Finite Element Analysis of Antennas and Arrays

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 xi1 Introduction 11.1 Numerical Simulation of Antennas 11.2 Finite Element Analysis Versus Other Numerical Methods 21.3 Frequency- Versus Time-Domain Simulations 51.4 Brief Review of Past Work 71.5 Overview of the Book 9References 112 Finite Element Formulation 172.1 Finite Element Formulation in the Frequency Domain 172.2 Finite Element Formulation in the Time Domain 242.3 Modeling of Complex Materials 272.3.1 Modeling of Electrically and Magnetically Lossy Materials 282.3.2 Modeling of Electrically Dispersive Materials 302.3.3 Modeling of Magnetically Dispersive Materials 362.3.4 Modeling of Doubly Dispersive Lossy Materials 402.3.5 Validation Examples 432.4 Solution of the Finite Element Equations 492.5 Higher-Order and Curvilinear Finite Elements 502.6 Summary 52References 533 Finite Element Mesh Truncation 553.1 Absorbing Boundary Conditions 553.1.1 First-Order Absorbing Boundary Condition 553.1.2 Second-Order Absorbing Boundary Condition 563.2 Perfectly Matched Layers 613.2.1 PML in Terms of Stretched Coordinates 623.2.2 PML as an Anisotropic Material Absorber 643.2.3 PML for Truncating the Computational Domain 653.2.4 Finite Element Implementation of PML 673.2.5 ABC-Backed, Complementary, CFS, and Second-Order PMLs 723.3 Boundary Integral Equations 763.3.1 Frequency-Domain Formulations 773.3.2 Time-Domain Formulations 863.3.3 Treatment of the Infinite Ground Plane 933.4 Summary 96References 974 Hybrid FETD–FDTD Technique 1004.1 FDTD Method 1014.2 PML Implementation in FDTD 1064.2.1 FDTD Stretched-Coordinate PML 1074.2.2 FDTD Anisotropic-Medium PML 1114.3 Near-to-Far-Field Transformation in FDTD 1134.4 Alternative FETD Formulation 1174.5 Equivalence Between FETD and FDTD 1204.6 Stable FETD–FDTD Interface 1244.6.1 Initial Approaches 1254.6.2 Stable Formulation 1284.7 Building Hybrid Meshes 1314.8 Wave-Equation Stabilization 1344.9 Validation Examples 1374.10 Summary 140References 1435 Antenna Source Modeling and Parameter Calculation 1475.1 Antenna Feed Modeling 1475.1.1 Current Probe 1485.1.2 Voltage Gap Generator 1525.1.3 Waveguide Feed Model 1555.2 Plane-Wave Excitation 1645.2.1 Total-Field Formulation 1675.2.2 Scattered-Field Formulation 1705.2.3 Total- and Scattered-Field Decomposition Approach 1715.3 Far-Field Pattern Computation 1765.4 Near-Field Visualization 1795.5 Summary 182References 1846 Modeling of Complex Structures 1876.1 Thin-Material Layers and Sheets 1886.1.1 Impedance Boundary Conditions 1886.1.2 Shell Element Formulation 1976.2 Thin Wires and Slots 2016.2.1 Thin Wires 2016.2.2 Thin Slots 2086.3 Lumped-Circuit Elements 2176.3.1 Coupled First-Order Equations 2186.3.2 Wave Equation 2196.3.3 Example 2226.4 Distributed Feed Network 2246.5 System-Level Coupling Example 2306.5.1 Internal Dispersive Material Calibration 2306.5.2 External Illumination and Aperture Coupling 2346.6 Summary 234References 2367 Antenna Simulation Examples 2407.1 Narrowband Antennas 2407.1.1 Coaxial-Fed Monopole Antenna 2407.1.2 Monopole Antennas on a Plate 2417.1.3 Patch Antennas on a Plate 2437.1.4 Conformal Patch Antenna Array 2457.2 Broadband Antennas 2477.2.1 Ridged Horn Antenna 2477.2.2 Sinuous Antenna 2497.2.3 Logarithmic Spiral Antenna 2517.2.4 Inverted Conical Spiral Antenna 2537.2.5 Antipodal Vivaldi Antenna 2547.2.6 Vlasov Antenna 2557.3 Antenna RCS Simulations 2577.3.1 Microstrip Patch Antenna 2587.3.2 Standard Gain Horn Antenna 2597.4 Summary 262References 2628 Axisymmetric Antenna Modeling 2648.1 Method of Analysis 2648.1.1 Finite Element Formulation 2648.1.2 Mesh Truncation Using Perfectly Matched Layers 2678.1.3 Mesh Truncation Using Boundary Integral Equations 2698.1.4 Far-Field Computation 2728.2 Application Examples 2738.2.1 Luneburg Lens 2738.2.2 Corrugated Horn 2768.2.3 Current Loop Inside a Radome 2818.3 Summary 282References 2829 Infinite Phased-Array Modeling 2849.1 Frequency-Domain Modeling 2859.1.1 Periodic Boundary Conditions 2859.1.2 Mesh Truncation Techniques 2949.1.3 Extension to Skew Arrays 2989.1.4 Extension to Scattering Analysis 3009.1.5 Application Examples 3009.2 Time-Domain Modeling 3039.2.1 Transformed Field Variable 3049.2.2 Mesh Truncation Techniques 3069.2.3 General Material Modeling 3109.2.4 Application Examples 3169.3 Approximation to Finite Arrays 3259.4 Summary 332References 33310 Finite Phased-Array Modeling 33610.1 Frequency-Domain Modeling 33710.1.1 FETI–DPEM1 Formulation 33710.1.2 FETI–DPEM2 Formulation 34510.1.3 Nonconforming Domain Decomposition 35010.1.4 Application Examples 35510.2 Time-Domain Modeling 36310.2.1 Dual-Field Domain-Decomposition Method 36410.2.2 Domain Decomposition for Iterative Solutions 37110.2.3 Application Examples 37610.3 Summary 382References 38511 Antenna–Platform Interaction Modeling 38811.1 Coupled Analysis 38911.1.1 FETI–DPEM with Domain Decomposition 39011.1.2 Hybrid FETD–FDTD with Domain Decomposition 39311.1.3 Hybrid FE–BI Method with FMM Acceleration 39911.2 Decoupled Analysis 40511.2.1 Near-Field Calculation 40611.2.2 Far-Field Evaluation by Numerical Methods 40611.2.3 Far-Field Evaluation by Asymptotic Techniques 40911.2.4 Direct and Iterative Improvements 41611.3 Summary 417References 41812 Numerical and Practical Considerations 42112.1 Choice of Simulation Technologies 42112.2 Frequency- Versus Time-Domain Simulation Tools 42212.3 Fast Frequency Sweep 42412.4 Numerical Convergence 42512.5 Domain Decomposition and Parallel Computing 42712.6 Verification and Validation of Predictions 42812.7 Summary 429References 429Index 431