Adaptive Stochastic Methods: In Computational Mathematics and Mechanics

✍ Scribed by Dmitry G. Arseniev; Vladimir M. Ivanov; Maxim L. Korenevsky

• Publisher: De Gruyter
• Year: 2018
• Tongue: English
• Leaves: 290
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Preface
Contents
Introduction: Statistical Computing Algorithms as a Subject of Adaptive Control
Part I: Evaluation of Integrals
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
Part II: Solution of Integral Equations
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