Monte Carlo Methods for Electromagnetics
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Features
- Explores the use of Monte Carlo methods for the solution of electromagnetic problems
- Presents Monte Carlo methods in a systematic way
- Provides solutions to Maxwell’s, Laplace’s, and Poisson’s equations using the finite difference method, Exodus method, and more
- Supplies MATLAB® code for many examples
- Collects information from several different publications
- Includes examples and end-of-chapter problems to highlight the application of Monte Carlo techniques in electromagnetics
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 Electromagnetics provides 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’s and Poisson’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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