Numerical techniques in electromagnetics / Matthew N.O. Sadiku.

Format:

Book

Author/Creator:

Sadiku, Matthew N. O.

Contributor:

Class of 1924 Book Fund.

Language:

English

Subjects (All):

Electromagnetism.

Numerical analysis.

Physical Description:

xiv, 743 pages : illustrations ; 25 cm

Edition:

Second edition.

Other Title:

Electromagnetics

Place of Publication:

Boca Raton : CRC Press, 2001.

Summary:

A bestseller in its first edition, Numerical Techniques in Electromagnetics: Second Edition shows how to pose, numerically analyze, and solve electromagnetic (EM) problems. It expands readers problem-solving skills with a variety of available numerical methods. The topics covered in the new edition include fundamental concepts in EM, numerical methods, finite difference methods, moment methods and finite element methods, transmission-line matrix or modeling (TLM), and Monte Carlo methods -- all in a simple, clear, easy-to-understand presentation ideal as a text, for self-study, and as a reference.

Contents:

1 Fundamental Concepts 1

1.2 Review of Electromagnetic Theory 2

1.2.1 Electrostatic Fields 3

1.2.2 Magnetostatic Fields 4

1.2.3 Time-varying Fields 5

1.2.4 Boundary Conditions 7

1.2.5 Wave Equations 7

1.2.6 Time-varying Potentials 9

1.2.7 Time-harmonic Fields 10

1.3 Classification of EM Problems 14

1.3.1 Classification of Solution Regions 14

1.3.2 Classification of Differential Equations 15

1.3.3 Classification of Boundary Conditions 18

1.4 Some Important Theorems 20

1.4.1 Superposition Principle 20

1.4.2 Uniqueness Theorem 21

2 Analytical Methods 27

2.2 Separation of Variables 28

2.3 Separation of Variables in Rectangular Coordinates 30

2.3.1 Laplace's Equations 30

2.3.2 Wave Equation 34

2.4 Separation of Variables in Cylindrical Coordinates 39

2.4.1 Laplace's Equation 40

2.4.2 Wave Equation 42

2.5 Separation of Variables in Spherical Coordinates 53

2.5.1 Laplace's Equation 54

2.5.2 Wave Equation 59

2.6 Some Useful Orthogonal Functions 68

2.7 Series Expansion 78

2.7.1 Poisson's Equation in a Cube 78

2.7.2 Poisson's Equation in a Cylinder 80

2.7.3 Strip Transmission Line 83

2.8 Practical Applications 88

2.8.1 Scattering by Dielectric Sphere 88

2.8.2 Scattering Cross Sections 92

2.9 Attenuation Due to Raindrops 95

3 Finite Difference Methods 121

3.2 Finite Difference Schemes 122

3.3 Finite Differencing of Parabolic PDEs 125

3.4 Finite Differencing of Hyperbolic PDEs 131

3.5 Finite Differencing of Elliptic PDEs 134

3.5.1 Band Matrix Method 137

3.5.2 Iterative Methods 137

3.6 Accuracy and Stability of FD Solutions 143

3.7 Practical Applications I

Guided Structures 147

3.7.1 Transmission Lines 148

3.7.2 Waveguides 154

3.8 Practical Applications II

Wave Scattering (FDTD) 159

3.8.1 Yee's Finite Difference Algorithm 160

3.8.2 Accuracy and Stability 163

3.8.3 Lattice Truncation Conditions 164

3.8.4 Initial Fields 167

3.8.5 Programming Aspects 168

3.9 Absorbing Boundary Conditions for FDTD 177

3.10 Finite Differencing for Nonrectangular Systems 186

3.10.1 Cylindrical Coordinates 186

3.10.2 Spherical Coordinates 190

3.11 Numerical Integration 193

3.11.1 Euler's Rule 196

3.11.2 Trapezoidal Rule 197

3.11.3 Simpson's Rule 197

3.11.4 Newton-Cotes Rules 198

3.11.5 Gaussian Rules 200

3.11.6 Multiple Integration 203

4 Variational Methods 235

4.2 Operators in Linear Spaces 236

4.3 Calculus of Variations 238

4.4 Construction of Functionals from PDEs 242

4.5 Rayleigh-Ritz Method 245

4.6 Weighted Residual Method 252

4.6.1 Collocation Method 253

4.6.2 Subdomain Method 254

4.6.3 Galerkin Method 254

4.6.4 Least Squares Method 255

4.7 Eigenvalue Problems 261

4.8 Practical Applications 268

5 Moment Methods 285

5.2 Integral Equations 286

5.2.1 Classification of Integral Equations 286

5.2.2 Connection Between Differential and Integral Equations 287

5.3 Green's Functions 290

5.3.1 For Free Space 292

5.3.2 For Domain with Conducting Boundaries 295

5.4 Applications I

Quasi-Static Problems 308

5.5 Applications II

Scattering Problems 313

5.5.1 Scattering by Conducting Cylinder 314

5.5.2 Scattering by an Arbitrary Array of Parallel Wires 317

5.6 Applications III

Radiation Problems 325

5.6.1 Hallen's Integral Equation 326

5.6.2 Pocklington's Integral Equation 327

5.6.3 Expansion and Weighting Functions 327

5.7 Applications IV

EM Absorption in the Human Body 338

5.7.1 Derivation of Integral Equations 339

5.7.2 Transformation to Matrix Equation (Discretization) 342

5.7.3 Evaluation of Matrix Elements 343

5.7.4 Solution of the Matrix Equation 345

6 Finite Element Method 377

6.2 Solution of Laplace's Equation 378

6.2.1 Finite Element Discretization 378

6.2.2 Element Governing Equations 380

6.2.3 Assembling of All Elements 383

6.2.4 Solving the Resulting Equations 386

6.3 Solution of Poisson's Equation 397

6.3.1 Deriving Element-governing Equations 397

6.3.2 Solving the Resulting Equations 399

6.4 Solution of the Wave Equation 400

6.5 Automatic Mesh Generation I

Rectangular Domains 407

6.6 Automatic Mesh Generation II

Arbitrary Domains 410

6.6.1 Definition of Blocks 411

6.6.2 Subdivision of Each Block 412

6.6.3 Connection of Individual Blocks 413

6.7 Bandwidth Reduction 420

6.8 Higher Order Elements 424

6.8.1 Pascal Triangle 425

6.8.2 Local Coordinates 426

6.8.3 Shape Functions 427

6.8.4 Fundamental Matrices 430

6.9 Three-Dimensional Elements 439

6.10 Finite Element Methods for Exterior Problems 444

6.10.1 Infinite Element Method 444

6.10.2 Boundary Element Method 446

6.10.3 Absorbing Boundary Conditions 446

7 Transmission-line-matrix Method 467

7.2 Transmission-line Equations 469

7.3 Solution of Diffusion Equation 473

7.4 Solution of Wave Equations 477

7.4.1 Equivalence Between Network and Field Parameters 477

7.4.2 Dispersion Relation of Propagation Velocity 481

7.4.3 Scattering Matrix 483

7.4.4 Boundary Representation 486

7.4.5 Computation of Fields and Frequency Response 487

7.4.6 Output Response and Accuracy of Results 487

7.5 Inhomogeneous and Lossy Media in TLM 493

7.5.1 General Two-Dimensional Shunt Node 494

7.5.2 Scattering Matrix 496

7.5.3 Representation of Lossy Boundaries 497

7.6 Three-Dimensional TLM Mesh 499

7.6.1 Series Nodes 499

7.6.2 Three-Dimensional Node 504

7.6.3 Boundary Conditions 507

7.7 Error Sources and Correction 517

7.7.1 Truncation Error 518

7.7.2 Coarseness Error 518

7.7.3 Velocity Error 519

7.7.4 Misalignment Error 519

7.8 Absorbing Boundary Conditions 519

8 Monte Carlo Methods 537

8.2 Generation of Random Numbers and Variables 538

8.3 Evaluation of Error 542

8.4 Numerical Integration 546

8.4.1 Crude Monte Carlo Integration 546

8.4.2 Monte Carlo Integration with Antithetic Variates 548

8.4.3 Improper Integrals 549

8.5 Solution of Potential Problems 550

8.5.1 Fixed Random Walk 552

8.5.2 Floating Random Walk 557

8.5.3 Exodus Method 559

8.6 Regional Monte Carlo Methods 574

9 Method of Lines 597

9.2 Solution of Laplace's Equation 598

9.2.1 Rectangular Coordinates 598

9.2.2 Cylindrical Coordinates 605

9.3 Solution of Wave Equation 609

9.3.1 Planar Microstrip Structures 612

9.3.2 Cylindrical Microstrip Structures 619

9.4 Time-Domain Solution 627

A Vector Relations 639

A.1 Vector Identities 639

A.2 Vector Theorems 639

A.3 Orthogonal Coordinates 640

B Solving Electromagnetic Problems Using C++ 643

B.2 A Brief Description of C++ 643

B.3 Object-Orientation 661

B.4 C++ Object-Oriented Language Features 665

C Numerical Techniques in C++ 677

D Solution of Simultaneous Equations 701

D.1 Elimination Methods 701

D.1.1 Gauss's Method 702

D.1.2 Cholesky's Method 703

D.2 Iterative Methods 706

D.2.1 Jacobi's Method 706

D.2.2 Gauss-Seidel Method 708

D.2.3 Relaxation Method 708

D.2.4 Gradient Methods 710

D.3 Matrix Inversion 713

D.4 Eigenvalue Problems 714

D.4.1 Iteration (or Power) Method 716

D.4.2 Jacobi's Method 717.

Notes:

Errata slip inserted.

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1924 Book Fund.

ISBN:

0849313953

OCLC:

56732934