A class of hybrid finite element methods for electromagnetics: a review

References

• Richmond , J. H. 1974 . Radiation and scattering by thin wire structures in a homogeneous conducting medium . IEEE Trans. Antennas Propagat. , Jan. : 124 – 126 .
   Google Scholar
• Burke G. J. , and Pogio A. J. , " Numerical Electromagnetics Code (NEC-1), Parts I, II, III: NEC Program Description ," Naval Ocean Systems Center , San Diego CA , NOSC TD 116 , 1980 , ( original version was published in 1977 ).
   Google Scholar
• Knott E. F. , and Senior T. B. A. , " Non-specular cross section study ," Air Force Avionics Laboratory Technical Report AFAL-TR-73–422 , Jan. 1974 ( also University of Michigan Radiation Laboratory Report 011764–1-T ).
   Google Scholar
• Newman , E. H. , Alexandropoulos , P. and Walton , E. K. 1984 . Polygonal plate modeling of realistic structures . IEEE Trans. Antennas Propagat. , July : 742 – 747 .
   Google Scholar
• Rao , S. M. , Wilton , D. R. and Glisson , A. W. 1982 . Electromagnetic scattering by surfaces of arbitrary shape . IEEE Trans. Antennas Propagat. , May : 409 – 418 .
   Google Scholar
• Schaubert , D. H. , Wilton , D. R. and Glisson , A. W. 1984 . A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies . IEEE Trans. Antennas Propagat. , Jan. : 77 – 85 .
   Google Scholar
• Tsai , C. , Massoudi , H. , Durney , C. H. and Iskander , M. F. 1986 . A procedure for calculating fields inside arbitrarily shaped inhomogeneous dielectric bodies using linear basis functions with the moment method . IEEE Trans. Microwave Theory Techn. , 34 Nov. : 1131 – 1139 .
   Web of Science ®Google Scholar
• Mei , K. K. 1974 . Unimoment method of solving antenna and scattering problems . IEEE Trans. Antennas Propagat. , 22 Nov. : 760 – 766 .
   Web of Science ®Google Scholar
• Umashankar , K. , Taflove , A. and Rao , S. M. 1986 . Electromagnetic scattering by arbitrarily shaped three-dimensional homogeneous lossy dielectric objects . IEEE Trans. Antennas Propagat. , 34 June : 758 – 766 .
   Web of Science ®Google Scholar
• Huddleston , P. L. , Medgyesi-Mitschang , L. N. and Putnam , J. M. 1986 . Combined field integral equation formulation for scattering by dielectrically coated conducting bodies . IEEE Trans. Antennas Propagat. , 34 April : 510 – 520 .
   Web of Science ®Google Scholar
• Taflove , A. and Umashankar , K. R. 1987 . The finite difference time-domain (FD-TD) method for electromagnetic scattering and interaction problems . J. Electromagnetic Waves Appl. , 1 : 243 – 267 .
   Web of Science ®Google Scholar
• Madsen , N. K. and Ziolkowski , R. W. 1988 . Numerical solution of Maxwell's equations in the time domain using irregular nonorthogonal grids . Wave Motion , 10 : 583 – 596 .
   Web of Science ®Google Scholar
• Shankar , V. , Hall , W. F. and Mohammadian , A. H. May 1989 . “ A time domain differential solver for electromagnetic scattering problems ” . In Proc. IEEE Vol. 77 , May , 709 – 721 .
   Google Scholar
• Graglia , R. D. , Uslenghi , P. L. E. and Zick , R. S. 1989 . Moment method with isoparametric elements for three-dimensional anisotropic scatterers . Proc. IEEE , 77 : 750 – 760 .
   Web of Science ®Google Scholar
• D'Angelo , J. and Mayergoyz , I. D. 1990 . Finite element methods for the solution of RF radiation and scattering problems . Electromagnetics , 10 : 177 – 199 .
   Web of Science ®Google Scholar
• Kunz , K. S. and Luebbers , R. J. 1993 . The Finite Difference Time Domain Method for Electromagnetics , CRC Press .
   Google Scholar
• Jin , J. M. , Volakis , J. L. and Collins , J. D. 1991 . A finite element-boundary integral method for scattering and radiation by twoand three-dimensional structures . IEEE Antennas Propagat. Magazine , 33 ( No. 3 ) June : 22 – 32 .
   Google Scholar
• Peterson , A. F. 1991 . Analysis of heterogeneous electromagnetic scatterers: research progress of the past decade . Proc. IEEE , 79 ( No. 10 ) Oct. : 1431 – 1441 .
   Google Scholar
• Fusco , M. A. , Smith , M. V. and Gordon , L. W. 1991 . A three-dimensional FDTD algorithm in curvilinear coordinates . IEEE Trans. Antennas Propagat. , 39 Oct. : 1463 – 1471 .
   Google Scholar
• Wu , C. , Wu , K.-L. , Zhi-Quiang , Bi and Litva , J. 1992 . Accurate characterization of planar printed antennas using finite-difference time-domain method . IEEE Trans. Antennas Propagat. , 40 May : 526 – 534 .
   Web of Science ®Google Scholar
• Sheen , D. M. , Ali , S. M. , Abruzahra , M. D. and Kong , J. A. 1990 . Application of three-dimensional finite-difference time-domain method to the analysis of planar microstrip circuits . IEEE Trans. Microwave Theory Techn. , 38 ( No. 7 ) July : 849 – 858 .
   Google Scholar
• Silvester , P. P. and Ferrari , R. L. 1990 . Finite Elements for Electrical Engineers , 2nd ed. , Cambridge , , U.K : Cambridge Univ. Press .
   Google Scholar
• Parker , J. W. , Ferraro , R. D. and Liewer , P. C. Distributed memory tangential finite elements for inhomogeneous scatterers in free space . 1992 URSI Radio Science Meeting . pp. 516 Chicago IL : URSI Digest .
   Google Scholar
• Chatterjee , A. , J. M. Jin and Volakis , J. L. “ Application of edge-based finite elements and vector ABCs in 3D scattering ” . 528 – 531 . Digest . 1992 IEEE AP-S Symposium
   Google Scholar
• Paulsen , D. D. , Boyse , W. E. and Lynch , D. R. 1992 . Continuous potential Maxwell's equations on node-based finite elements . IEEE Trans. Antennas Propagat. , 40 Oct. : 1192 – 1200 .
   Google Scholar
• Morgan , M. A. , ed. 1990 . Finite Element and Finite Difference Methods in Electromagnetic Scattering , New York : Elsevier .
   Google Scholar
• Chatterjee , A. , Jin , J. M. and Volakis , J. L. 1993 . A finite element formulation with absorbing boundary conditions for three-dimensional scattering . IEEE Trans. Antennas Propagat. , Feb.
   Google Scholar
• Jin , J.-M. and Volakis , J. L. 1990 . TM scattering by an inhomogeneously filled aperture in a thick ground plane . IEE Proceedings, Part H , 137 ( No. 3 ) June : 153 – 159 .
   Google Scholar
• Jin , J.-M. and Volakis , J. L. 1990 . TE scattering by an inhomogeneously filled aperture in a thick conducting plane . IEEE Trans. Antennas Propagat. , AP-38 August : 1280 – 1286 .
   Google Scholar
• Collins , J. D. , Jin , J.-M. and Volakis , J. L. 1990 . A combined finite element-boundary element formulation for solution of two-dimensional problems via CGFFT . Electromagnetics , 10 : 423 – 437 .
   Web of Science ®Google Scholar
• Jin , J. M. and Volakis , J. L. 1991 . A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures . IEEE Trans. Antennas Propagat. , AP-39 January : 97 – 104 .
   Google Scholar
• Jin , J. M. and Volakis , J. L. 1991 . Electromagnetic scattering by and transmission through a three-dimensional slot in a thick conducting plane . IEEE Trans. Antennas Propagat. , AP-39 April : 543 – 550 .
   Web of Science ®Google Scholar
• Jin , J. M. and Volakis , J. L. 1991 . Scattering and radiation from microstrip patch antennas and arrays residing in a cavity . IEEE Trans. Antennas Propagat. , AP-39 Nov. : 1598 – 1604 .
   Web of Science ®Google Scholar
• Jin , J. M. , Volakis , J. L. , Yu , C. L. and Woo , A. 1992 . Modeling of resistive sheets in the context of finite element solutions . IEEE Trans. Antennas Propagat. , 40 June : 727 – 731 .
   Web of Science ®Google Scholar
• Chatterjee , A. , Jin , J. M. and Volakis , J. L. 1992 . Computation of cavity resonances using edge-based finite elements . IEEE Trans. Microwave Theory Techn. , Nov.
   Google Scholar
• Jin , J. M. , Volakis , J. L. and Liepa , V. V. 1992 . A fictitious absorber for truncating finite element meshes in scattering . IEE Proceedings, Part H , 139 ( No. 5 ) Oct. : 472 – 476 .
   Google Scholar
• Gong , J. , Volakis , J. L. , Chatterjee , A. and Jin , J. M. “ Characterization of cavitybacked conformal antennas and arrays using a hybrid finite element method with tetrahedral elements ” . 1629 – 1631 . Chicago IL : Digest . 1992 IEEE Antennas Propagat. Symposium
   Google Scholar
• Volakis , J. L. and Jin , J. M. 1992 . A technique to substantially lower the resonant frequency of the microstrip patch antenna . IEEE Trans. Microwave Theory Techn. Letters , 2 ( No. 7 ) July : 292 – 293 .
   Google Scholar
• Senior , T. B. A. 1985 . Combined resistive and conductive sheets . IEEE Trans. Antennas Propagat. , AP-33 : 577 – 579 .
   Web of Science ®Google Scholar
• Ramahi , O. M. and Mittra , R. 1989 . Finite element analysis of dielectric scatterers using the absorbing boundary conditions . IEEE Trans. Magnetics , 25 ( No. 4 ) July : 3043 – 3045 .
   Google Scholar
• Bossavit , A. and Mayergoyz , I. 1989 . Edge-elements for scattering problems . IEEE Trans. Magnetics , 25 ( No. 4 ) July : 2816 – 2821 .
   Google Scholar
• Barton , M. L. and Cendes , Z. J. 1987 . New vector finite elements for three-dimensional magnetic field computations . J. Appl. Phys. , 61 ( No. 8 ) : 3919 – 3921 .
   Google Scholar
• Whitney , H. 1957 . Geometric Integration Theory , Princeton Univ. Press .
   Google Scholar
• Azizur Rahman , B. M. and Davies , J. B. 1984 . Penalty function improvement of waveguide solution by finite elements . IEEE Trans. Microwave Theory Techn. , MTT-32 ( No. 8 ) Aug.
   Google Scholar
• Rahman , B. M. A. and Davies , J. B. 1984 . Penalty function improvement of waveguide solution by limite elements . IEEE Trans. Microwave Theory Tech. , MTT-32 Aug. : 922 – 928 .
   Google Scholar
• Kempel , L. C. and Volakis , J. L. A finite element-boundary integral method for cavities in a circular cylinder . 1993 IEEE AP-S Symposium and URSI Meeting . Ann Arbor , MI. .
   Google Scholar
• Antilla , G. E and Alexopoulos , N. G. Radiation and scattering from complex 3D curvilinear geometries using a hybrid finite element-integral equation method . 1992 IEEE Antennas Propagat. Symposium . pp. 1758 – 1761 . Chicago , IL : Digest .
   Google Scholar
• Crowley , C. W. , Silvester , P. P. and Hurwitz , H. Jr. 1988 . Covariant projection elements for 3D vector field problems . IEEE Trans. Magnetics , 24 ( No. 1 ) Jan. : 397 – 400 .
   Google Scholar
• Bossavit , A. 1988 . A rationale for edge-elements in 3D fields computations . IEEE Trans. Magnetics , 24 ( No. 1 ) Jan. : 74 – 79 .
   Google Scholar
• Silvester , P. and Hsieh , M. S. 1971 . Finite element solution of 2-dimensional exterior field problems . Proc. Inst. Elec. Eng. , 118 Dec. : 1743 – 1747 .
   Web of Science ®Google Scholar
• McDonald , B. H. and Wexler , A. 1972 . Finite element solution of unbounded field problems . IEEE Trans. Microwave Theory Techn. , MTT-20 Dec. : 841 – 847 .
   Web of Science ®Google Scholar
• Jin , J. M. and Liepa , V. V. 1988 . A note on hybrid finite element method for solving scattering problems . IEEE Trans. Antennas Propagat. , 36 ( No. 10 ) Oct. : 1486 – 1490 .
   Google Scholar
• Jin , J. M. and Volakis , J. L. 1989 . A new technique for characterizing diffraction by inhomogeneously filled slots of arbitrary cross section in a thick conducting plane . IEE Electronics Letters , 25 ( No. 17 ) 17 Aug. : 1121 – 1122 .
   Google Scholar
• Wu , K. L. , Delisle , G. Y. , Fang , D. G. and Lecours , M. 1990 . “ Coupled finite element and boundary element methods in electromagnetic scattering ” . In Finite Element and Finite Difference Method in Electromagnetic Scattering , Edited by: Morgan , M. A. New York : Elsevier . Chapter 3
   Google Scholar
• Yuan , X. , Lynch , D. R. and Strohbehn , J. W. 1990 . Coupling of finite element and moment methods for electromagnetic scattering from inhomogeneous objects . IEEE Trans. Antennas Propagat. , 38 March : 386 – 393 .
   Web of Science ®Google Scholar
• Jeng , S. K. and Tzeng , S.-T. 1991 . Scattering by a cavity-backed slit in a ground plane; TM case . IEEE Trans. Antennas Propagat. , 39 May : 661 – 663 .
   Web of Science ®Google Scholar
• Barkeshli , K. and Volakis , J. L. 1990 . On the implementation and accuracy of the conjugate gradient FFT method . IEEE Antennas Propagat. Magazine , 32 ( No. 2 ) April : 20 – 26 .
   Google Scholar
• Bayliss , A. and Turkel , E. 1980 . Radiation boundary conditions for wave-like equations . Comm. Pure Appl. Math. , 33 : 707 – 725 .
   Web of Science ®Google Scholar
• Engquist , B. and Majda , A. 1977 . Absorbing boundary conditions for the numerical simulation of waves . Math. Comp. , 31 : 629 – 651 .
   Web of Science ®Google Scholar
• Webb , J. P. and Kanellopoulos , V. N. 1989 . Absorbing boundary conditions for finite element solution of the vector wave equation . Microwave and Opt. Techn. Letters , 2 ( No. 10 ) Oct. : 370 – 372 .
   Google Scholar
• Chatterjee , A. and Volakis , J. L. Conformal absorbing boundary conditions for the vector wave equation . Microwave and Opt. Techn. Letters. , submitted to
   Google Scholar
• Givoli , D. 1992 . Numerical Methods for Problems in Infinite Domains , New York : Elsevier .
   Google Scholar
• SDRC I-DEAS . Milford OH , , USA : Structural Dynamics Research Corp .
   Google Scholar
• Sabonnadière , J.-C. and Coulomb , J.-L. 1987 . Finite Element Methods in CAD: Electric and Magnetic Fields , New York : Springer-Verlag . English trans. by S. Salon
   Google Scholar
• Rincaid , D. R. and Oppe , T. C. 1982 . “ ITPACK on supercomputers ” . In Lecture Notes in Math , 151 – 161 . Berlin : Springer-Verlag . Numerical Methods
   Google Scholar
• Chatterjee , A. , Volakis , J. L. and Windheiser , D. 1993 . On the optimization of finite element code for 3D scattering computation . 9th Annual Review of Progress in Applied Computational Electromagnetics (ACES) . March 1993 , Monterey , CA .
   Google Scholar
• Golub , G. H. and Van Loan , C. F. 1985 . Matrix Computations , Baltimore , MD : Johns Hopkins Univ. Press .
   Google Scholar
• Volakis , J. L. and Barkeshli , K. 1991 . “ Applications of the conjugate gradient FFT method to radiation and scattering ” . In Applications of the Conjugate Gradient Method to Electromagnetics and Signal Analysis , Edited by: Sarkar , T. K. New York : Elsevier .
   Google Scholar
• Peterson , A. F. , Ray , S. L. , Chan , C. H. and Mittra , R. 1991 . “ Numerical implementations of the conjugate gradient method and the CG-FFT for electromagnetic scattering ” . In Applications of the Conjugate Gradient Method to Electromagnetics and Signal Analysis , Edited by: Sarkar , T. K. New York : Elsevier .
   Google Scholar
• Jin , J. M. and Volakis , J. L. 1992 . Biconjugate gradient FFT solution for scattering by planar plates . Electromagnetics , 12 : 105 – 119 .
   Web of Science ®Google Scholar
• Cátedra , M. F. , Gago , E. and Nuño , L. 1989 . A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the Fast Fourier Transform . IEEE Trans. Antennas Propagat. , 39 May : 528 – 537 .
   Google Scholar
• Zwamborn , P. and van den Berg , P. M. 1992 . The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems . IEEE Trans. Microwave Theory Techn. , 40 Sept. : 1757 – 1766 .
   Web of Science ®Google Scholar
• Sarkar , T. K. 1987 . On the application of the generalized biconjugate gradient method . J. Electromagnetic Waves Appl. , 1 ( No. 3 ) : 223 – 242 .
   Google Scholar
• Jin , J. M. and Volakis , J. L. Sept. 1991 . “ Radiation and scattering from microstrip patch antennas via a hybrid finite element method ” . In Int. Conference on Electromagnetics in Aerospace Appl , Sept. , 195 – 198 . Italy : Politecnico di Torino . Conference Proceedings
   Google Scholar
• Shively , D. G. , Bailey , M. C. , Cockrell , C. R. and Deshpande , M. D. 1993 . Scattering from microstrip patch antennas using subdomain basis functions . Electromagnetics , to appear
   Google Scholar
• Pico Rivera , CA : Courtesy of Northrop Corp . B2 Division
   Google Scholar
• Woo , A. , Schuh , M. , Simon , M. , Wang , H. G. and Sanders , M. L. Dec. 1991 . “ Radar cross-section measurement data of a simple rectangular cavity ” . Dec. , China Lake , CA : Naval Weapons Center . Technical Report NWC TM7132
   Google Scholar