Monte Carlo methods in boundary value problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Berlin [u.a.]
Springer
1991
|
| Series: | Springer series in computational physics
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002875588&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XII, 283 S. graph. Darst. |
| ISBN: | 3540530010 0387530010 |
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MARC
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| 100 | 1 | |a Sabel'fel'd, Karl K. |d 1953- |e Verfasser |0 (DE-588)121181529 |4 aut | |
| 240 | 1 | 0 | |a Metody Monte-Karlo v kraevych zadačach |
| 245 | 1 | 0 | |a Monte Carlo methods in boundary value problems |c Karl K. Sabelfeld |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1991 | |
| 300 | |a XII, 283 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in computational physics | |
| 650 | 7 | |a Monte-Carlo, méthode de |2 ram | |
| 650 | 7 | |a Problèmes aux limites |2 ram | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Monte Carlo method | |
| 650 | 0 | 7 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
1. General Schemes for Constructing Scalar
and Vector Monte Carlo Algorithms
for Solving Boundary Value Problems 5
1.1 Random Walks on Boundary and Inside the Domain Algorithms 5
1.1.1 Monte Carlo Algorithms 5
1.1.2 Scalar and Vector Walk Inside the Domain Algorithms 9
1.1.3 Walk on Boundary Algorithms 15
1.1.4 Probabilistic Representations
in the Form of Continual Integrals 16
1.2 Random Walks and Approximations of Random Processes .. 18
1.2.1 Walk Inside the Domain Processes 18
1.2.2 Walk on Boundary Processes 25
1.2.3 Approximation of Wiener Processes 27
1.2.4 Simulation of Random Fields 31
1.2.5 Stochastic Problems and Double Randomization .... 47
2. Monte Carlo Algorithms for Solving Integral Equations 50
2.1 Algorithms Based on Numerical Analytical Continuation .... 50
2.1.1 Statement of the Problem and the Main Definitions .. 50
2.1.2 Analytical Continuation of Neumann Series Based
on the Spectral Parameter Transformation 53
2.1.3 Transformations
of theType A = ^(r/) = ao + aiT? + a27/2 + 60
2.2 Asymptotically Unbiased Estimates
Based on Singular Approximation of the Kernel 64
2.2.1 Finite Dimensional Case and One Point Approximation 65
2.2.2 Systems of Integral Equations 68
2.2.3 General Case of the Kernel Approximation 71
2.3 The Eigen value Problem for the Integral Operators 74
2.3.1 Calculation of Eigen values on the Basis
of the Transformation A = ip(r/) 74
2.3.2 Calculation of Eigen values
by Asymptotically Unbiased Estimates 76
VII
2.4 Alternative Constructions of the Resolvent:
Modifications and Numerical Experiments 78
2.4.1 Continuation by the Mittag Leffler Method Combined
with the Transformation A = i(i + p)/(i — p) 78
2.4.2 Generalized Summation Methods 79
2.4.3 Transformation and Convergence Acceleration
of Series. Euler Summation 80
2.4.4 Pade Approximation of the Resolvent
and Approximation by Continued Fractions 83
2.4.5 Methods of Regularization of Analytical Continuation
for Solving Integral Equations 87
3. Monte Carlo Algorithms for Solving Boundary
Value Problems of the Potential Theory 91
3.1 The Walk on Boundary Algorithms for Solving
Interior and Exterior Boundary Value Problems
of the Potential Theory 91
3.1.1 Boundary Integral Equations 91
3.1.2 Interior Dirichlet and Exterior Neumann Problems .. 94
3.1.3 Interior Neumann, Exterior Dirichlet,
and the Third Boundary Value Problems 100
3.1.4 Dirichlet and Neumann Problems
for the Helmholtz Equation 104
3.1.5 The Variance, the Error and the Cost
of the Walk on Boundary Algorithms 107
3.2 Walk Inside the Domain Algorithms 110
3.2.1 General Scheme for Constructing Monte Carlo
Estimates on the Walk Inside the Domain Processes . 110
3.2.2 Non homogeneous Equations and Global Walk
on Spheres Algorithm for Calculating the Solution
and Derivative Fields 117
3.2.3 The Walk on Small Spheres
and on Other Standard Domains 121
3.3 Numerical Solution of Some Test and Applied Problems
of Potential Theory in Deterministic and Stochastic Formulation 127
3.3.1 Numerical Experiments:
Solution of Test Problems of Potential Theory 127
3.3.2 Calculation of the Capture Coefficient
of Highly Dispersed Aerosols (3D) 130
VIII
4. Monte Carlo Algorithms for Solving High Order Equations
and the Elasticity Problems 143
4.1 Biharmonic Problem 143
4.1.1 Vector Walk on Circles Algorithm for Solving the
Plate Bending Problem for Simply Supported Plates . 145
4.1.2 Plates with Arbitrary Boundaries 148
4.1.3 Direct and Adjoint Algorithms for Calculating
the Fields of Solution and Derivatives 159
4.2 Metaharmonic Equations 161
4.2.1 Mean Value Theorems for Metaharmonic Equations . 161
4.2.2 Vector Walk on Spheres Algorithm 163
4.2.3 Scalar Algorithms 169
4.3 Spatial Problems of the Elasticity Theory 170
4.3.1 Walk on Boundary Algorithms for the Lame Equation 171
4.3.2 Walk on Spheres Algorithm
for the First Boundary Value Problem 176
4.4 Application to Stochastic Elasticity Problems 183
4.4.1 The Bending Problem
for a Plate Lying on an Elastic Base 183
4.4.2 Random Loads 188
5. Monte Carlo Algorithms for Solving Diffusion Problems 191
5.1 Walk on Boundary Algorithms for the Heat Equation 191
5.1.1 Generalization of Isotropic Walk
on Boundary Processes to the Nonstationary Case ... 191
5.1.2 The Variance and Cost of the Walk
on Boundary Algorithms 198
5.1.3 Diffusion Equation in a Half space.
Direct Monte Carlo Scheme 203
5.1.4 Adjoint Scheme 206
5.1.5 Nonhomogeneous Case 213
5.1.6 Calculation of Derivatives 215
5.2 The Walk Inside the Domain Algorithms 219
5.2.1 Cauchy Problem 219
5.2.2 Use of the Laplace Transform 223
5.3 Particle Diffusion in Random Velocity Fields 228
5.3.1 Particle Diffusion in Local Isotropic Velocity Fields . 228
5.3.2 Calculation of Statistical Characteristics of a Cloud . 238
5.3.3 Statistical Model of the Turbulent Velocity Field
for a Horizontally Homogeneous Boundary Layer ... 245
5.4 Applications to Diffusion Problems 254
5.4.1 Distribution of the First Passage Time for Particles
Moving in Classical Isotropic Random Velocity Fields 254
5.4.2 Spread of Clouds of Particles of Aerosol Insecticide
in Arboreal Canopies 259
IX
5.4.3 Diffuse Deposition
of Polydispersed Aerosol Particles in Pipes 260
5.4.4 Simulation of the Growth
of Nuclei Highly Dispersed Aerosol Particles 263
References 275
Subject Index 281
X
|
| any_adam_object | 1 |
| author | Sabel'fel'd, Karl K. 1953- |
| author_GND | (DE-588)121181529 |
| author_facet | Sabel'fel'd, Karl K. 1953- |
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| id | DE-604.BV004683159 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T08:21:18Z |
| institution | BVB |
| isbn | 3540530010 0387530010 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002875588 |
| oclc_num | 22664994 |
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| owner_facet | DE-91 DE-BY-TUM DE-703 DE-384 DE-29T DE-706 DE-83 DE-188 |
| physical | XII, 283 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in computational physics |
| spellingShingle | Sabel'fel'd, Karl K. 1953- Monte Carlo methods in boundary value problems Monte-Carlo, méthode de ram Problèmes aux limites ram Boundary value problems Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Integralgleichung (DE-588)4027229-1 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4027229-1 (DE-588)4048395-2 |
| title | Monte Carlo methods in boundary value problems |
| title_alt | Metody Monte-Karlo v kraevych zadačach |
| title_auth | Monte Carlo methods in boundary value problems |
| title_exact_search | Monte Carlo methods in boundary value problems |
| title_full | Monte Carlo methods in boundary value problems Karl K. Sabelfeld |
| title_fullStr | Monte Carlo methods in boundary value problems Karl K. Sabelfeld |
| title_full_unstemmed | Monte Carlo methods in boundary value problems Karl K. Sabelfeld |
| title_short | Monte Carlo methods in boundary value problems |
| title_sort | monte carlo methods in boundary value problems |
| topic | Monte-Carlo, méthode de ram Problèmes aux limites ram Boundary value problems Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Integralgleichung (DE-588)4027229-1 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Monte-Carlo, méthode de Problèmes aux limites Boundary value problems Monte Carlo method Monte-Carlo-Simulation Integralgleichung Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002875588&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sabelfeldkarlk metodymontekarlovkraevychzadacach AT sabelfeldkarlk montecarlomethodsinboundaryvalueproblems |
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