### Numerical Techniques in Electromagnetics

### Numerical Techniques in Electromagnetics

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As the availability of powerful computer resources has grown over the last three decades, the art of computation of electromagnetic (EM) problems has also grown - exponentially. Despite this dramatic growth, however, the EM community lacked a comprehensive text on the computational techniques used to solve EM problems. The first edition of Numerical Techniques in Electromagnetics filled that gap and became the reference of choice for thousands of engineers, researchers, and students.

The Second Edition of this bestselling text reflects the continuing increase in awareness and use of numerical techniques and incorporates advances and refinements made in recent years. Most notable among these are the improvements made to the standard algorithm for the finite difference time domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transmission-line-matrix methods. The author also added a chapter on the method of lines.

Numerical Techniques in Electromagnetics continues to teach readers how to pose, numerically analyze, and solve EM problems, give them the ability to expand their problem-solving skills using a variety of methods, and prepare them for research in electromagnetism. Now the Second Edition goes even further toward providing a comprehensive resource that addresses all of the most useful computation methods for EM problems.

FUNDAMENTAL CONCEPTS

Review of Electromagnetic Theory

Classification of EM Problem

Some Important Theorems

ANALYTICAL METHODS

Separation of Variables

Separation of Variables in Rectangular Coordinates

Separation of Variables in Cylindrical Coordinates

Separation of Variables in Spherical Coordinates

Some Useful Orthogonal Functions

Series Expansion

Practical Applications

Attenuation Due to Raindrops

FINITE DIFFERENCE METHODS

Finite Difference Schemes

Finite Differencing of Parabolic PDEs

Finite Differencing of Hyperbolic PDEs

Finite Differencing of Elliptic PDEs

Accuracy and Stability of FD Solutions

Practical Application I - Guided Structures

Practical Applications II - Wave Scattering

Absorbing Boundary Conditions for FDTD

Finite Differencing for Nonrectangular Systems

Numerical Integration

VARIATIONAL METHODS

Operators in Linear Spaces

Calculus of Variations

Construction of Functionals from PDEs

Rayleigh-Ritz Method

Weighted Residual Method

Eigenvalue Problems

Practical Applications

MOMENT METHODS

Integral Equations

Green's Functions

Applications I - Quasi-Static Problems

Applications II - Scattering Problems

Applications III - Radiation Problems

Application IV - EM Absorption in the Human Body

FINITE ELEMENT METHOD

Solution of Laplace's Equation

Solution of Poisson's Equation

Solution of the Wave Equation

Automatic Mesh Generation I - Rectangular Domains

Automatic Mesh Generation II - Arbitrary Domains

Bandwidth Reduction

Higher Order Elements

Three-Dimensional Elements

Finite Element Methods for Exterior Problems

TRANSMISSION-LINE-MATRIX METHOD

Transmission-Line Equations

Solution of Diffusion Equation

Solution of Wave Equations

Inhomogeneous and Lossy Media in TLM

Three-Dimensional TLM Mesh

Error Sources and Correction

Absorbing Boundary Conditions

MONTE CARLO METHODS

Generation of Random Numbers and Variables

Evaluation of Error

Numerical Integration

Solution of Potential Problems

Regional Monte Carlo Methods

METHOD OF LINES

Solution of Laplace's Equation

Solution of Wave Equation

Time-Domain Solution

APPENDICES

Vector Relations

Solving Electromagnetic Problems Using C++

Numerical Techniques in C++

Solution of Simultaneous Equations

Answers to Odd-Numbered Problems

Index

Each chapter also contains an Introduction, Concluding Remarks, References, and Problems

As the availability of powerful computer resources has grown over the last three decades, the art of computation of electromagnetic (EM) problems has also grown - exponentially. Despite this dramatic growth, however, the EM community lacked a comprehensive text on the computational techniques used to solve EM problems. The first edition of Numerical Techniques in Electromagnetics filled that gap and became the reference of choice for thousands of engineers, researchers, and students.

The Second Edition of this bestselling text reflects the continuing increase in awareness and use of numerical techniques and incorporates advances and refinements made in recent years. Most notable among these are the improvements made to the standard algorithm for the finite difference time domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transmission-line-matrix methods. The author also added a chapter on the method of lines.

Numerical Techniques in Electromagnetics continues to teach readers how to pose, numerically analyze, and solve EM problems, give them the ability to expand their problem-solving skills using a variety of methods, and prepare them for research in electromagnetism. Now the Second Edition goes even further toward providing a comprehensive resource that addresses all of the most useful computation methods for EM problems.

FUNDAMENTAL CONCEPTS

Review of Electromagnetic Theory

Classification of EM Problem

Some Important Theorems

ANALYTICAL METHODS

Separation of Variables

Separation of Variables in Rectangular Coordinates

Separation of Variables in Cylindrical Coordinates

Separation of Variables in Spherical Coordinates

Some Useful Orthogonal Functions

Series Expansion

Practical Applications

Attenuation Due to Raindrops

FINITE DIFFERENCE METHODS

Finite Difference Schemes

Finite Differencing of Parabolic PDEs

Finite Differencing of Hyperbolic PDEs

Finite Differencing of Elliptic PDEs

Accuracy and Stability of FD Solutions

Practical Application I - Guided Structures

Practical Applications II - Wave Scattering

Absorbing Boundary Conditions for FDTD

Finite Differencing for Nonrectangular Systems

Numerical Integration

VARIATIONAL METHODS

Operators in Linear Spaces

Calculus of Variations

Construction of Functionals from PDEs

Rayleigh-Ritz Method

Weighted Residual Method

Eigenvalue Problems

Practical Applications

MOMENT METHODS

Integral Equations

Green's Functions

Applications I - Quasi-Static Problems

Applications II - Scattering Problems

Applications III - Radiation Problems

Application IV - EM Absorption in the Human Body

FINITE ELEMENT METHOD

Solution of Laplace's Equation

Solution of Poisson's Equation

Solution of the Wave Equation

Automatic Mesh Generation I - Rectangular Domains

Automatic Mesh Generation II - Arbitrary Domains

Bandwidth Reduction

Higher Order Elements

Three-Dimensional Elements

Finite Element Methods for Exterior Problems

TRANSMISSION-LINE-MATRIX METHOD

Transmission-Line Equations

Solution of Diffusion Equation

Solution of Wave Equations

Inhomogeneous and Lossy Media in TLM

Three-Dimensional TLM Mesh

Error Sources and Correction

Absorbing Boundary Conditions

MONTE CARLO METHODS

Generation of Random Numbers and Variables

Evaluation of Error

Numerical Integration

Solution of Potential Problems

Regional Monte Carlo Methods

METHOD OF LINES

Solution of Laplace's Equation

Solution of Wave Equation

Time-Domain Solution

APPENDICES

Vector Relations

Solving Electromagnetic Problems Using C++

Numerical Techniques in C++

Solution of Simultaneous Equations

Answers to Odd-Numbered Problems

Index

Each chapter also contains an Introduction, Concluding Remarks, References, and Problems

As the availability of powerful computer resources has grown over the last three decades, the art of computation of electromagnetic (EM) problems has also grown - exponentially. Despite this dramatic growth, however, the EM community lacked a comprehensive text on the computational techniques used to solve EM problems. The first edition of Numerical Techniques in Electromagnetics filled that gap and became the reference of choice for thousands of engineers, researchers, and students.

The Second Edition of this bestselling text reflects the continuing increase in awareness and use of numerical techniques and incorporates advances and refinements made in recent years. Most notable among these are the improvements made to the standard algorithm for the finite difference time domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transmission-line-matrix methods. The author also added a chapter on the method of lines.

Numerical Techniques in Electromagnetics continues to teach readers how to pose, numerically analyze, and solve EM problems, give them the ability to expand their problem-solving skills using a variety of methods, and prepare them for research in electromagnetism. Now the Second Edition goes even further toward providing a comprehensive resource that addresses all of the most useful computation methods for EM problems.

FUNDAMENTAL CONCEPTS

Review of Electromagnetic Theory

Classification of EM Problem

Some Important Theorems

ANALYTICAL METHODS

Separation of Variables

Separation of Variables in Rectangular Coordinates

Separation of Variables in Cylindrical Coordinates

Separation of Variables in Spherical Coordinates

Some Useful Orthogonal Functions

Series Expansion

Practical Applications

Attenuation Due to Raindrops

FINITE DIFFERENCE METHODS

Finite Difference Schemes

Finite Differencing of Parabolic PDEs

Finite Differencing of Hyperbolic PDEs

Finite Differencing of Elliptic PDEs

Accuracy and Stability of FD Solutions

Practical Application I - Guided Structures

Practical Applications II - Wave Scattering

Absorbing Boundary Conditions for FDTD

Finite Differencing for Nonrectangular Systems

Numerical Integration

VARIATIONAL METHODS

Operators in Linear Spaces

Calculus of Variations

Construction of Functionals from PDEs

Rayleigh-Ritz Method

Weighted Residual Method

Eigenvalue Problems

Practical Applications

MOMENT METHODS

Integral Equations

Green's Functions

Applications I - Quasi-Static Problems

Applications II - Scattering Problems

Applications III - Radiation Problems

Application IV - EM Absorption in the Human Body

FINITE ELEMENT METHOD

Solution of Laplace's Equation

Solution of Poisson's Equation

Solution of the Wave Equation

Automatic Mesh Generation I - Rectangular Domains

Automatic Mesh Generation II - Arbitrary Domains

Bandwidth Reduction

Higher Order Elements

Three-Dimensional Elements

Finite Element Methods for Exterior Problems

TRANSMISSION-LINE-MATRIX METHOD

Transmission-Line Equations

Solution of Diffusion Equation

Solution of Wave Equations

Inhomogeneous and Lossy Media in TLM

Three-Dimensional TLM Mesh

Error Sources and Correction

Absorbing Boundary Conditions

MONTE CARLO METHODS

Generation of Random Numbers and Variables

Evaluation of Error

Numerical Integration

Solution of Potential Problems

Regional Monte Carlo Methods

METHOD OF LINES

Solution of Laplace's Equation

Solution of Wave Equation

Time-Domain Solution

APPENDICES

Vector Relations

Solving Electromagnetic Problems Using C++

Numerical Techniques in C++

Solution of Simultaneous Equations

Answers to Odd-Numbered Problems

Index

Each chapter also contains an Introduction, Concluding Remarks, References, and Problems

FUNDAMENTAL CONCEPTS

Review of Electromagnetic Theory

Classification of EM Problem

Some Important Theorems

ANALYTICAL METHODS

Separation of Variables

Separation of Variables in Rectangular Coordinates

Separation of Variables in Cylindrical Coordinates

Separation of Variables in Spherical Coordinates

Some Useful Orthogonal Functions

Series Expansion

Practical Applications

Attenuation Due to Raindrops

FINITE DIFFERENCE METHODS

Finite Difference Schemes

Finite Differencing of Parabolic PDEs

Finite Differencing of Hyperbolic PDEs

Finite Differencing of Elliptic PDEs

Accuracy and Stability of FD Solutions

Practical Application I - Guided Structures

Practical Applications II - Wave Scattering

Absorbing Boundary Conditions for FDTD

Finite Differencing for Nonrectangular Systems

Numerical Integration

VARIATIONAL METHODS

Operators in Linear Spaces

Calculus of Variations

Construction of Functionals from PDEs

Rayleigh-Ritz Method

Weighted Residual Method

Eigenvalue Problems

Practical Applications

MOMENT METHODS

Integral Equations

Green's Functions

Applications I - Quasi-Static Problems

Applications II - Scattering Problems

Applications III - Radiation Problems

Application IV - EM Absorption in the Human Body

FINITE ELEMENT METHOD

Solution of Laplace's Equation

Solution of Poisson's Equation

Solution of the Wave Equation

Automatic Mesh Generation I - Rectangular Domains

Automatic Mesh Generation II - Arbitrary Domains

Bandwidth Reduction

Higher Order Elements

Three-Dimensional Elements

Finite Element Methods for Exterior Problems

TRANSMISSION-LINE-MATRIX METHOD

Transmission-Line Equations

Solution of Diffusion Equation

Solution of Wave Equations

Inhomogeneous and Lossy Media in TLM

Three-Dimensional TLM Mesh

Error Sources and Correction

Absorbing Boundary Conditions

MONTE CARLO METHODS

Generation of Random Numbers and Variables

Evaluation of Error

Numerical Integration

Solution of Potential Problems

Regional Monte Carlo Methods

METHOD OF LINES

Solution of Laplace's Equation

Solution of Wave Equation

Time-Domain Solution

APPENDICES

Vector Relations

Solving Electromagnetic Problems Using C++

Numerical Techniques in C++

Solution of Simultaneous Equations

Answers to Odd-Numbered Problems

Index

Each chapter also contains an Introduction, Concluding Remarks, References, and Problems

FUNDAMENTAL CONCEPTS

Review of Electromagnetic Theory

Classification of EM Problem

Some Important Theorems

ANALYTICAL METHODS

Separation of Variables

Separation of Variables in Rectangular Coordinates

Separation of Variables in Cylindrical Coordinates

Separation of Variables in Spherical Coordinates

Some Useful Orthogonal Functions

Series Expansion

Practical Applications

Attenuation Due to Raindrops

FINITE DIFFERENCE METHODS

Finite Difference Schemes

Finite Differencing of Parabolic PDEs

Finite Differencing of Hyperbolic PDEs

Finite Differencing of Elliptic PDEs

Accuracy and Stability of FD Solutions

Practical Application I - Guided Structures

Practical Applications II - Wave Scattering

Absorbing Boundary Conditions for FDTD

Finite Differencing for Nonrectangular Systems

Numerical Integration

VARIATIONAL METHODS

Operators in Linear Spaces

Calculus of Variations

Construction of Functionals from PDEs

Rayleigh-Ritz Method

Weighted Residual Method

Eigenvalue Problems

Practical Applications

MOMENT METHODS

Integral Equations

Green's Functions

Applications I - Quasi-Static Problems

Applications II - Scattering Problems

Applications III - Radiation Problems

Application IV - EM Absorption in the Human Body

FINITE ELEMENT METHOD

Solution of Laplace's Equation

Solution of Poisson's Equation

Solution of the Wave Equation

Automatic Mesh Generation I - Rectangular Domains

Automatic Mesh Generation II - Arbitrary Domains

Bandwidth Reduction

Higher Order Elements

Three-Dimensional Elements

Finite Element Methods for Exterior Problems

TRANSMISSION-LINE-MATRIX METHOD

Transmission-Line Equations

Solution of Diffusion Equation

Solution of Wave Equations

Inhomogeneous and Lossy Media in TLM

Three-Dimensional TLM Mesh

Error Sources and Correction

Absorbing Boundary Conditions

MONTE CARLO METHODS

Generation of Random Numbers and Variables

Evaluation of Error

Numerical Integration

Solution of Potential Problems

Regional Monte Carlo Methods

METHOD OF LINES

Solution of Laplace's Equation

Solution of Wave Equation

Time-Domain Solution

APPENDICES

Vector Relations

Solving Electromagnetic Problems Using C++

Numerical Techniques in C++

Solution of Simultaneous Equations

Answers to Odd-Numbered Problems

Index

Each chapter also contains an Introduction, Concluding Remarks, References, and Problems

FUNDAMENTAL CONCEPTS

Review of Electromagnetic Theory

Classification of EM Problem

Some Important Theorems

ANALYTICAL METHODS

Separation of Variables

Separation of Variables in Rectangular Coordinates

Separation of Variables in Cylindrical Coordinates

Separation of Variables in Spherical Coordinates

Some Useful Orthogonal Functions

Series Expansion

Practical Applications

Attenuation Due to Raindrops

FINITE DIFFERENCE METHODS

Finite Difference Schemes

Finite Differencing of Parabolic PDEs

Finite Differencing of Hyperbolic PDEs

Finite Differencing of Elliptic PDEs

Accuracy and Stability of FD Solutions

Practical Application I - Guided Structures

Practical Applications II - Wave Scattering

Absorbing Boundary Conditions for FDTD

Finite Differencing for Nonrectangular Systems

Numerical Integration

VARIATIONAL METHODS

Operators in Linear Spaces

Calculus of Variations

Construction of Functionals from PDEs

Rayleigh-Ritz Method

Weighted Residual Method

Eigenvalue Problems

Practical Applications

MOMENT METHODS

Integral Equations

Green's Functions

Applications I - Quasi-Static Problems

Applications II - Scattering Problems

Applications III - Radiation Problems

Application IV - EM Absorption in the Human Body

FINITE ELEMENT METHOD

Solution of Laplace's Equation

Solution of Poisson's Equation

Solution of the Wave Equation

Automatic Mesh Generation I - Rectangular Domains

Automatic Mesh Generation II - Arbitrary Domains

Bandwidth Reduction

Higher Order Elements

Three-Dimensional Elements

Finite Element Methods for Exterior Problems

TRANSMISSION-LINE-MATRIX METHOD

Transmission-Line Equations

Solution of Diffusion Equation

Solution of Wave Equations

Inhomogeneous and Lossy Media in TLM

Three-Dimensional TLM Mesh

Error Sources and Correction

Absorbing Boundary Conditions

MONTE CARLO METHODS

Generation of Random Numbers and Variables

Evaluation of Error

Numerical Integration

Solution of Potential Problems

Regional Monte Carlo Methods

METHOD OF LINES

Solution of Laplace's Equation

Solution of Wave Equation

Time-Domain Solution

APPENDICES

Vector Relations

Solving Electromagnetic Problems Using C++

Numerical Techniques in C++

Solution of Simultaneous Equations

Answers to Odd-Numbered Problems

Index

Each chapter also contains an Introduction, Concluding Remarks, References, and Problems