Monte Carlo Methods for Electromagnetics

by Matthew N.O. Sadiku

• ISBN13: 9781439800720
• ISBN10: 1439800723
• Format: Nonspecific Binding
• Copyright: 2018-10-03
• Publisher: Taylor & Francis

Summary

Until now, novices had to painstakingly dig through the literature to discover how to use Monte Carlo techniques for solving electromagnetic problems. Written by one of the foremost researchers in the field, Monte Carlo Methods for Electromagneticsprovides a solid understanding of these methods and their applications in electromagnetic computation. Including much of his own work, the author brings together essential information from several different publications. Using a simple, clear writing style, the author begins with a historical background and review of electromagnetic theory. After addressing probability and statistics, he introduces the finite difference method as well as the fixed and floating random walk Monte Carlo methods. The text then applies the Exodus method to Laplace#xE2;#xAC;"s and Poisson#xE2;#xAC;"s equations and presents Monte Carlo techniques for handing Neumann problems. It also deals with whole field computation using the Markov chain, applies Monte Carlo methods to time-varying diffusion problems, and explores wave scattering due to random rough surfaces. The final chapter covers multidimensional integration. Although numerical techniques have become the standard tools for solving practical, complex electromagnetic problems, there is no book currently available that focuses exclusively on Monte Carlo techniques for electromagnetics. Alleviating this problem, this book describes Monte Carlo methods as they are used in the field of electromagnetics.

Table of Contents

Introduction

Why Monte Carlo?

Historical Background

Applications of MCMs

Review of Electromagnetic Theory

Probability and Statistics

Generation of Random Numbers

Statistical Tests of Pseudorandom Numbers

Generation of Random Variates

Generation of Continuous Random Variates

Evaluation of Error

Summary

Finite Difference Method

Finite Differences

Finite Differencing of Parabolic PDEs

Finite Differencing of Hyperbolic PDEs

Finite Differencing of Elliptic PDEs

Accuracy and Stability of Finite Difference Solutions

Maxwell's Equations

Summary

Fixed Random Walk

Introduction

Solution of Laplace's Equation

Solution of Poisson's Equation

Solution of Axisymmetric Problems

Summary

Floating Random Walk

Introduction

Rectangular Solution Regions

Axisymmetric Solution Regions

Summary

The Exodus Method

Solution of Laplace's Equation

Solution of Poisson's Equation

Summary

Neumann Problems

Governing Equations

Triangular Mesh Method

Computing Procedure

Summary

Whole Field Computation

Introduction

Regular Monte Carlo Method

Absorbing Markov Chains

Summary

Time-Varying Problems

Introduction

Diffusion Equation

Rectangular Solution Region

Cylindrical Solution Region

Summary

Scattering from Random Rough Surfaces

Introduction

Scattering of by 1-D Random Rough Surfaces

Scattering of by 2-D Random Rough Surfaces

Summary

Multidimensional Integration

Introduction

Crude Monte Carlo Integration

Monte Carlo Integration with Antithetic Variates

Improper Integrals

Summary

References and Problems appear at the end of each chapter

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