Solving maxwell equations in a closed cabvity, and the question of ‘spurious modes’

IEEE Transactions on Magnetics

Volumn 26, Issue 2, 1990, Pages 702-705

  Bossavit, A ^a  

^a EDF R AND D   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTROMAGNETISM;

CLOSED CAVITY; EDGE-ELEMENTS; EIGENMODES; MAXWELL EQUATIONS; SPURIOUS MODES;

RESONATORS, CAVITY;

EID: 0025399769     PISSN: 00189464     EISSN: 19410069     Source Type: Journal    
DOI: 10.1109/20.106414     Document Type: Article

References (31)

1. D. Baldomir: “Differential forms and electromagnetism in 3-dimensional Euclidean space R 3 ”, IEE Proc., Pt. A , 133 , 3 (1986), pp. 139–43.
2. I. Bardi: “Improved Finite-Element Formulation in Terms of the Two-Component Component Magnetic Vector Potential for Dilectric Waveguides”, Compumag Conference, Tokyo (1989), to appear.
3. S. Bates, B. Cathers: “Analysis of spurious eigenmodes in finite element equations”, Int, J. Numer. Meth, Engng. , 23 (1986), pp. 1131–43.
4. M.L. Barton, Z.J. Cendes: New vector finite elements for three dimensional magnetic fields computations”, J. Appl. Phys. , 61, 8 (1987), pp. 3919–21.
5. T. Belytschko, W.K. Lin, J.S.J. Ong: “Mixed variational principles and stabilization of spurious modes in the 9-node element”, Comp , Meth , Appl Mech. Engng., 62 (1987), pp. 275–92.
6. A. Bossavit: “A Rationale for ‘Edge-Elements’ in 3-D Fields Computations”, IEEE Trans. , MAG-24, 1 (1989), pp. 74–79.
7. A. Bossavit: “Edge-elements for scattering problems”, to appear, Comp. Meth. Appl. Mech. Engng„ 1989.
8. C.H. Chen, C.D. Lien: The variational principle for non-self adjoint electro magnetic problems”, IEEE Trans. , MTT-28 (1980), pp. 878–86.
9. Z.J. Csendes, P. Silvester: “Numerical Solution of Dielectric Loaded Waveguides: I–Finite Element Analysis”, IEEE Trans., MTT-l8 , 12 (1970), pp. 1124–31.
10. J. B. Davies, A. Fernandez, G.Y. Philippou: “Finite Element Analysis of all Modes in Cavities with Circular Symmetry”, IEEE Trans., MTT-30, 11 (1982), pp. 1975–80.
11. G.A. Deschamps: “Electromagnetics and Differential Forms”, Proc. IEEE , 69, 6 (1981), pp. 676–96.
12. J. Dodziuk: “Finite-Difference Approach to the Hodge Theory of Harmonic Forms”, Amer. J. Math., 98, 1 (1976), pp. 79–104.
13. R.L. Ferrari: “Complementary variational formulations for eddy-current problems using the field variables E and H directly”, IEE Proc., Pt. A, 132 , 4 (1985), pp. 157–64.
14. K.O. Friedrichs: “Differential Forms on Riemannian Manifolds”, Comm. Pure Appl. Math., 3 (1953), pp. 551–90.
15. P. Hammond, T.D. Tsiboukis: “Dual finite-elements calculations for static electric and magnetic fields”, IEE Proc. , Pt. A, 130 , 3 (1983), pp. 105–15.
16. M. Hano: “Vector Finite-Element Solution of Anisotropic Waveguides Using Novel Triangular Elements”, Electr. & Comm. in Japan, Pt. 2 , 71 , 8 (1988), pp. 71–80.
17. M. Hara, T. Wada, T. Fukasawa, F. Kikuchi: “A Three Dimensional Analysis of RF Electromagnetic Fields by the Finite Element Method”, IEEE Trans., MAG-19 , 6 (1983), pp. 2417–20.
18. K. Hayata, M. Koshiba, M. Eguchi, M. Suzuki: “Vectorial Finite-Element Method Without any Spurious Solutions for Dielectric Waveguiding Problems Using Transverse Magnetic Field Component”, IEEE Trans., MTT-34, 11 (1986), 1120–24.
19. M. Ikeuchi, K. Inoue, H. Sawami, H. Niki: “Spurious Solutions in the Finite-Element Analysis of Microstrip Lines”, Electrical Engng. in Japan, 4 (1978), pp. 415–22.
20. F. Kikuchi: “Mixed and penalty formulations for finite elements analysis of an eigenvalue problem in electro magnetism”, Comp. Meth, Appl. Mech, Engng. , 64 (1987), pp. 509–21.
21. A.J. Kobelansky, J.P. Webb: “Eliminating Spurious Modes in Finite-Element Waveguide Problems by Using Divergence-Free Fields”, Electronics Letters 22, 11 (1986), pp. 569–70.
22. J. Komorowski: “On Finite-dimensional Approximations of the Exterior Differential, Codifferential and Laplacian on a Riemannian Manifold”, Bull. Acad. Polonaise Sc. (Math., Astr., Phys.), 23, 9 (1975), pp. 999–1005.
23. A. Konrad: “On the Reduction of the Number of Spurious Modes in the Vectorial Finite Element Solution of Three-Dimensional Cavities and Waveguides”, IEEE Trans., MTT-34, 2 (1986), pp. 224–27.
24. BE. MacNeal, R.H. MacNeal, R.N. Coppolino: “Spurious Modes of Electromagnetic Vector Potential Finite Elements”, The MacNeal Schwendler Corporation, Los Angeles 1989.
25. J. Penman, J.R. Fraser: “Dual and Complementary Energy Methods in Electromagnetism”, IEEE Trans. , MAG-19 , 6 (1983), pp. 2311–16.
26. J. Svedin: “A Fast Converging Finite-Element Procedure without Spurious Modes for Waveguide Propagation Analysis”, URSI Int. Symposium, Stockholm (1989), pp. 46–48.
27. T. Teichmann, E.P. Wigner: “Electromagnetic Field Expansions in Loss-Free Cavities Excited Through Holes”, J. Appl. Phys., 24, 3 (1953), pp. 262–67.
28. J.P. Webb, G.L. Maile, R.L. Ferrari: Finite-element solution of three-dimensional dimensional electromagnetic problems”, IEE Proc., H - 130 , 2 (1983), pp. 1 53–59.
29. J.P. Webb: “The Finite Element Method for Finding Modes of Dielectric-Loaded Cavities”, IEEE Trans. , MTT-33 , 7 (1985), pp. 635–39.
30. H. Whitney: Geometric Integration Theory , Princeton U.P. (Princeton), 1957.
31. S.H. Wong, Z.J. Cendes: “Combined Finite Element-Modal Solution of Three-Dimensional Eddy-Current Problems”, IEEE Trans., MAG-24 , 6 (1988), pp. 2685–87.