Finite Element Analysis of Antennas and Arrays

Antenna technologies have received renewed interest because of the rapid development of wireless devices and advanced defense applications. Consequently, highly accurate and efficient modeling and simulation tools are needed to satisfy the demand for sophisticated antenna designs. Finite Element Analysis of Antennas and Arrays covers all the technical aspects in the analysis of complex antennas and arrays using the finite element method.

Jian-Ming Jin, PhD, is a Professor and Director of the Electromagnetics Laboratory and Center for Computational Electromagnetics at the University of Illinois at Urbana-Champaign. He authored The Finite Element Method in Electromagnetics (Wiley) and Electromagnetic Analysis and Design in Magnetic Resonance Imaging; coauthored Computation of Special Functions (Wiley); and coedited Fast and Efficient Algorithms in Computational Electromagnetics. A Fellow of the IEEE, he is listed by ISI among the world's most cited authors.

Douglas J. Riley, PhD, received his doctorate in electrical engineering from Virginia Polytechnic Institute and has over twenty years of experience in the research, development, and practical application of time-domain methods for computational electromagnetics. A Technical Fellow with the Northrop Grumman Space Technology Sector, he was previously a Technical Fellow with Northrop Grumman Mission Systems and a Distinguished Member of the Technical Staff with Sandia National Laboratories.

Preface	p. xi
Introduction	p. 1
Numerical Simulation of Antennas	p. 1
Finite Element Analysis Versus Other Numerical Methods	p. 2
Frequency-Versus Time-Domain Simulations	p. 5
Brief Review of Past Work	p. 7
Overview of the Book	p. 9
References	p. 11
Finite Element Formulation	p. 17
Finite Element Formulation in the Frequency Domain	p. 17
Finite Element Formulation in the Time Domain	p. 24
Modeling of Complex Materials	p. 27
Modeling of Electrically and Magnetically Lossy Materials	p. 28
Modeling of Electrically Dispersive Materials	p. 30
Modeling of Magnetically Dispersive Materials	p. 36
Modeling of Doubly Dispersive Lossy Materials	p. 40
Validation Examples	p. 43
Solution of the Finite Element Equations	p. 49
Higher-Order and Curvilinear Finite Elements	p. 50
Summary	p. 52
References	p. 53
Finite Element Mesh Truncation	p. 55
Absorbing Boundary Conditions	p. 55
First-Order Absorbing Boundary Condition	p. 55
Second-Order Absorbing Boundary Condition	p. 56
Perfectly Matched Layers	p. 61
PML in Terms of Stretched Coordinates	p. 62
PML as an Anisotropic Material Absorber	p. 64
PML for Truncating the Computational Domain	p. 65
Finite Element Implementation of PML	p. 67
ABC-Backed, Complementary, CFS, and Second-Order PMLs	p. 72
Boundary Integral Equations	p. 76
Frequency-Domain Formulations	p. 77
Time-Domain Formulations	p. 86
Treatment of the Infinite Ground Plane	p. 93
Summary	p. 96
References	p. 97
Hybrid FETD-FDTD Technique	p. 100
FDTD Method	p. 101
PML Implementation in FDTD	p. 106
FDTD Stretched-Coordinate PML	p. 107
FDTD Anisotropic-Medium PML	p. 111
Near-to-Far-Field Transformation in FDTD	p. 113
Alternative FETD Formulation	p. 117
Equivalence Between FETD and FDTD	p. 120
Stable FETD-FDTD Interface	p. 124
Initial Approaches	p. 125
Stable Formulation	p. 128
Building Hybrid Meshes	p. 131
Wave-Equation Stabilization	p. 134
Validation Examples	p. 137
Summary	p. 140
References	p. 143
Antenna Source Modeling and Parameter Calculation	p. 147
Antenna Feed Modeling	p. 147
Current Probe	p. 148
Voltage Gap Generator	p. 152
Waveguide Feed Model	p. 155
Plane-Wave Excitation	p. 164
Total-Field Formulation	p. 167
Scattered-Field Formulation	p. 170
Total-and Scattered-Field Decomposition Approach	p. 171
Far-Field Pattern Computation	p. 176
Near-Field Visualization	p. 179
Summary	p. 182
References	p. 184
Modeling of Complex Structures	p. 187
Thin-Material Layers and Sheets	p. 188
Impedance Boundary Conditions	p. 188
Shell Element Formulation	p. 197
Thin Wires and Slots	p. 201
Thin Wires	p. 201
Thin Slots	p. 208
Lumped-Circuit Elements	p. 217
Coupled First-Order Equations	p. 218
Wave Equation	p. 219
Example	p. 222
Distributed Feed Network	p. 224
System-Level Coupling Example	p. 230
Internal Dispersive Material Calibration	p. 230
External Illumination and Aperture Coupling	p. 234
Summary	p. 234
References	p. 236
Antenna Simulation Examples	p. 240
Narrowband Antennas	p. 240
Coaxial-Fed Monopole Antenna	p. 240
Monopole Antennas on a Plate	p. 241
Patch Antennas on a Plate	p. 243
Conformal Patch Antenna Array	p. 245
Broadband Antennas	p. 247
Ridged Horn Antenna	p. 247
Sinuous Antenna	p. 249
Logarithmic Spiral Antenna	p. 251
Inverted Conical Spiral Antenna	p. 253
Antipodal Vivaldi Antenna	p. 254
Vlasov Antenna	p. 255
Antenna RCS Simulations	p. 257
Microstrip Patch Antenna	p. 258
Standard Gain Horn Antenna	p. 259
Summary	p. 262
References	p. 262
Axisymmetric Antenna Modeling	p. 264
Method of Analysis	p. 264
Finite Element Formulation	p. 264
Mesh Truncation Using Perfectly Matched Layers	p. 267
Mesh Truncation Using Boundary Integral Equations	p. 269
Far-Field Computation	p. 272
Application Examples	p. 273
Luneburg Lens	p. 273
Corrugated Horn	p. 276
Current Loop Inside a Radome	p. 281
Summary	p. 282
References	p. 282
Infinite Phased-Array Modeling	p. 284
Frequency-Domain Modeling	p. 285
Periodic Boundary Conditions	p. 285
Mesh Truncation Techniques	p. 294
Extension to Skew Arrays	p. 298
Extension to Scattering Analysis	p. 300
Application Examples	p. 300
Time-Domain Modeling	p. 303
Transformed Field Variable	p. 304
Mesh Truncation Techniques	p. 306
General Material Modeling	p. 310
Application Examples	p. 316
Approximation to Finite Arrays	p. 325
Summary	p. 332
References	p. 333
Finite Phased-Array Modeling	p. 336
Frequency-Domain Modeling	p. 337
FETI-DPEM1 Formulation	p. 337
FETI-DPEM2 Formulation	p. 345
Nonconforming Domain Decomposition	p. 350
Application Examples	p. 355
Time-Domain Modeling	p. 363
Dual-Field Domain-Decomposition Method	p. 364
Domain Decomposition for Iterative Solutions	p. 371
Application Examples	p. 376
Summary	p. 382
References	p. 385
Antenna-Platform Interaction Modeling	p. 388
Coupled Analysis	p. 389
FETI-DPEM with Domain Decomposition	p. 390
Hybrid FETD-FDTD with Domain Decomposition	p. 393
Hybrid FE-BI Method with FMM Acceleration	p. 399
Decoupled Analysis	p. 405
Near-Field Calculation	p. 406
Far-Field Evaluation by Numerical Methods	p. 406
Far-Field Evaluation by Asymptotic Techniques	p. 409
Direct and Interative Improvements	p. 416
Summary	p. 417
References	p. 418
Numerical and Practical Considerations	p. 421
Choice of Simulation Technologies	p. 421
Frequency-Versus Time-Domain Simulation Tools	p. 422
Fast Frequency Sweep	p. 424
Numerical Convergence	p. 425
Domain Decomposition and Parallel Computing	p. 427
Verification and Validation of Predictions	p. 428
Summary	p. 429
References	p. 429
Index	p. 431
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