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References

  1. J. C. Nedelec, “A new family of mixed finite elements in R3,” Numer. Methods, vol. 30, pp. 57–81, 1986.

    Article  Google Scholar 

  2. M. L. Barton and Z. J. Cendes, “New vector finite elements for three-dimensional magnetic field computation,” J. Appl. Phys., vol. 61, pp. 3919–3921, 1987. doi: 10.1063/1.338584

    Article  Google Scholar 

  3. Z. J. Cendes, “Vector finite elements for electromagnetic field computations,” IEEE Trans. Magn., vol. MAG-27, no. 5, pp. 3958–3966, Sept. 1991. doi: 10.1109/20.104970

    Article  Google Scholar 

  4. J. P. Webb, “Edge elements and what they can do for you,” IEEE Trans. Magn., vol. MAG-29, pp. 1460–1465, Mar. 1993. doi: 10.1109/20.250678

    Article  Google Scholar 

  5. G. Mur, “The finite-element modeling of three-dimensional electromagnetic fields using edge and nodal elements,” IEEE Trans. Antennas Propag., vol. 41, no. 7, pp. 948–953, July 1993. doi: 10.1109/8.237627

    Article  Google Scholar 

  6. H. Anton, I. Bivens, and S. Davis, Calculaus, 7th ed. New York: Wiley, 2002, pp. 1075-1090.

    Google Scholar 

  7. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 4th ed., vol. 1: Basic Formulation of Linear Problems. New York: McGraw-Hill, 1989.

    Google Scholar 

  8. D. Zwillinger, Handbook of Integration. Boston: Jones and Barlett, 1992.

    Book  Google Scholar 

  9. E. W. Cheney and D. R. Kincaid, Numerical Mathematics and Computing, 5th ed. Monterey: Brooks Cole, 2003.

    MATH  Google Scholar 

  10. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover Publications, 1972.

    MATH  Google Scholar 

  11. G. R. Cowper, “Gaussian quadrature formulas for triangles,” Int. J. Numer. Methods Eng., vol. 7, pp. 405–408, 1973. doi: 10.1002/nme.1620070316

    Article  Google Scholar 

  12. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NewJersey, 1962.

    MATH  Google Scholar 

  13. D. M. Young, Iterative Solution of Large Linear Systems. New York: Dover Publications, 2003.

    Google Scholar 

  14. Y. Saads, Iterative Methods for Sparse Linear Systems. Boston: PWS Publishing, 1996.

    Google Scholar 

  15. A. M. Bruaset, A Survey of Preconditioned Iterative Methods. London, UK: Chapman & Hall, 1995.

    MATH  Google Scholar 

  16. A. Chatterjee, J. M. Jin, and J. L. Volakis, “Edge-based finite elements and vector ABC’s applied to 3-D scattering,” IEEE Trans. Antennas Propag., vol. 41, no. 2, pp. 221–226, Feb. 1993. doi: 10.1109/8.214614

    Article  Google Scholar 

  17. J. M. Jin and J. L. Volakis, “A hybrid finite element method for scattering and radiation by microstrip patch antennas and arrays residing in a cavity,” IEEE Trans. Antennas Propag., vol. 39, no. 11, pp. 1598–1604, Nov. 1991. doi: 10.1109/8.102775

    Article  Google Scholar 

  18. A. C. Polycarpou, C. A. Balanis, J. T. Aberle, and C. Birtcher, “Radiation and scattering from ferrite-tuned cavity-backed slot antennas: Theory and experiment,” IEEE Trans. Antennas Propag., vol. 46, no. 9, pp. 1297–1306, 1998. doi: 10.1109/8.719973

    Article  Google Scholar 

  19. D. T. McGrath and V. P. Pyati, “Phased array antenna analysis with the hybrid finite element method,” IEEE Trans. Antennas Propag., vol. 42, no. 12, pp. 1625–1630, Dec. 1994. doi: 10.1109/8.362811

    Article  Google Scholar 

  20. A. Chatterjee, J. M. Jin, and J. L. Volakis, “Computation of cavity resonances using edge-based finite elements,” IEEE Trans. Microw. Theory Tech., vol. MTT-40, pp. 2106-2108, Nov. 1992. doi: 10.1109/22.168771

    Article  Google Scholar 

  21. J. M. Jin and V. V. Liepa, “Application of hybrid finite element method to electromagnetic scattering from coated cylinders,” IEEE Trans. Antennas Propag., vol. 36, no. 1, pp. 50–54, Jan. 1988. doi: 10.1109/8.1074

    Article  Google Scholar 

  22. D.-H. Han, A. C. Polycarpou, and C. A. Balanis, “Hybrid analysis of reflector antennas including higher-order interactions and blockage effects,” IEEE Trans. Antennas Propag., vol. 50, no. 11, pp. 1514–1524, 2002. doi: 10.1109/TAP.2002.803952

    Article  Google Scholar 

  23. M. N. O. Sadiku, Numerical Techniques in Electromagnetics, 2nd ed. Boca Raton: CRC Press, 2001.

    MATH  Google Scholar 

  24. C. A. Balanis, Advanced Engineering Electromagnetics. New York: Wiley, 1989.

    Google Scholar 

  25. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method, 2nd ed. Boston: Artech House, 2000.

    MATH  Google Scholar 

  26. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics. Boca Ratorn: CRC Press, 1993.

    Google Scholar 

  27. B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput., vol. 31, pp. 329–351, 1977.

    Article  MathSciNet  Google Scholar 

  28. A. Bayliss and E. Turkel, “Radiation boundary conditions for wave-like equations,” Commun. Pure Appl. Math., vol. 33, pp. 707–725, 1980.

    Article  MathSciNet  Google Scholar 

  29. A. Bayliss, M. Gunzburger, and E. Turkel, “Boundary conditions for the numerical solution of elliptic equations in exterior regions,” SIAM J. Appl. Math., vol. 42, pp. 430–451, 1982. doi: 10.1137/0142032

    Article  MathSciNet  Google Scholar 

  30. A. F. Peterson, “Absorbing boundary conditions for the vector wave equation,” Microw. Opt. Technol. Lett., vol. 1, pp. 62–64, 1988.

    Article  Google Scholar 

  31. J. P. Webb and V. N. Kanellopoulos, “Absorbing boundary conditions for the finite element solution of the vector wave equation,” Microw. Opt. Technol. Lett., vol. 2, pp. 370–372, 1989.

    Article  Google Scholar 

  32. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, no. 2, pp. 185–200, Oct. 1994. doi: 10.1006/jcph.1994.1159

    Article  MathSciNet  Google Scholar 

  33. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag., vol. 43, no. 12, pp. 1460–1463, 1995. doi: 10.1109/8.477075

    Article  Google Scholar 

  34. U. Pekel and R. Mittra, “A finite element method frequency domain application of the perfectly matched layer (PML) concept,” Microw. Opt. Technol. Lett., vol. 9, no. 3, pp. 117–122, June 1995.

    Article  Google Scholar 

  35. A. C. Polycarpou, M. R. Lyons, and C. A. Balanis, “A two-dimensional finite-element formulation of the perfectly matched layer,” IEEE Microw. Guided Wave Lett., vol. 8, pp. 30–32, Jan. 1997.

    Article  Google Scholar 

  36. P. Silvester, “High-order polynomial triangular finite elements for potential problems,” Int. J. Eng. Sci., vol. 7, pp. 849–861, 1969. doi: 10.1016/0020–7225(69)90065–2

    Article  Google Scholar 

  37. P. Silvester, “A general high-order finite-element waveguide analysis program,” IEEE Trans. Microw. Theory Tech., vol. MTT-17, pp. 204–210, Apr. 1969. doi: 10.1109/TMTT.1969.1126932

    Article  Google Scholar 

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Polycarpou, A.C. (2006). Two-Dimensional Boundary-Value Problems. In: Introduction to the Finite Element Method in Electromagnetics. Synthesis Lectures on Computational Electromagnetics. Springer, Cham. https://doi.org/10.1007/978-3-031-01689-9_2

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