Spurious Modes in Finite-Element Methods

IEEE Antennas and Propagation Magazine

Volumn 37, Issue 5, 1995, Pages 12-24

  Sun, Din ^a   Yuan, Xingchao ^a   Manges, John ^b   Cendes, Zoltan ^b  

^a ANSOFT CORPORATION   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; MATHEMATICAL OPERATORS; MAXWELL EQUATIONS; VECTORS;

SPURIOUS MODES; VECTOR WAVE EQUATION;

ELECTROMAGNETIC WAVE PROPAGATION;

EID: 0029387323     PISSN: 10459243     EISSN: None     Source Type: Journal    
DOI: 10.1109/74.475860     Document Type: Article

References (47)

1. A. Konrad, “Vector Variational Formulation of Electromagnetic Fields in Anisotropic Media,” IEEE Transactions on Microwave Theory and Techniques, MTT-24, 1976, pp. 553–559.
2. M. Hara, T. Wada, T. Fukasawa, and F. Kikuchi, “Three- Dimensional Analysis of RF Electromagnetic Field by the Finite-element method,” IEEE Transactions on Magnetics, MAG-19 1983, pp. 2417–2420.
3. J. R. Winkler and J. B. Davies, “Elimination of Spurious Modes in Finite Element Analysis,” Journal of Computational Physics, 56, 1984, pp. 1–14
4. K. Paulsen and D. Lynch, “Elimination of Vector Parasites in Finite Element Maxwell Solutions,” IEEE Transactions on Microwave Theory and Techniques, MTT-39, March, 1991.
5. P. P. Silvester and G. Pelosi (eds.), Finite Elements for Wave Problems, New York, IEEE Press, 1994.
6. M. Hano, “Finite-Element Analysis of Dielectric-Loaded Waveguides,” IEEE Transactions on Microwave Theory and Techniques, MTT-32, 1984, pp. 1275–1279.
7. S. H. Wong and Z. J. Cendes, “Combined Finite Element-Modal Solution of Three-Dimensional Eddy Current Problems,” IEEE Transactions on Magnetics, MAG-24, 1988, pp. 2685–2687.
8. S. H. Wong and Z. J. Cendes, “Numerically Stable Finite-element Methods for the Galerkin Solution of Eddy Current Problems,” IEEE Transactions on Magnetics, MAG-25, 1989. pp. 3019–3021.
9. C. W. Crowley, P. P. Silvester, and H. Hurwitz, “Covariant Projection Elements for 3D Vector Field Problems,” Ieee Transactions on Magnetics, MAG-24, 1988, pp. 397–400.
10. A. Bossavit and I. Mayergoyz, “Edge-Elements for Scattering Problems,” IEEE Transactions on Magnetics, MAG-25, 1989, pp. 2816–2821.
11. Z. J. Cendes, “Overview of CAE/CAD/AI Electromagnetic Field Computation,” in A. Konrad (ed.), Proceedings of the Second IEEE Conference on Electromagnetic Field Computation, Schenectady, NY, 1987.
12. J. F. Lee, D. K. Sun, and Z. J. Cendes, “Tangential Vector Finite Elements for Electromagnetic Field Computation,” IEEE Transactions on Magnetics, MAG-27, 1991. pp. 4032–4035.
13. A. F. Peterson, “Vector Finite Element Formulation for Scattering from Two-Dimensional Heterogeneous Bodies,” IEEE Transactions on Antennas and Propagation, AP-43, 3, 1994, pp. 357–365.
14. Z. J. Cendes, D. Hudak, J. F. Lee, and D. K. Sun, Development of New Methods for Predicting the Bistatic Electromagnetic Scattering from Absorbing Shapes, RADC Final Report, Hanscom Air Force Base, MA, April, 1986.
15. Z. J. Cendes, “Vector Finite Elements for Electromagnetic Field Computation,” IEEE Transactions on Magnetics, MAG-27, 1991, pp. 3953–3966.
16. P. Silvester, “Finite Element Solution of Homogeneous Waveguide Problems,” Alta Frequenza, 38, 1969, pp. 313–317.
17. Z. J. Cendes and P. Silvester, “Numerical Solution of Dielectric Loaded Waveguides. I - Finite-Element Analysis,” IEEE Transactions on Microwave Theory and Techniques, MTT-18, 1971, pp. I124-1131.
18. S. Ahmed and P. Daly, “Finite-Element Methods for Inhomogenous Waveguides,” IEE Proceedings, 11 6, 1969, pp. 1661–1664.
19. A. Konrad, “Triangular Finite Elements for Vector Fields in Electromagnetics,” PhD Thesis, Department of Electrical Engineering, McGill University, 1974.
20. Z. J. Cendes and S. H. Wong, “C1 Quadratic Interpolation Over Arbitrary Point Sets,” IEEE Computer Graphics and Applications, November 1987, pp. 8–15.
21. D. Lynch and K. Paulsen, “Origin of Vector Parasites in Numerical Maxwell Solutions,” IEEE Transactions on Microwave Theory and Techniques, MTT-39, March, 1991.
22. X. Yuan, D. R. Lynch, and K. Paulsen, “Importance of Normal Field Continuity in Inhomogeneous Scattering Calculations,” IEEE Transactions on Microwave Theory and Techniques, MTT-39, 4, 1991, pp. 638-641.
23. J. P. Webb, G. L. Maile, and R. L. Ferrari “Finite-Element Solution of Three-Dimensional Electromagnetic Problems,” IEE Proceedings, 130, Pt. H, 2, 1983, pp. 153–159.
24. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic Scattering by Surfaces of Arbitrary Shape,” IEEE Transactions on Antennas and Propagation, AP-30, 1982, pp. 409–418.
25. S. Wandzura, “Electric Current Basis Functions for Curved Surfaces,” Electromagnetics, 12, 1992, pp. 77–91.
26. A. Bossavit, “Whitney Forms: A Class of Finite Elements for Three-Dimensional Computations in Electromagnetism,” IEE Proceedings, 135, Pt. A, 8, 1988, pp. 493–500.
27. R. Albanese and G. Rubinacci, “Magnetostatic Field Computations in Terms of Two-Component Vector Potentials,” International Journal for Numerical Methods in Engineering, 2 9, March 1990, pp. 515–532.
28. J. Webb, “Edge Elements and what they can do for you,” IEEE Transactions on Magnetics, MAG-29,1993, pp. 1460–65.
29. J. P. Webb and B. Forghani, “A Single Scalar Potential Method for 3D Magnetostatics Using Edge Elements,” IEEE Transactions on Magnetics, MAG-25, 1989, pp. 4126–4128.
30. J. P. Webb and B. Forghani, “The Low-Frequency Performance of H-¢ and T -Ω Methods using Edge Elements for 3D Eddy Current Problems,” IEEE Transactions on Magnetics, MAG-29, 1993, pp. 2461–2463.
31. P. Dular, A. Nicolet, A. Genon, and W. Legros, “A Discrete Sequence Associated with Mixed Finite Elements and its Gauge Condition for Vector Potentials,” IEEE Transactions on Magnetics, MAG-31, 1995, pp. 1356–1359.
32. I. Bardi, O. Biro, K. Preis, G. Vrisk, K. Richter, “Nodal and Edge Element Analysis of Inhomogeneously Loaded 3D Cavities,” IEEE Transactions on Magnetics, MAG-28, 1992, pp. 1142–1145.
33. J. B. Manges and Z. J. Cendes, “A Generalized Tree-Cotree Gauge for Magnetic Field Computation,” IEEE Transactions on Magnetics, MAG-31, May 1995, pp. 1342–1347.
34. J. C. Nedelec, “Mixed Elements in R3,” Numer. Math., 35, 1980, pp. 315–341.
35. HFSS User's Manual, Hewlett-Packard Company, Palo Alto, CA, 1990.
36. Z. J. Cendes, D. N. Shenton, and H. Shanassar, “Magnetic Field Computation Using Delaunay Triangulation and Complementary Finite-element methods,” IEEE Transactions on Magnetics, MAG-19,6, November 1983, pp. 2551–2554.
37. D. N. Shenton and Z. J. Cendes, “Three-Dimensional Finite Element Mesh Generation Using Delaunay Tessellation,” IEEE Transactions on Magnetics, MAG-21, 1985, pp. 2535–2538.
38. Maxwell SI Eminence Users' Manual, Ansoft Corporation, Pittsburgh, P A, 1994.
39. J. L. Yao Bi, L. Nicolas, and A. Nicolas, “H(curl) Elements on Hexahedral and Vector ABC's for Unbounded Microwave Problems,” IEEE Transactions on Magnetics, MAG-31, May 1995, pp. 1538–1531.
40. T. V. Yioultsis and T. D. Tsiboukis, “Vector Finite Element Analysis of Waveguide Discontinuities Involving Anisotropic Media,” IEEE Transactions on Magnetics, MAG-31, May 1995, pp. 1550–1553.
41. A. Ahagon and T. Kashimoto, “Three-Dimensional Electromagnetic Wave Analysis using High Order Edge Elements,” IEEE Transactions on Magnetics, MAG-31, May 1995, pp. 1753–1756.
42. J. F. Lee, D. K. Sun and Z. J. Cendes, “Full-Wave Analysis of Dielectric Waveguides using Tangential Vector Finite Elements,” IEEE Transactions on Microwave Theory and Techniques, MTT- 39,8, 1991, pp. 1262–1271.
43. Z. J. Cendes and J. F. Lee, “The Transfinite-element Method for Modeling MMIC Devices,” IEEE Transactions on Microwave Theory and Techniques, MTT-36, 12, 1988, pp. 1639–1649.
44. X. Yuan, D. K. Sun and Z. J. Cendes, “AWEFEM: A Fast Method for Computing the Spectral Response of Microwave Devices over a Broad Bandwidth,” IEEE Transactions on Microwave Theory and Techniques, submitted.
45. A. F. Peterson, “Absorbing Boundary Conditions for the Vector Wave Equation,” Microwave and Guided Wave Letters, 1,2, April 1988.
46. J. P. Webb and V. N. Kanellopoulos, “Absorbing Boundary Conditions for the Finite Element Solution of the Vector Wave Equation,” Microwave and Guided Wave Letters, 2, 10, October 1989.
47. Y. Li and Z. J. Cendes, “High-Accuracy Absorbing Boundary Conditions,” IEEE Transactions on Magnetics, MAG-31, May 1995, pp. 1524–1529.