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Finite Element Analysis of Antennas and Arrays

Finite Element Analysis of Antennas and Arrays

Jian-Ming Jin, Douglas J. Riley

ISBN: 978-0-470-40972-5

Feb 2009, Wiley-IEEE Press

472 pages



The Most Complete, Up-to-Date Coverage of the Finite Element Analysis and Modeling of Antennas and Arrays

Aimed at researchers as well as practical engineers—and packed with over 200 illustrations including twenty-two color plates—Finite Element Analysis of Antennas and Arrays presents:

  • Time- and frequency-domain formulations and mesh truncation techniques

  • Antenna source modeling and parameter calculation

  • Modeling of complex materials and fine geometrical details

  • Analysis and modeling of narrowband and broadband antennas

  • Analysis and modeling of infinite and finite phased-array antennas

  • Analysis and modeling of antenna and platform interactions

Recognizing the strengths of other numerical methods, this book goes beyond the finite element method and covers hybrid techniques that combine the finite element method with the finite difference time-domain method, the method of moments, and the high-frequency asymptotic methods to efficiently deal with a variety of complex antenna problems.

Complemented with numerous examples, this cutting-edge resource fully demonstrates the power and capabilities of the finite element analysis and its many practical applications.



Chapter 1: Introduction.

1.1 Numerical Simulation of Antennas.

1.2 Finite Element Analysis vs. Other Numerical Methods.

1.3 Frequency- vs. Time-Domain Simulations.

1.4 Brief Review of Past Work.

1.5 Overview of This Book.


Chapter 2: Finite Element Formulation.

2.1 Finite Element Formulation in the Frequency Domain.

2.2 Finite Element Formulation in the Time Domain.

2.3 Modeling of Complex Materials.

2.3.1 Modeling of Electrically and Magnetically Lossy Materials.

2.3.2 Modeling of Electrically Dispersive Materials.

2.3.3 Modeling of Magnetically Dispersive Materials.

2.3.4 Modeling of Doubly Dispersive Lossy Materials.

2.4 Solution of the Finite Element Equations.

2.5 Higher-Order and Curvilinear Finite Elements.

2.6 Summary.


Chapter 3: Finite Element Mesh Truncation.

3.1 Absorbing Boundary Conditions.

3.1.1 First-Order Absorbing Boundary Condition.

3.1.2 Second-Order Absorbing Boundary Condition.

3.2 Perfectly Matched Layers.

3.2.1 PML in Terms of Stretched Coordinates.

3.2.2 PML as an Anisotropic Material Absorber.

3.2.3 PML for Truncating Computational Domain.

3.2.4 Finite Element Implementation of PML.

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

3.3 Boundary Integral Equations.

3.3.1 Frequency-Domain Formulations.

3.3.2 Time-Domain Formulations.

3.3.3 Treatment of Infinite Ground Plane.

3.4 Summary.


Chapter 4: Hybrid FETD-FDTD Technique.

4.1 The FDTD Method.

4.2 PML Implementation in FDTD.

4.2.1 FDTD Stretched-Coordinate PML.

4.2.2 FDTD Anisotropic PML.

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

4.4 Alternative FETD Formulation.

4.5 Equivalence between FETD and FDTD.

4.6 Stable FETD-FDTD Interface.

4.6.1 Initial Approaches.

4.6.2 Stable Formulation.

4.7 Building Hybrid Meshes.

4.8 Wave-Equation Stablization.

4.9 Validation Examples.

4.10 Summary.


Chapter 5: Antenna Source Modeling and Parameter Calculation.

5.1 Antenna Feed Modeling.

5.1.1 Current Probe.

5.1.2 Voltage Gap Generator.

5.1.3 Waveguide Feed Model.

5.2 Plane-Wave Excitation.

5.2.1 Total-Field Formulation.

5.2.2 Scattered-Field Formulation.

5.2.3 Total- and Scattered-Field Decomposition Approach .

5.3 Far-Field Pattern Computation.

5.4 Near-Field Visualization.

5.5 Summary.


Chapter 6: Modeling of Complex Structures.

6.1 Thin Material Layers and Sheets.

6.1.1 Impedance Boundary Conditions.

6.1.2 Shell Element Formulation.

6.2 Thin Wires and Slots.

6.2.1 Thin Wires.

6.2.2 Thin Slots.

6.3 Lumped Circuit Elements.

6.3.1 Coupled First-Order Equations.

6.3.2 Wave Equation.

6.3.3 Example.

6.4 Distributed Feed Network.

6.5 System-Level Coupling Example.

6.5.1 Internal Dispersive Material Calibration.

6.5.2 External Illumination and Aperture Coupling.

6.6 Summary.


Chapter 7: Antenna Simulation Examples.

7.1 Narrowband Antennas.

7.1.1 Coaxial-fed Monopole Antenna.

7.1.2 Monopole Antennas on a Plate.

7.1.3 Patch Antennas on a Plate.

7.1.4 Conformal Patch Antenna Array.

7.2 Broadband Antennas.

7.2.1 Ridged Horn Antenna.

7.2.2 Sinuous Antenna.

7.2.3 Logarithmic Spiral Antenna.

7.2.4 Inverted Conical Spiral Antenna.

7.2.5 Antipodal Vivaldi Antenna.

7.2.6 Vlasov Antenna.

7.3 Antenna RCS Simulations.

7.3.1 Microstrip Patch Antenna.

7.3.2 Standard Gain Horn Antenna.

7.4 Summary.


Chapter 8: Axisymmetric Antenna Modeling.

8.1 Method of Analysis.

8.1.1 Finite Element Formulation.

8.1.2 Mesh Truncation Using Perfectly Matched Layers.

8.1.3 Mesh Truncation Using Boundary Integral Equations.

8.2 Application Examples.

8.2.1 Luneburg Lens.

8.2.2 Corrugated Horn.

8.2.3 Current Loop Inside a Radome.

8.3 Summary.


Chapter 9: Infinite Phased Array Modeling.

9.1 Frequency-Domain Modeling.

9.1.1 Periodic Boundary Conditions.

9.1.2 Mesh Truncation Techniques.

9.1.3 Extension to Skew Arrays.

9.1.4 Extension to Scattering Analysis.

9.1.5 Application Examples.

9.2 Time-Domain Modeling.

9.2.1 Transformed Field Variable.

9.2.2 Mesh Truncation Techniques.

9.2.3 General Material Modeling.

9.2.4 Application Examples.

9.3 Approximation to Finite Arrays.

9.4 Summary.


Chapter 10: Finite Phased Array Modeling.

10.1 Frequency-Domain Modeling.

10.1.1 The FETI-DPEM1 Formulation.

10.1.2 The FETI-DPEM2 Formulation.

10.1.3 Nonconforming Domain Decomposition.

10.1.4 Application Examples.

10.2 Time-Domain Modeling.

10.2.1 The Dual-Field Domain Decomposition Method.

10.2.2 Domain Decomposition for Iterative Solutions.

10.2.3 Application Examples.

10.3 Summary.


Chapter 11: Antenna-Platform Interaction Modeling.

11.1 Coupled Analysis.

11.1.1 FETI-DPEM with Domain Decomposition.

11.1.2 Hybrid FETD-FDTD with Domain Decomposition.

11.1.3 Hybrid FE-BI Method with FMM Acceleration.

11.2 Decoupled Analysis.

11.2.1 Near-Field Calculation.

11.2.2 Far-Field Evaluation by Numerical Methods.

11.2.3 Far-Field Evaluation by Asymptotic Techniques.

11.2.4 Direct and Iterative Improvements.

11.3 Summary.


Chapter 12: Numerical and Practical Considerations.

12.1 Choice of Simulation Technologies.

12.2 Frequency- vs. Time-Domain Simulation Tools.

12.3 Fast Frequency Sweep.

12.4 Numerical Convergence.

12.5 Domain Decomposition and Parallel Computing.

12.6 Verification and Validation of Predictions.

12.7 Summary.