Adaptive Stochastic Methods: In Computational Mathematics and Mechanics

Dmitry G. Arseniev; Vladimir M. Ivanov; Maxim L. Korenevsky

Book

Adaptive Stochastic Methods

In Computational Mathematics and Mechanics

Dmitry G. Arseniev , Vladimir M. Ivanov and Maxim L. Korenevsky

Language: English

Published/Copyright: 2018

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About this book

This monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics.

Contents

Part I: Evaluation of Integrals
Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals
Sequential Monte Carlo Method and Adaptive Integration
Methods of Adaptive Integration Based on Piecewise Approximation
Methods of Adaptive Integration Based on Global Approximation
Numerical Experiments
Adaptive Importance Sampling Method Based on Piecewise Constant Approximation

Part II: Solution of Integral Equations
Semi-Statistical Method of Solving Integral Equations Numerically
Problem of Vibration Conductivity
Problem on Ideal-Fluid Flow Around an Airfoil
First Basic Problem of Elasticity Theory
Second Basic Problem of Elasticity Theory
Projectional and Statistical Method of Solving Integral Equations Numerically

Author / Editor information

Dmitry Arsenyev, Vladimir Ivanov and Maxim Korenevskii, St. Petersburg Polytechnical University, Russia.

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Frontmatter
I

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Preface
V

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Contents
VII

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Introduction: Statistical Computing Algorithms as a Subject of Adaptive Control
1

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Part I: Evaluation of Integrals
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1. Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals
9

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2. Sequential Monte Carlo Method and Adaptive Integration
27

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3. Methods of Adaptive Integration Based on Piecewise Approximation
59

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4. Methods of Adaptive Integration Based on Global Approximation
83

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5. Numerical Experiments
111

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6. Adaptive Importance Sampling Method Based on Piecewise Constant Approximation
123

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Part II: Solution of Integral Equations
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7. Semi-Statistical Method of Solving Integral Equations Numerically
151

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8. Problem of Vibration Conductivity
173

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9. Problem on Ideal-Fluid Flow Around an Airfoil
193

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10. First Basic Problem of Elasticity Theory
215

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11. Second Basic Problem of Elasticity Theory
231

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12. Projectional and Statistical Method of Solving Integral Equations Numerically
241

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Afterword
271

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Bibliography
273

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Index
277

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

January 9, 2018

eBook ISBN:

9783110554632

Hardcover published on:

January 9, 2018

Hardcover ISBN:

9783110553642

Pages and Images/Illustrations in book

Front matter:

12

Main content:

278

Illustrations:

50

https://doi.org/10.1515/9783110554632

eBook ISBN: 9783110554632

Hardcover ISBN: 9783110553642

Keywords for this book

Monte-Carlo-Integration; Computermathematik; Adaptive Control

Audience(s) for this book

Researchers in Mathematics and Physics as well as in Mechanical Engineering.

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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Adaptive Stochastic Methods

Overview

About this book

Author / Editor information

Topics

Table of contents

Frontmatter

Preface

Contents

Introduction: Statistical Computing Algorithms as a Subject of Adaptive Control

1. Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals

2. Sequential Monte Carlo Method and Adaptive Integration

3. Methods of Adaptive Integration Based on Piecewise Approximation

4. Methods of Adaptive Integration Based on Global Approximation

5. Numerical Experiments

6. Adaptive Importance Sampling Method Based on Piecewise Constant Approximation

7. Semi-Statistical Method of Solving Integral Equations Numerically

8. Problem of Vibration Conductivity

9. Problem on Ideal-Fluid Flow Around an Airfoil

10. First Basic Problem of Elasticity Theory

11. Second Basic Problem of Elasticity Theory

12. Projectional and Statistical Method of Solving Integral Equations Numerically

Afterword

Bibliography

Index

Bibliographic data