Finite Element Analysis of Antennas and Arrays

Preface xi

1 Introduction 1

1.1 Numerical Simulation of Antennas 1

1.2 Finite Element Analysis Versus Other Numerical Methods 2

1.3 Frequency- Versus Time-Domain Simulations 5

1.4 Brief Review of Past Work 7

1.5 Overview of the Book 9

References 11

2 Finite Element Formulation 17

2.1 Finite Element Formulation in the Frequency Domain 17

2.2 Finite Element Formulation in the Time Domain 24

2.3 Modeling of Complex Materials 27

2.3.1 Modeling of Electrically and Magnetically Lossy Materials 28

2.3.2 Modeling of Electrically Dispersive Materials 30

2.3.3 Modeling of Magnetically Dispersive Materials 36

2.3.4 Modeling of Doubly Dispersive Lossy Materials 40

2.3.5 Validation Examples 43

2.4 Solution of the Finite Element Equations 49

2.5 Higher-Order and Curvilinear Finite Elements 50

2.6 Summary 52

References 53

3 Finite Element Mesh Truncation 55

3.1 Absorbing Boundary Conditions 55

3.1.1 First-Order Absorbing Boundary Condition 55

3.1.2 Second-Order Absorbing Boundary Condition 56

3.2 Perfectly Matched Layers 61

3.2.1 PML in Terms of Stretched Coordinates 62

3.2.2 PML as an Anisotropic Material Absorber 64

3.2.3 PML for Truncating the Computational Domain 65

3.2.4 Finite Element Implementation of PML 67

3.2.5 ABC-Backed, Complementary, CFS, and Second-Order PMLs 72

3.3 Boundary Integral Equations 76

3.3.1 Frequency-Domain Formulations 77

3.3.2 Time-Domain Formulations 86

3.3.3 Treatment of the Infinite Ground Plane 93

3.4 Summary 96

References 97

4 Hybrid FETD–FDTD Technique 100

4.1 FDTD Method 101

4.2 PML Implementation in FDTD 106

4.2.1 FDTD Stretched-Coordinate PML 107

4.2.2 FDTD Anisotropic-Medium PML 111

4.3 Near-to-Far-Field Transformation in FDTD 113

4.4 Alternative FETD Formulation 117

4.5 Equivalence Between FETD and FDTD 120

4.6 Stable FETD–FDTD Interface 124

4.6.1 Initial Approaches 125

4.6.2 Stable Formulation 128

4.7 Building Hybrid Meshes 131

4.8 Wave-Equation Stabilization 134

4.9 Validation Examples 137

4.10 Summary 140

References 143

5 Antenna Source Modeling and Parameter Calculation 147

5.1 Antenna Feed Modeling 147

5.1.1 Current Probe 148

5.1.2 Voltage Gap Generator 152

5.1.3 Waveguide Feed Model 155

5.2 Plane-Wave Excitation 164

5.2.1 Total-Field Formulation 167

5.2.2 Scattered-Field Formulation 170

5.2.3 Total- and Scattered-Field Decomposition Approach 171

5.3 Far-Field Pattern Computation 176

5.4 Near-Field Visualization 179

5.5 Summary 182

References 184

6 Modeling of Complex Structures 187

6.1 Thin-Material Layers and Sheets 188

6.1.1 Impedance Boundary Conditions 188

6.1.2 Shell Element Formulation 197

6.2 Thin Wires and Slots 201

6.2.1 Thin Wires 201

6.2.2 Thin Slots 208

6.3 Lumped-Circuit Elements 217

6.3.1 Coupled First-Order Equations 218

6.3.2 Wave Equation 219

6.3.3 Example 222

6.4 Distributed Feed Network 224

6.5 System-Level Coupling Example 230

6.5.1 Internal Dispersive Material Calibration 230

6.5.2 External Illumination and Aperture Coupling 234

6.6 Summary 234

References 236

7 Antenna Simulation Examples 240

7.1 Narrowband Antennas 240

7.1.1 Coaxial-Fed Monopole Antenna 240

7.1.2 Monopole Antennas on a Plate 241

7.1.3 Patch Antennas on a Plate 243

7.1.4 Conformal Patch Antenna Array 245

7.2 Broadband Antennas 247

7.2.1 Ridged Horn Antenna 247

7.2.2 Sinuous Antenna 249

7.2.3 Logarithmic Spiral Antenna 251

7.2.4 Inverted Conical Spiral Antenna 253

7.2.5 Antipodal Vivaldi Antenna 254

7.2.6 Vlasov Antenna 255

7.3 Antenna RCS Simulations 257

7.3.1 Microstrip Patch Antenna 258

7.3.2 Standard Gain Horn Antenna 259

7.4 Summary 262

References 262

8 Axisymmetric Antenna Modeling 264

8.1 Method of Analysis 264

8.1.1 Finite Element Formulation 264

8.1.2 Mesh Truncation Using Perfectly Matched Layers 267

8.1.3 Mesh Truncation Using Boundary Integral Equations 269

8.1.4 Far-Field Computation 272

8.2 Application Examples 273

8.2.1 Luneburg Lens 273

8.2.2 Corrugated Horn 276

8.2.3 Current Loop Inside a Radome 281

8.3 Summary 282

References 282

9 Infinite Phased-Array Modeling 284

9.1 Frequency-Domain Modeling 285

9.1.1 Periodic Boundary Conditions 285

9.1.2 Mesh Truncation Techniques 294

9.1.3 Extension to Skew Arrays 298

9.1.4 Extension to Scattering Analysis 300

9.1.5 Application Examples 300

9.2 Time-Domain Modeling 303

9.2.1 Transformed Field Variable 304

9.2.2 Mesh Truncation Techniques 306

9.2.3 General Material Modeling 310

9.2.4 Application Examples 316

9.3 Approximation to Finite Arrays 325

9.4 Summary 332

References 333

10 Finite Phased-Array Modeling 336

10.1 Frequency-Domain Modeling 337

10.1.1 FETI–DPEM1 Formulation 337

10.1.2 FETI–DPEM2 Formulation 345

10.1.3 Nonconforming Domain Decomposition 350

10.1.4 Application Examples 355

10.2 Time-Domain Modeling 363

10.2.1 Dual-Field Domain-Decomposition Method 364

10.2.2 Domain Decomposition for Iterative Solutions 371

10.2.3 Application Examples 376

10.3 Summary 382

References 385

11 Antenna–Platform Interaction Modeling 388

11.1 Coupled Analysis 389

11.1.1 FETI–DPEM with Domain Decomposition 390

11.1.2 Hybrid FETD–FDTD with Domain Decomposition 393

11.1.3 Hybrid FE–BI Method with FMM Acceleration 399

11.2 Decoupled Analysis 405

11.2.1 Near-Field Calculation 406

11.2.2 Far-Field Evaluation by Numerical Methods 406

11.2.3 Far-Field Evaluation by Asymptotic Techniques 409

11.2.4 Direct and Iterative Improvements 416

11.3 Summary 417

References 418

12 Numerical and Practical Considerations 421

12.1 Choice of Simulation Technologies 421

12.2 Frequency- Versus Time-Domain Simulation Tools 422

12.3 Fast Frequency Sweep 424

12.4 Numerical Convergence 425

12.5 Domain Decomposition and Parallel Computing 427

12.6 Verification and Validation of Predictions 428

12.7 Summary 429

References 429

Index 431