Preface to the second edition .................................. xv
Preface to the first edition ................................. xvii
Acknowledgements .............................................. xxi
To the reader ............................................... xxiii
List of notation ............................................. xxiv
1 An overview of computational electromagnetics for RF and
microwave applications ....................................... 1
1.1 Introduction ............................................ 1
1.2 Full-wave СЕМ techniques ................................ 3
1.3 The method of moments (MoM) ............................. 8
1.4 The finite difference time domain (FDTD) method ........ 10
1.5 The finite element method (FEM) ........................ 13
1.6 Other methods .......................................... 16
1.7 The СЕМ modelling process .............................. 17
1.8 Verification and validation ............................ 19
1.9 Convergence and extrapolation .......................... 23
1.10 Extending the limits of full-wave СЕМ methods .......... 24
1.11 СЕМ: the future ........................................ 25
1.12 A "road map" of this book .............................. 28
References .................................................. 29
2 The finite difference time domain method:
a one-dimensional introduction .............................. 32
David B. Davidson and James T. Aberle
2.1 Introduction ........................................... 32
2.2 An overview of finite differences ...................... 33
2.3 A very brief history of the FDTD ....................... 36
2.4 A one-dimensional introduction to the FDTD ............. 37
2.5 Obtaining wideband data using the FDTD ................. 52
2.6 Numerical dispersion in FDTD simulations ............... 64
2.7 The Courant stability criterion derived by von
Neumann analysis ....................................... 67
2.8 Conclusion ............................................. 71
References .................................................. 71
Problems and assignments .................................... 72
3 The finite difference time domain method in two and three
dimensions .................................................. 74
3.1 Introduction ........................................... 74
3.2 The 2D FDTD algorithm .................................. 74
3.3 The PML absorbing boundary condition ................... 96
3.4 The 3D FDTD algorithm ................................. 109
3.5 Commercial implementations ............................ 117
3.6 Further reading ....................................... 124
3.7 Conclusions ........................................... 125
References ................................................. 126
Problems and assignments ................................... 127
4 A one-dimensional introduction to the method of moments:
modelling thin wires and infinite cylinders .............. 130
4.1 Introduction .......................................... 130
4.2 An electrostatic example .............................. 131
4.5 The method of weighted residuals ...................... 150
4.6 Scattering from infinite cylinders .................... 152
4.7 Further reading ....................................... 160
4.8 Conclusions ........................................... 162
References ................................................. 162
Problems and assignments ................................... 164
5 The application of the FEKO and NEC-2 codes to thin-wire
antenna modelling .......................................... 166
5.1 Introduction .......................................... 166
5.2 An introductory example: the dipole ................... 168
5.3 A wire antenna array: the Yagi-Uda antenna ............ 172
5.4 A log-periodic antenna ................................ 177
5.5 An axial mode helix antenna ........................... 185
5.6 A Wu-King loaded dipole ............................... 193
5.7 Conclusions ........................................... 199
References ................................................. 199
6 The method of moments for surface modelling ................ 201
6.1 Electric and magnetic field integral equations ........ 201
6.2 The Rao-Wilton-Glisson (RWG) element .................. 203
6.3 A mixed potential electric field integral equation
for electromagnetic scattering by surfaces of
arbitrary shape ....................................... 206
6.4 Some examples of surface modelling .................... 218
6.5 Modelling homogeneous material bodies using
equivalent currents ................................... 224
6.6 Scattering from a dielectric sphere ................... 226
6.7 Computational implications of surface and volume
modelling with the MoM ................................ 228
6.8 Hybrid MoM/asymptotic techniques for large problems ... 230
6.9 Other approaches for the solution of
electromagnetically large problems .................... 237
6.10 Further reading ....................................... 258
6.11 Concluding comments ................................... 260
References ................................................. 260
Problem .................................................... 263
7 The method of moments and stratified media: theory ......... 264
7.1 Introduction .......................................... 264
7.2 Dyadic Green functions: some introductory notes ....... 264
7.3 A static example of a stratified medium problem: the
grounded dielectric slab .............................. 266
7.4 The Sommerfeld potentials ............................. 269
7.5 Evaluating the Sommerfeld integrals ................... 278
7.6 MoM solution using the Sommerfeld potentials .......... 289
7.7 Further reading ....................................... 297
References ................................................. 298
Assignments ................................................ 299
8 The method of moments and stratified media: practical
applications of a commercial code .......................... 300
8.1 Printed antenna and microstrip technology: a brief
review ................................................ 300
8.2 A simple patch antenna ................................ 301
8.3 Mutual coupling between microstrip antennas ........... 303
8.4 An array with "scan blindness" ........................ 308
8.5 A concluding discussion of stratified media
formulations .......................................... 314
References ................................................. 315
9 A one-dimensional introduction to the finite element
method ..................................................... 317
9.1 Introduction .......................................... 317
9.2 The variational boundary value problem: the
transmission line problem revisited ................... 318
9.3 Improving and generalizing the FEM solution ........... 331
9.4 Further reading ....................................... 339
9.5 Conclusions ........................................... 340
References ................................................. 340
Problems and assignments ................................... 341
10 The finite element method in two dimensions: scalar and
vector elements ............................................ 342
10.1 Introduction .......................................... 342
10.2 Finite element solution of the Laplace equation in
two dimensions using scalar elements .................. 343
10.3 The Galerkin (weighted residual) formulation .......... 359
10.4 Simplex coordinates ................................... 364
10.5 The high-frequency variational functional ............. 367
10.6 The null space of the curl operator and spurious
modes ................................................. 367
10.7 Vector (edge) elements ................................ 371
10.8 Application to waveguide eigenvalue analysis .......... 378
10.9 Waveguide dispersion analysis ......................... 394
10.10 Further reading ...................................... 400
10.11 Conclusions .......................................... 402
References ................................................. 403
Problems and assignments ................................... 406
11 The finite element method in three dimensions .............. 407
11.1 The three-dimensional Whitney element ................. 407
11.2 Higher-order elements ................................. 415
11.3 The FEM from the variational boundary value problem
viewpoint ............................................. 427
11.4 A deterministic 3D application: waveguide obstacle
analysis .............................................. 429
11.5 Application to two waveguide discontinuity problems ... 432
11.6 Open-region finite element method formulations:
absorbing boundary conditions (ABCs) .................. 441
11.7 Further reading ....................................... 444
11.8 Conclusions ........................................... 445
References ................................................. 445
Problems and assignments ................................... 448
12 A selection of more advanced topics in full-wave
computational electromagnetics ............................. 451
12.1 Hybrid finite element/method of moments
formulations .......................................... 451
12.2 An application of the FEM/MoM hybrid - GSM base
stations .............................................. 454
12.3 Time domain FEM ....................................... 457
12.4 Sparse matrix solvers ................................. 468
12.5 A posteriori error estimation and adaptive meshing .... 473
12.6 Further reading and conclusions ....................... 478
References ................................................. 481
Appendix A: The Whitney element ............................... 484
Appendix B: The Newmark-β time-stepping algorithm ............. 486
References ........................................ 488
Appendix C: On the convergence of the MoM ..................... 489
Reference ......................................... 490
Appendix D: Useful formulas for simplex coordinates ........... 491
Appendix E: Web resources ..................................... 493
Appendix F: Matlab files supporting this text ................. 496
Index ......................................................... 498
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