Numerical Techniques in Electromagnetics, Second Edition

Matthew N.O. Sadiku

CRC Press, Jul 12, 2000 - Technology & Engineering - 760 pages

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.

Contents

• Fundamental Concepts: 1
• 12 Review of Electromagnetic Theory: 2
• 121 Electrostatic Fields: 3
• 122 Magnetostatic Fields: 4
• 123 Timevarying Fields: 5
• 124 Boundary Conditions: 7
• 126 Timevarying Potentials: 9
• 127 Timeharmonic Fields: 10
• 13 Classification of EM Problems: 14
• 132 Classification of Differential Equations: 15
• 133 Classification of Boundary Conditions: 18
• 14 Some Important Theorems: 20
• 142 Uniqueness Theorem: 21
• References: 23
• Analytical Methods: 27
• 22 Separation of Variables: 28
• 23 Separation of Variables in Rectangular Coordinates: 30
• 232 Wave Equation: 34
• 24 Separation of Variables in Cylindrical Coordinates: 39
• 241 Laplaces Equation: 40
• 242 Wave Equation: 42
• 25 Separation of Variables in Spherical Coordinates: 53
• 251 Laplaces Equation: 54
• 252 Wave Equation: 59
• 26 Some Useful Orthogonal Functions: 68
• 27 Series Expansion: 78
• 272 Poissons Equation in a Cylinder: 80
• 273 Strip Transmission Line: 83
• 28 Practical Applications: 88
• 282 Scattering Cross Sections: 92
• 29 Attenuation Due to Raindrops: 95
• 210 Concluding Remarks: 105
• References: 106
• Problems: 107
• Finite Difference Methods: 121
• 32 Finite Difference Schemes: 122
• 33 Finite Differencing of Parabolic PDEs: 125
• 34 Finite Differencing of Hyperbolic PDEs: 131
• 35 Finite Differencing of Elliptic PDEs: 134
• 351 Band Matrix Method: 137
• 36 Accuracy and Stability of FD Solutions: 143
• 37 Practical Applications I Guided Structures: 147
• 371 Transmission Lines: 148
• 372 Waveguides: 154
• 38 Practical Applications II Wave Scattering FDTD: 159
• 381 Yees Finite Difference Algorithm: 160
• 382 Accuracy and Stability: 163
• 383 Lattice Truncation Conditions: 164
• 384 Initial Fields: 167
• 385 Programming Aspects: 168
• 39 Absorbing Boundary Conditions for FDTD: 177
• 310 Finite Differencing for Nonrectangular Systems: 186
• 3102 Spherical Coordinates: 190
• 311 Numerical Integration: 193
• 3111 Eulers Rule: 196
• 3112 Trapezoidal Rule: 197
• 3114 NewtonCotes Rules: 198
• 3115 Gaussian Rules: 200
• 3116 Multiple Integration: 203
• 312 Concluding Remarks: 208
• References: 210
• Problems: 219
• Variational Methods: 235
• 42 Operators n Linear Spaces: 236
• 43 Calculus of Variations: 238
• 44 Construction of Functionals from PDEs: 242
• 45 RayleighRitz Method: 245
• 46 Weighted Residual Method: 252
• 461 Collocation Method: 253
• 462 Subdomain Method: 254
• 464 Least Squares Method: 255
• 47 Eigenvalue Problems: 261
• 48 Practical Applications: 268
• 49 Concluding Remarks: 274
• References: 275
• Problems: 279
• Moment Methods: 285
• 52 Integral Equations: 286
• 522 Connection Between Differential and Integral Equations: 287
• 53 Greens Functions: 290
• 531 For Free Space: 292
• 532 For Domain with Conducting Boundaries: 295
• 54 Applications I QuasiStatic Problems: 308
• 55 Applications II Scattering Problems: 313
• 551 Scattering by Conducting Cylinder: 314
• 552 Scattering by an Arbitrary Array of Parallel Wires: 317
• 56 Applications III Radiation Problems: 325
• 561 Hallens Integral Equation: 326
• 562 Pocklingtons Integral Equation: 327
• 57 Applications IV EM Absorption in the Human Body: 338
• 571 Derivation of Integral Equations: 339
• 572 Transformation to Matrix Equation Discretization: 342
• 573 Evaluation of Matrix Elements: 343
• 574 Solution of the Matrix Equation: 345
• 58 Concluding Remarks: 347
• References: 357
• Problems: 363
• Finite Element Method: 377
• 62 Solution of Laplaces Equation: 378
• 622 Element Governing Equations: 380
• 623 Assembling of All Elements: 383
• 624 Solving the Resulting Equations: 386
• 63 Solution of Poissons Equation: 397
• 632 Solving the Resulting Equations: 399
• 64 Solution of the Wave Equation: 400
• 65 Automatic Mesh Generation I Rectangular Domains: 407
• 66 Automatic Mesh Generation II Arbitrary Domains: 410
• 661 Definition of Blocks: 411
• 662 Subdivision of Each Block: 412
• 663 Connection of Individual Blocks: 413
• 67 Bandwidth Reduction: 420
• 68 Higher Order Elements: 424
• 681 Pascal Triangle: 425
• 682 Local Coordinates: 426
• 683 Shape Functions: 427
• 684 Fundamental Matrices: 430
• 69 ThreeDimensional Elements: 439
• 610 Finite Element Methods for Exterior Problems: 444
• 6102 Boundary Element Method: 446
• 611 Concluding Remarks: 448
• References: 449
• Problems: 458
• Transmissionlinematrix Method: 467
• 72 Transmissionline Equations: 469
• 73 Solution of Diffusion Equation: 473
• 74 Solution of Wave Equations: 477
• 742 Dispersion Relation of Propagation Velocity: 481
• 743 Scattering Matrix: 483
• 744 Boundary Representation: 486
• 745 Computation of Fields and Frequency Response: 487
• 75 Inhomogeneous and Lossy Media in TLM: 493
• 751 General TwoDimensional Shunt Node: 494
• 752 Scattering Matrix: 496
• 753 Representation of Lossy Boundaries: 497
• 76 ThreeDimensional TLM Mesh: 499
• 762 ThreeDimensional Node: 504
• 763 Boundary Conditions: 507
• 77 Error Sources and Correction: 517
• 771 Truncation Error: 518
• 773 Velocity Error: 519
• 79 Concluding Remarks: 521
• References: 523
• Problems: 529
• Monte Carlo Methods: 537
• 82 Generation of Random Numbers and Variables: 538
• 83 Evaluation of Error: 542
• 84 Numerical Integration: 546
• 842 Monte Carlo Integration with Antithetic Variâtes: 548
• 843 Improper Integrals: 549
• 85 Solution of Potential Problems: 550
• 851 Fixed Random Walk: 552
• 852 Floating Random Walk: 557
• 853 Exodus Method: 559
• 86 Regional Monte Carlo Methods: 574
• 87 Concluding Remarks: 581
• References: 582
• Problems: 588
• Method of Lines: 597
• 92 Solution of Laplaces Equation: 598
• 922 Cylindrical Coordinates: 605
• 93 Solution of Wave Equation: 609
• 931 Planar Microstrip Structures: 612
• 932 Cylindrical Microstrip Structures: 619
• 94 TimeDomain Solution: 627
• 95 Concluding Remarks: 629
• Problems: 635
• Vector Relations: 639
• A3 Orthogonal Coordinates: 640
• Solving Electromagnetic Problems Using C++: 643
• B3 ObjectOrientation: 661
• B4 C++ ObjectOriented Language Features: 665
• B5 A Final Note: 674
• References: 675
• Numerical Techniques in С: 677
• Solution of Simultaneous Equations: 701
• D11 Gausss Method: 702
• D12 Choleskys Method: 703
• D2 Iterative Methods: 706
• D22 GaussSeidel Method: 708
• D24 Gradient Methods: 710
• D3 Matrix Inversion: 713
• D4 Eigenvalue Problems: 714
• D41 Iteration or Power Method: 716
• D42 Jacobis Method: 717
• Answers to OddNumbered Problems: 725
• Index: 741

Bibliographic information

• Title: Numerical Techniques in Electromagnetics, Second Edition
• Author: Matthew N.O. Sadiku
• Edition: 2, revised
• Publisher: CRC Press, 2000
• ISBN: 0849313953, 9780849313950
• Length: 760 pages
• Subjects: Technology & Engineering / Electrical; Technology & Engineering / Microwaves