35
3.1 Finite Differences..........................................................................................35
3.2 Finite Differencing of Parabolic PDEs.......................................................38
3.3 Finite Differencing of Hyperbolic PDEs....................................................45
3.4 Finite Differencing of Elliptic PDEs...........................................................49
3.4.1 Band Matrix Method........................................................................ 51
3.4.2 Iterative Method................................................................................ 51
3.5 Accuracy and Stability of Finite Difference Solutions............................60
3.6 Maxwell’s Equations.....................................................................................63
3.7 Summary........................................................................................................ 67
References................................................................................................................ 67
4. Fixed Random Walk..................................................................................... 69
4.1 Introduction...................................................................................................69
4.2 Solution of Laplace’s Equation.................................................................... 70
4.2.1 One-Dimensional Case.................................................................... 70
4.2.2 Two-Dimensional Case....................................................................71
4.2.3 Three-Dimensional Case.................................................................75
4.3 Solution of Poisson’s Equation....................................................................82
4.4 Solution of Axisymmetric Problems..........................................................83
4.5 Summary........................................................................................................98
References.............................................................................................................. 100
Problems................................................................................................................ 100
5. Floating Random Walk.............................................................................. 105
5.1 Introduction................................................................................................. 105
5.2 Rectangular Solution Regions................................................................... 106
5.2.1 Laplace’s Equation.......................................................................... 106
5.2.2 Poisson’s Equation.......................................................................... 108
5.3 Axisymmetric Solution Regions............................................................... 115
5.3.1 Laplace’s Equation.......................................................................... 115
5.3.2 Poisson’s Equation.......................................................................... 116
5.3.3 Homogeneous Media..................................................................... 117
5.3.4 Inhomogeneous Media.................................................................. 118
5.3.5 The Computing Procedure............................................................ 119
5.4 Summary......................................................................................................122
References.............................................................................................................. 123
Problems................................................................................................................ 123
6. The Exodus Method................................................................................... 127
6.1 Solution of Laplace’s Equation.................................................................. 127
6.1.1 Rectangular Solution Region........................................................ 128
6.1.2 Axisymmetric Solution Region..................................................... 129
6.1.3 Exodus Method............................................................................... 130
6.2 Solution of Poisson’s Equation.................................................................. 137
6.2.1 Rectangular Solution Region........................................................ 137
6.2.2 Axisymmetric Solution Region..................................................... 138
6.2.3 Transition and Transient Probabilities......................................... 139
6.2.4 Exodus Method............................................................................... 140
6.2.5 Fixed Random Walk....................................................................... 142
6.3 Summary...................................................................................................... 147
References.............................................................................................................. 147
Problems................................................................................................................ 147
7. Neumann Problems.................................................................................... 151
7.1 Governing Equations................................................................................. 151
7.2 Triangular Mesh Method........................................................................... 153
7.2.1 One Corner on the Boundary........................................................ 153
7.2.2 Two Corners on the Boundary...................................................... 154
7.3 Computing Procedure................................................................................ 155
7.4 Summary...................................................................................................... 158
References.............................................................................................................. 158
Problems................................................................................................................ 158
8. Whole Field Computation......................................................................... 161
8.1 Introduction................................................................................................. 161
8.2 Regular Monte Carlo Method................................................................... 162
8.3 Absorbing Markov Chains........................................................................ 163
8.4 Summary...................................................................................................... 171
References.............................................................................................................. 172
Problems................................................................................................................ 172
9. Time-Varying Problems............................................................................ 175
9.1 Introduction................................................................................................. 175
9.2 Diffusion Equation..................................................................................... 175
9.3 Rectangular Solution Region.................................................................... 176
9.3.1 One-Dimensional Case.................................................................. 176
9.3.2 Two-Dimensional Case.................................................................. 181
9.4 Cylindrical Solution Region...................................................................... 183
9.4.1 One-Dimensional Case.................................................................. 183
9.4.2 Two-Dimensional Case.................................................................. 187
9.5 Summary...................................................................................................... 193
References.............................................................................................................. 193
Problems................................................................................................................ 194
10. Scattering from Random Rough Surfaces.......................................... 197
10.1 Introduction................................................................................................. 197
10.2 Scattering by 1-Dimensional Random Rough Surfaces........................ 198
10.3 Scattering by 2-Dimensional Random Rough Surfaces........................200
10.4 Summary......................................................................................................203
References..............................................................................................................203
11. Multidimensional Integration............................................................... 207
11.1 Introduction................................................................................................. 207
11.2 Crude Monte Carlo Integration................................................................ 207
11.3 Monte Carlo Integration with Antithetic Variates................................. 210
11.4 Improper Integrals...................................................................................... 211
11.5 Summary...................................................................................................... 214
References.............................................................................................................. 214
Problems................................................................................................................ 214
Index...................................................................................................................... 217

:50bb

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感谢楼主分享

收藏了，看看

thx for sharing dude

thank you !

好书啊，楼主太牛了，十分感谢！！:31bb

thanks.......................

好东西，没想到真有MonteCarlo法的电磁计算

貌似这种方法太原始了！

不过也是值得一看的

谢谢分享
:crackle.GIF

楼主太牛了，十分感谢！！

呵呵 这本书我也发了

谢谢楼主  已经下了{:soso__8961432591078930798_3:}