Finite Element Analysis of Complex Antennas and Arrays

Various technical issues are addressed in the frequency- and time-domain finite element analysis of complex antennas and arrays that may consist of fine structures and composite materials. The paper starts with the finite element formulation of a generic antenna problem. Formulation for the modeling of general electrically and magnetically dispersive, lossy, and anisotropic materials in the time-domain finite element analysis is presented for the first time. This is followed by discussion of three typical techniques for truncation of the finite element computational domain via the use of absorbing boundary conditions, perfectly matched layers, and boundary integral equations. It then describes the modeling of antenna feeds using a current probe (including an improved model), a voltage gap, and a waveguide port boundary condition. After that, numerical approaches to modeling infinite phased arrays, large finite arrays, and antenna-platform interaction are presented, including two novel domain decomposition algorithms in both the frequency and time domains. Numerical examples are given to demonstrate the capability and application of the finite element analysis of a variety of complex antennas and arrays.

[1]  Enhancing the Modeling Capability of the FE-BI Method for Simulation of Cavity-Backed Antennas and Arrays , 2006 .

[2]  Jian-Ming Jin,et al.  A Single-Boundary Implicit and FFT-Accelerated Time-Domain Finite Element-Boundary Integral Solver , 2007, IEEE Transactions on Antennas and Propagation.

[3]  Jian-Ming Jin,et al.  A Vector Dual-Primal Finite Element Tearing and Interconnecting Method for Solving 3-D Large-Scale Electromagnetic Problems , 2006 .

[4]  Jianming Jin,et al.  Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite-element method , 1993 .

[5]  Constantine A. Balanis,et al.  Ferrite-loaded cavity-backed antennas including nonuniform and nonlinear magnetization effects , 2003 .

[6]  Jian-Ming Jin,et al.  HYBRID FEM/SBR METHOD TO COMPUTE THE RADIATION PATTERN FROM A MICROSTRIP PATCH ANTENNA IN A COMPLEX GEOMETRY , 1996 .

[7]  C.S. Liang,et al.  A quantitative study of Luneberg-lens reflectors , 2005, IEEE Antennas and Propagation Magazine.

[8]  Raj Mittra,et al.  Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers , 1996 .

[9]  Jian-Ming Jin,et al.  Higher-order finite element analysis of finite-by-infinite arrays , 2004, IEEE Antennas and Propagation Society Symposium, 2004..

[10]  Jianming Jin,et al.  A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems , 2001 .

[11]  Jianming Jin,et al.  A finite-element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures , 1991 .

[12]  Jianming Jin,et al.  A hybrid finite element method for scattering and radiation by microstrip path antennas and arrays residing in a cavity , 1991 .

[13]  D. J. Riley,et al.  Interfacing unstructured tetrahedron grids to structured-grid FDTD , 1995 .

[14]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[15]  Jian-Ming Jin,et al.  A New Dual-Primal Domain Decomposition Approach for Finite Element Simulation of 3-D Large-Scale Electromagnetic Problems , 2007, IEEE Transactions on Antennas and Propagation.

[16]  Ial Hor.  Finite-Element Time-Domain Analysis of Axisymmetrical Radiators , 1994 .

[17]  N. Alexopoulos,et al.  Radiation and scattering from complex 3D curvilinear geometries using a hybrid finite element-integral equation approach , 1992, IEEE Antennas and Propagation Society International Symposium 1992 Digest.

[18]  Jian-Ming Jin,et al.  The Finite Element Method in Electromagnetics , 1993 .

[19]  Andrew F. Peterson,et al.  Absorbing boundary conditions for the vector wave equation , 1988 .

[20]  T. Eibert,et al.  Hybrid/sup 2/: combining the three-dimensional hybrid finite element-boundary integral technique for planar multilayered media with the uniform geometrical theory of diffraction , 2002 .

[21]  Jin-Fa Lee,et al.  A symmetric FEM-IE formulation with a single-level IE-QR algorithm for solving electromagnetic radiation and scattering problems , 2004, IEEE Transactions on Antennas and Propagation.

[22]  T. Eibert,et al.  Calculation of unbounded field problems in free space by a 3D FEM/BEM-hybrid approach , 1996 .

[23]  Jian-Ming Jin,et al.  On the variational formulation of hybrid finite element-boundary integral techniques for electromagnetic analysis , 2004, IEEE Transactions on Antennas and Propagation.

[24]  K. Mei.  Uni-moment method of solving antenna and scattering problems , 1973 .

[25]  J. Zapata,et al.  Generalized-scattering-matrix analysis of a class of finite arrays of coupled antennas by using 3-D FEM and spherical mode expansion , 2005, IEEE Transactions on Antennas and Propagation.

[26]  Jon P. Webb,et al.  Absorbing boundary conditions for the finite element solution of the vector wave equation , 1989 .

[27]  Jianming Jin,et al.  Analysis of periodic structures via a time-domain finite-element formulation with a Floquet ABC , 2006, IEEE Transactions on Antennas and Propagation.

[28]  M. Feliziani,et al.  Mixed finite-difference/Whitney-elements time domain (FD/WE-TD) method , 1998 .

[29]  Jian-Ming Jin,et al.  Time-domain finite-element simulation of three-dimensional scattering and radiation problems using perfectly matched layers , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[30]  Jian-Ming Jin,et al.  An accurate waveguide port boundary condition for the time-domain finite-element method , 2005 .

[31]  Ramachandra Achar,et al.  Simultaneous time and frequency domain solutions of EM problems using finite element and CFH techniques , 1996 .

[32]  A. Hessel,et al.  Performance of probe-fed microstrip-patch element phased arrays , 1988 .

[33]  Jian-Ming Jin,et al.  A novel dual-field time-domain finite-element domain-decomposition method for computational electromagnetics , 2006 .

[34]  Zheng Lou,et al.  Modeling and simulation of broad-band antennas using the time-domain finite element method , 2005 .

[35]  J.-C. Verite,et al.  A mixed fem-biem method to solve 3-D eddy-current problems , 1982 .

[36]  D. Hoppe,et al.  A hybrid finite-element method for axisymmetric waveguide-fed horns , 1996 .

[37]  Jian-Ming Jin,et al.  Time‐domain finite‐element simulation of cavity‐backed microstrip patch antennas , 2002 .

[38]  Frederik Edelvik,et al.  Hybrid Solvers for the Maxwell Equations in Time-Domain , 2002 .

[39]  D. Schaubert,et al.  Elimination of impedance anomalies in single- and dual-polarized endfire tapered slot phased arrays , 2000 .

[40]  Jin-Fa Lee,et al.  A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays , 2005 .

[41]  Jian-Ming Jin,et al.  A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering , 2002 .

[42]  V. Pyati,et al.  Phased array antenna analysis with the hybrid finite element method , 1994 .

[43]  Jin-Fa Lee,et al.  A perfectly matched anisotropic absorber for use as an absorbing boundary condition , 1995 .

[44]  Jian-Ming Jin,et al.  Analysis of conformal antennas on a complex platform , 2003, IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450).

[45]  C. E. Baum,et al.  Scanning and impedance properties of TEM horn arrays for transient radiation , 1999 .

[46]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[47]  I. Fukai,et al.  Finite element method for unbounded field problems and application to two‐dimensional taper , 1983 .

[48]  Jian-Ming Jin,et al.  Calculation of radiation patterns of microstrip antennas on cylindrical bodies of arbitrary cross section , 1997 .

[49]  Jianming Jin,et al.  On the formulation of hybrid finite-element and boundary-integral methods for 3-D scattering , 1998 .

[50]  Jian-Ming Jin,et al.  Fast frequency-sweep analysis of cavity-backed microstrip patch antennas , 1999 .

[51]  E. Lucas,et al.  A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays , 1995 .

[52]  Jian-Ming Jin,et al.  Fast frequency-sweep analysis of microstrip antennas on dispersive substrate , 1999 .

[53]  T. Cwik,et al.  Modeling radiation with an efficient hybrid finite-element integral-equation waveguide mode-matching technique , 1997 .

[54]  Modeling conformal antennas on metallic prolate spheroid surfaces using a hybrid finite element method , 2004, IEEE Transactions on Antennas and Propagation.

[55]  Weng Cho Chew,et al.  A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates , 1994 .

[56]  Jian-Ming Jin,et al.  Stable Coaxial Waveguide Port Algorithm for the Time Domain Finite Element Method , 2004 .

[57]  Jianming Jin,et al.  Application of hybrid finite element method to electromagnetic scattering from coated cylinders , 1988 .

[58]  S. Gedney.  An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices , 1996 .

[59]  X. Yuan.  Three-dimensional electromagnetic scattering from inhomogeneous objects by the hybrid moment and finite element method , 1990 .

[60]  Stephen D. Gedney,et al.  A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium , 2000 .

[61]  Stephen D. Gedney,et al.  Convolution PML (CPML): An efficient FDTD implementation of the CFS–PML for arbitrary media , 2000 .

[62]  Alessandro Toscano,et al.  FEM-BEM formulation for the analysis of cavity-backed patch antennas on chiral substrates , 2003 .

[63]  Jian-Ming Jin,et al.  A fast higher-order time-domain finite element-boundary integral method for 3-D electromagnetic scattering analysis , 2002 .

[64]  Jian-Ming Jin,et al.  A dual-field domain-decomposition method for the time-domain finite-element analysis of large finite arrays , 2007, J. Comput. Phys..

[65]  John L. Volakis,et al.  Array decomposition method for the accurate analysis of finite arrays , 2003 .

[66]  P. Monk,et al.  Gauss Point Mass Lumping Schemes for Maxwell's Equations , 1998 .

[67]  Juan Zapata,et al.  Full-wave analysis of cavity-backed and probe-fed microstrip patch arrays by a hybrid mode-matching generalized scattering matrix and finite-element method , 1998 .

[68]  Jian-Ming Jin,et al.  A three-dimensional time-domain finite-element formulation for periodic structures , 2006, IEEE Transactions on Antennas and Propagation.

[69]  D. J. Riley,et al.  VOLMAX: a solid-model-based, transient volumetric Maxwell solver using hybrid grids , 1997 .

[70]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[71]  Jian-Ming Jin,et al.  Finite‐element analysis of phased‐array antennas , 2004 .

[72]  M. L. Barton,et al.  New vector finite elements for three‐dimensional magnetic field computation , 1987 .

[73]  R. Fernandez-Recio,et al.  Fully Coupled Multi-Hybrid FEM-PO/PTD-UTD Method for the Analysis of Radiation Problems , 2007, IEEE Transactions on Magnetics.

[74]  Christophe Geuzaine,et al.  An FETD approach for the modeling of antennas , 2000 .

[75]  Gabriel Rebeiz,et al.  Dual-polarized sinuous antennas on silicon dielectric lenses , 2010, 2010 IEEE Antennas and Propagation Society International Symposium.

[76]  A. Barka,et al.  Domain Decomposition Method Based on Generalized Scattering Matrix for Installed Performance of Antennas on Aircraft , 2007, IEEE Transactions on Antennas and Propagation.

[77]  Jian-Ming Jin,et al.  Complex coordinate stretching as a generalized absorbing boundary condition , 1997 .

[78]  Jian-Ming Jin,et al.  Finite element analysis of complex axisymmetric radiating structures , 1999 .

[79]  M. D. Deshpande,et al.  Radiation characteristics of cavity backed aperture antennas in finite ground plane using the hybrid FEM/MoM technique and geometrical theory of diffraction , 1996 .

[80]  Isaak D. Mayergoyz,et al.  Finite Element Methods for the Solution of RF Radiation And Scattering Problems , 1990 .

[81]  R. Mittra,et al.  Computational Methods for Electromagnetics , 1997 .

[82]  Jian-Ming Jin,et al.  On the development of a higher-order PML , 2005, SBMO/IEEE MTT-S International Conference on Microwave and Optoelectronics, 2005..

[83]  W. Chew,et al.  Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates , 1997 .

[84]  Jian-Ming Jin,et al.  A fast, higher order three‐dimensional finite‐element analysis of microwave waveguide devices , 2002 .

[85]  Jin-Fa Lee,et al.  A Domain Decomposition Method With Nonconformal Meshes for Finite Periodic and Semi-Periodic Structures , 2007, IEEE Transactions on Antennas and Propagation.

[86]  Javier Monge,et al.  A CAD-oriented method to analyze and design radiating structures based on bodies of revolution by using finite elements and generalized scattering matrix , 2006, IEEE Transactions on Antennas and Propagation.

[87]  Thomas Rylander,et al.  Stable FEM-FDTD hybrid method for Maxwell's equations , 2000 .

[88]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[89]  Fredrik Edelvik,et al.  An unconditionally stable subcell model for arbitrarily oriented thin wires in the FETD method , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[90]  Jian-Ming Jin,et al.  Perfectly matched layers in three dimensions for the time-domain finite element method , 2004, IEEE Antennas and Propagation Society Symposium, 2004..

[91]  Thomas Rylander,et al.  Stability of Explicit-Implicit Hybrid Time-Stepping Schemes for Maxwell's Equations , 2002 .

[92]  Jianming Jin,et al.  A field picture of wave propagation in inhomogeneous dielectric lenses , 1999 .