Analytical and Computational Methods in

Achieve optimal microwave system performance by mastering the principles and methods underlying today's powerful computational tools and commercial software in electromagnetics. This authoritative resource offers you clear and complete explanation of this essential electromagnetics knowledge, providing you with the analytical background you need to understand such key approaches as MoM (method of moments), FDTD (Finite Difference Time Domain) and FEM (Finite Element Method), and Green's functions. This comprehensive book includes all math necessary to master the material. Moreover, it features numerous solved problems that help ensure your understanding of key concepts throughout the book. To keep you from being bogged down with complex mathematical details (vector calculus) and coding, this comprehensive volume places emphasis on the analysis of the scalar wave equation in Cartesian coordinates. The book also includes multiple choice questions, appropriate for self study or courses, that help clarify concepts without any mathematical burden. Packed with over 1,300 equations, most of the problems presented in the book can be solved using nothing more than calculator. CD-ROM-Included! Includes time-saving Matlabreg; source code for the problems presented in the book which can be easily modified to help you solve similar problems in the field.

Ramesh Garg is a professor in the Electronics and Electrical Communication Engineering Department at the Indiana Institute of Technology, Kharagpur, India.

Basic Principles of Electromagnetic Theory - Maxwell's Equations
Constitutive Relations
Electrical Properties of the Medium
Interface and Boundary Conditions
Skin Depth
Poynting Vector and Power Flow
Image Currents and Equivalence Principle
Reciprocity Theorem
Differential Equations in Electromagnetics
Vector Potentials
Phase Velocity, Group Velocity and Dispersion, Characteristics of Transmission Lines
Charge and Current Singularities
Classification of Methods of Analysis
Mathematical Framework in Electromagnetics
Overview of Analytical and Computational Methods
Analytical Methods and Orthogonal Functions - Introduction
Method of Separation of Variables
Orthogonality Condition
Sturn-Liouville Differential Equation
Eigenfunction Expansion Method
Vector Space/Function Space
Operators and their Matrix Representation
Delta-Function and Source Representations
Green's Functions - Introduction
Direct Construction Approach for Green's Function
Eigenfunction Expansion of Green's Function
Green's Function in Spectral Domain
Examples
Green's Function for Unbounded Region
Contour Integration and Conformal Mapping - Introduction
Calculus of Residues
Evaluation of Definite Improper Integrals
Conformal Mapping of Complex Functions
Schwarz-Christoffel Transformation
Quasi-Static Analysis of Planar Transmission Lines
Some Useful Mappings for Planar Transmission Lines
Fourier Transform Method - Introduction
Reduction of PDE to Ordinary Differential Equation/Algebraic Equation
Solution of Differential Equations with Unbounded Regions
Radiation from Two-Dimensional Apertures
Stationary Phase Method
Green's Function for the Quasi-Static Analysis of Microstrip Line
Introduction to Computational Methods
Elements of Computational Methods
Basis Functions
Convergence and Discretization Error
Stability of Numerical Solutions
Accuracy of Numerical Solutions
Spurious Solutions
Formulations for the Computational Methods
Method of Finite Differences
Finite Difference Approximations
Treatment of Interface and Boundary Conditions
Numerical Dispersion
Finite Difference Analysis of Guiding Structures: Microstrip Line, Ridge Waveguide, etc
Finite Difference Time Domain Analysis - Pulse Propagation in a Transmission Line
FDTD Analysis in One-Dimension
Applications of One-Dimension
Analysis to Reflection at an Interface
Propagation Constant Determination
Material Absorber Design
FDTD Analysis in Two- and Three- Dimensions
Implementation of Boundary Conditions in FDTD
Advances in FDTD
Variational Methods
Calculus of Variations
Stationary Functional and Euler Equations
The Ritz Variational Method and its Applications to the Solution of Laplace Equation
Waveguide Modes and Resonant Frequencies of Cavities
Construction of Functionals from PDE
Method of Weighed Residuals
Finite Element Method
Basic Steps in Finite Element Analysis
FEM Analysis in One- and Two-Dimensions
Rectangular and Triangular Elements
Mesh Generation
Weighted Residual Formulation for FEM
Examples: Inhomogeneously Filled Capacitor
Cut-off Frequency of Waveguide Modes, etc
Method of Moments - Introduction
Solution of Integral Equations Using MoM
Fast Multipole Solution Methods for MoM
Comparison of FDM, FDTD, FEM, and MoM
Hybrid Computational Methods
Examples: Charge Distribution on a Wire, Stripline Analysis, Wire Dipole Antenna, Scattering from a Conducting Cylinder, etc
Appendices
About the Author
Index
Table of Contents provided by Publisher. All Rights Reserved.

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Analytical and Computational Methods in Electromagnetics

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