COMPUTATIONAL ELECTROMAGNETICS FOR RF AND MICROWAVE ENGINEERING

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COMPUTATIONAL ELECTROMAGNETICS FOR RF AND MICROWAVE ENGINEERING
DAVID B. DAVIDSON
Cambridge University Press 2005

1 An overview of computational electromagnetics for RF and microwave applications 1
   1.1 Introduction 1
   1.2 Full-wave CEM techniques 4
   1.3 The method of moments (MoM) 7
   1.4 The finite difference time domain (FDTD) method 9
   1.5 The finite element method (FEM) 13
   1.6 Other methods 16
   1.7 The CEM modelling process 17
   1.8 Verification and validation 19
   1.9 Extending the limits of full-wave CEM methods 22
   1.10 CEM: the future 24
   1.11 A “road map” of this book 25
   References 27

2 The finite difference time domain method: a one-dimensional introduction
   David B. Davidson and James T. Aberle 29
   2.1 Introduction 29
   2.2 An overview of finite differences 30
   2.3 A very brief history of the FDTD 32
   2.4 A one-dimensional introduction to the FDTD 33
   2.5 Obtaining wideband data using the FDTD 48
   2.6 Numerical dispersion in FDTD simulations 60
   2.7 Conclusion 66

3 The finite difference time domain method in two and three dimensions 68
   3.1 Introduction 68
   3.2 The 2D FDTD algorithm 69
   3.3 The PML absorbing boundary condition 94
   3.4 The 3D FDTD algorithm 106
   3.5 Commercial implementations 107
   3.6 Further reading 114
   3.7 Conclusions 115
   References 116

4 A one-dimensional introduction to the method of moments: thin-wire modelling 118
   4.1 Introduction 118
   4.2 An electrostatic example 119
   4.3 Thin-wire electrodynamics and the MoM 126
   4.4 More on basis functions 132
   4.5 The method of weighted residuals 139
   4.6 Further reading 142
   4.7 Conclusions 144
   References 144

5 The application of the FEKO and NEC-2 codes to thin-wire antenna modelling 146
   5.1 Introductory comments 146
   5.2 An introductory example: the dipole 149
   5.3 A wire antenna array: the Yagi–Uda antenna 153
   5.4 A log-periodic antenna 159
   5.5 An axial mode helix antenna 167
   5.6 A Wu–King loaded dipole 175
   5.7 Conclusions 182
   References 183

6 The method of moments for surface modelling 184
   6.1 Electric and magnetic field integral equations 184
   6.2 The Rao–Wilton–Glisson (RWG) element 186
   6.3 Some examples of surface modelling 189
   6.4 Modelling homogeneous material bodies using equivalent currents 196
   6.5 Scattering from a dielectric sphere 197
   6.6 Computational implications of surface and volume modeling with the MoM 199
   6.7 Hybrid MoM/asymptotic techniques for large problems 200
   6.8 Other approaches for the solution of electromagnetically large
   problems 208
   6.9 Further reading 225
   6.10 Concluding comments 227
   References 228

7 The method of moments and stratified media: theory 231
   7.1 Introduction 231
   7.2 Dyadic Green functions: some introductory notes 232
   7.3 A static example of a stratified medium problem: the grounded dielectric slab 233
   7.4 The Sommerfeld potentials 237
   7.5 Evaluating the Sommerfeld integrals 247
   7.6 MoM solution using the Sommerfeld potentials 260
   7.7 Further reading 268
   References 269

8 The method of moments and stratified media: practical applications of a commercial code 271
   8.1 Printed antenna and microstrip technology: a brief review 271
   8.2 A single patch antenna 273
   8.3 Mutual coupling between microstrip antennas 273
   8.4 An array with “scan blindness” 280
   8.5 A concluding discussion of stratified media formulations 286
   References 287

9 An introduction to the finite element method 289
   9.1 Introduction 289
   9.2 Variational and Galerkin weighted residual formulations: the Laplace equation 291
   9.3 Simplex coordinates 303
   9.4 The high-frequency variational functional 305
   9.5 Spurious modes 306
   9.6 Vector (edge) elements 309
   9.7 Application to waveguide eigenvalue analysis 317
   9.8 The three-dimensional Whitney element 328
   9.9 Further reading 331
   9.10 Conclusions 332
   References 333

10 A selection of more advanced topics on the finite element method 336
   10.1 Higher-order elements 337
   10.2 The FEM from the variational boundary value problem viewpoint 343
   10.3 A deterministic 3D application: waveguide obstacle analysis 345
   10.4 Application to two waveguide discontinuity problems 349
   10.5 Hybrid finite element/method of moments formulations 358
   10.6 An application of the FEM/MoM hybrid – GSM base stations 362
   10.7 The time domain FEM 365
   10.8 Sparse matrix solvers 372
   10.9 A posteriori error estimation and adaptive meshing 378
   10.10 Further reading and conclusions 384

References 386
Appendix A The Whitney element 390
Appendix B The Newmark-β time-stepping algorithm 392
Appendix C On the convergence of the MoM 395
Appendix D Suggested exercises and assignments 397
Appendix E Useful formulas for simplex coordinates 401
Appendix F Web resources 403
Index 405

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