Monte Carlo methods for applied scientists:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey u. a.
World Scientific
2008
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 291 S. |
| ISBN: | 9810223293 9789810223298 |
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MARC
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| 245 | 1 | 0 | |a Monte Carlo methods for applied scientists |c Ivan T. Dimov |
| 264 | 1 | |a New Jersey u. a. |b World Scientific |c 2008 | |
| 300 | |a XV, 291 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-007800355 | ||
Record in the Search Index
| _version_ | 1804126109391912960 |
|---|---|
| adam_text | Contents
Preface
vii
Acknowledgements
ix
1.
Introduction
1
2.
Basic Results of Monte Carlo Integration
11
2.1
Convergence and Error Analysis of Monte Carlo
Methods
............................ 11
2.2
Integral Evaluation
...................... 13
2.2.1
Plain (Crude) Monte Carlo Algorithm
....... 13
2.2.2
Geometric Monte Carlo Algorithm
......... 14
2.2.3
Computational Complexity of Monte Carlo
Algorithms
...................... 15
2.3
Monte Carlo Methods with Reduced Error
......... 16
2.3.1
Separation of Principal Part
............ 16
2.3.2
Integration on
a Subdomain
............ 17
2.3.3
Symmetrization of the Integrand
.......... 18
2.3.4
Importance Sampling Algorithm
.......... 20
2.3.5
Weight Functions Approach
............ 21
2.4
Superconvergent
Monte Carlo Algorithms
......... 22
2.4.1
Error Analysis
.................... 23
2.4.2
A Simple Example
.................. 26
2.5
Adaptive Monte Carlo Algorithms for Practical
Computations
......................... 29
2.5.1
Superconvergent
Adaptive Monte Carlo
Algorithm and Error Estimates
.......... 30
xii
Morite Carlo
Methods for Applied Scientists
2.5.2
Implementation of Adaptive Monte Carlo
Algorithms. Numerical Tests
............ 34
2.5.3
Discussion
...................... 37
2.6
Random Interpolation Quadratures
............. 39
2.7
Some Basic Facts about
Quasi-Monte
Carlo Methods
... 43
2.8
Exercises
........................... 46
3.
Optimal Monte Carlo Method for Multidimensional
Integrals of Smooth Functions
49
3.1
Introduction
.......................... 49
3.2
Description of the Method and Theoretical Estimates
. . 52
3.3
Estimates of the Computational Complexity
........ 55
3.4
Numerical Tests
....................... 60
3.5
Concluding Remarks
..................... 63
4.
Iterative Monte Carlo Methods for Linear Equations
67
4.1
Iterative Monte Carlo Algorithms
.............. 68
4.2
Solving Linear Systems and Matrix Inversion
....... 74
4.3
Convergence and Mapping
.................. 77
4.4
A Highly Convergent Algorithm for Systems of Linear
Algebraic Equations
..................... 81
4.5
Balancing of Errors
...................... 84
4.6
Estimators
.......................... 86
4.7
A Refined Iterative Monte Carlo Approach for Linear
Systems and Matrix Inversion Problem
........... 88
4.7.1
Formulation of the Problem
............ 88
4.7.2
Refined Iterative Monte Carlo Algorithms
.... 89
4.7.3
Discussion of the Numerical Results
........ 94
4.7.4
Conclusion
...................... 99
5.
Markov Chain Monte Carlo Methods for Eigenvalue Problems
101
5.1
Formulation of the Problems
................ 103
5.1.1
Bilinear Form of Matrix Powers
.......... 104
5.1.2
Eigenvalues of Matrices
............... 104
5.2
Almost Optimal Markov Chain Monte Carlo
....... 106
5.2.1 MC
Algorithm for Computing Bilinear Forms
of Matrix Powers (t Akh)
............. 107
Contents xiii
5.2.2 MC
Algorithm for
Computing
Extremal
Eigeirvalues...................... 109
5.2.3 Robust MC
Algorithms............... Ill
5.2.4 Interpolation
ЛІС
Algorithms
............ 112
5.3
Computational Complexity
................. 115
5.3.1
Method for Choosing the Number of
iterations
к
...................... 116
5-.3.2 Method for Choosing the Number of
Chains
........................ 117
5.4
Applicability and Acceleration Analysis
.......... 118
5.5
Conclusion
.......................... 131
6.
Monte
Cario
Methods for Boundary-Value Problems (BVP)
133
6.1
BVP for Elliptic Equations
................. 133
6.2
Grid Monte Carlo Algorithm
................ 134
6.3
Grid-Free Monte Carlo Algorithms
............. 135
6.3.1
Local Integral Representation
........... 136
6.3.2
Monte Carlo Algorithms
.............. 144
6.3.3
Parallel Implementation of the Grid-Free
Algorithm and Numerical Results
......... 154
6.3.4
Concluding Remarks
................ 159
7.
Superconvergent
Monte Carlo for Density Function
Simulation by B-Splines
161
7.1
Problem Formulation
..................... 162
7.2
The Methods
......................... 163
7.3
Error Balancing
........................ 169
7.4
Concluding Remarks
..................... 170
8.
Solving Non-Linear Equations
171
8.1
Formulation of the Problems
................ 171
8.2
A Monte Carlo Method for Solving Non-linear Integral
Equations of
Fredholm
Type
................ 173
8.3
An Efficient Algorithm
.................... 179
8.4
Numerical Examples
..................... 191
9.
Algorithmic Efficiency for Different Computer Models
195
9.1
Parallel Efficiency Criterion
................. 195
xiv
Monte
Carlo Methods for Applied Scientists
9.2
Markov Chain Algorithms for Linear Algebra
Problems
........................... 197
9.3
Algorithms for Boundary Value Problems
......... 204
9.3.1
Algorithm
Λ
(Grid Algorithm)
........... 205
9.3.2
Algorithm
β
(Random Jumps on Mesh Points
Algorithm)
...................... 208
9.3.3
Algorithm
С
(Grid-Free Algorithm)
........ 211
9.3.4
Discussion
...................... 213
9.3.5
Vector Monte Carlo Algorithms
.......... 214
10.
Applications for Transport Modeling in Semiconductors
and Nanowires
219
10.1
The Boltzmann Transport
.................. 219
10.1.1
Numerical Monte Carlo Approach
......... 222
10.1.2
Convergence Proof
................. 224
10.1.3
Error Analysis and Algorithmic Complexity
. . . 225
10.2
The Quantum Kinetic Equation
............... 227
10.2.1
Physical Aspects
................... 230
10.2.2
The Monte Carlo Algorithm
............ 233
10.2.3
Monte Carlo Solution
................ 234
10.3
The Wigner Quantum-Transport Equation
......... 237
10.3.1
The Integral Form of the Wigner Equation
.... 242
10.3.2
The Monte Carlo Algorithm
............ 243
10.3.3
The Neumann Series Convergency
......... 245
10.4
A Grid Computing Application to Modeling of Carrier
Transport in Nanowires
................... 247
10.4.1
Physical Model
................... 247
10.4.2-
The Monte Carlo Method
.............. 249
10.4.3
Grid Implementation and Numerical Results
. . . 251
10.5
Conclusion
.......................... 254
Appendix A Jumps on Mesh Octahedra Monte Carlo
257
Appendix
В
Performance Analysis for Different Monte
Carlo Algorithms
263
Appendix
С
Sample Answers of Exercises
265
Appendix
D
Symbol Table
273
Contents xv
Bibliography
275
Subject Index
285
Author Index
289
|
| any_adam_object | 1 |
| author | Dimov, Ivan 1952- |
| author_GND | (DE-588)1043787461 |
| author_facet | Dimov, Ivan 1952- |
| author_role | aut |
| author_sort | Dimov, Ivan 1952- |
| author_variant | i d id |
| building | Verbundindex |
| bvnumber | BV011582643 |
| classification_rvk | SK 840 |
| ctrlnum | (OCoLC)634644998 (DE-599)BVBBV011582643 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011582643 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:12:14Z |
| institution | BVB |
| isbn | 9810223293 9789810223298 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007800355 |
| oclc_num | 634644998 |
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| owner | DE-355 DE-BY-UBR DE-384 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-83 |
| physical | XV, 291 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Dimov, Ivan 1952- Verfasser (DE-588)1043787461 aut Monte Carlo methods for applied scientists Ivan T. Dimov New Jersey u. a. World Scientific 2008 XV, 291 S. txt rdacontent n rdamedia nc rdacarrier Anwendung (DE-588)4196864-5 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s Anwendung (DE-588)4196864-5 s DE-604 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007800355&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dimov, Ivan 1952- Monte Carlo methods for applied scientists Anwendung (DE-588)4196864-5 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4196864-5 (DE-588)4240945-7 |
| title | Monte Carlo methods for applied scientists |
| title_auth | Monte Carlo methods for applied scientists |
| title_exact_search | Monte Carlo methods for applied scientists |
| title_full | Monte Carlo methods for applied scientists Ivan T. Dimov |
| title_fullStr | Monte Carlo methods for applied scientists Ivan T. Dimov |
| title_full_unstemmed | Monte Carlo methods for applied scientists Ivan T. Dimov |
| title_short | Monte Carlo methods for applied scientists |
| title_sort | monte carlo methods for applied scientists |
| topic | Anwendung (DE-588)4196864-5 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Anwendung Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007800355&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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