Mathematical analysis of a finite element method without spurious solutions for computation of dielectric waveguides. (English) Zbl 0741.65095

See the preview in Zbl 0727.65111.


65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
35P15 Estimates of eigenvalues in context of PDEs


Zbl 0727.65111
Full Text: DOI EuDML


[1] Bonnet, A.S. (1988): Analyse mathématique de la propagation de modes guides dans les fibres optiques. Ecole National Superieure de Techniques Avancées. Rapport de Recherche 229, Paris
[2] Bossavit, A. (1989): Simplicial finite element for scattering problems in electromagnetism. Comput. Methods Appl. Mech. Eng.76, 299-316 · Zbl 0688.73076 · doi:10.1016/0045-7825(89)90062-5
[3] Bossavit, A. (1990): Solving Maxwell equations in a closed cavity and the question of spurious modes. IEEE Trans. Magn.26, n. 2, 702-705 · doi:10.1109/20.106414
[4] Ciarlet, P.G. (1978): The finite element method for elliptic problems. North-Holland, Amsterdam · Zbl 0383.65058
[5] Dautray, R., Lions, J. (1985): Analyse mathématique et calcul numérique. Masson, Paris · Zbl 0642.35001
[6] Descloux, J., Nassif, N., Rappaz, J. (1978): On spectral approximation. The problem of convergence. Error estimates for the Galerkin method. RAIRO Analyse Num./Num. Anal.12, n. 2, 97-112 · Zbl 0393.65024
[7] García Lomba, G. (1991): Resolución mediante un método de elementos finitos lagrangianos de un problema espectral relacionado con la propagación en guías de ondas. Internal Report, Dept. of Appl. Math., Univ. of Santiago de Compostela, Spain
[8] Girault, V., Raviart, P.A. (1986): Finite Element methods for Navier-Stokes equations. Theory and algorithms. Springer, Heidelberg Berlin New York · Zbl 0585.65077
[9] Gruber, R., Rappaz, J. (1985): Finite Element Methods in Linear Ideal Magnetohydrodynamics. Springer, Heidelberg Berlin New York · Zbl 0573.76001
[10] Hara, M., Wada, T., Fukasawa, T., Kikuchi, F. (1983): A three dimensional analysis of RF electromagnetic fields by the finite element method. IEEE Trans Magn.19, n. 6, 2417-2420 · doi:10.1109/TMAG.1983.1062816
[11] Kikuchi, F. (1987): Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism. Comput. Methods. Appl. Mech. Eng.64, 509-521 · Zbl 0644.65087 · doi:10.1016/0045-7825(87)90053-3
[12] Konrad, A. (1986): On the reduction of the number of spurious modes in the vectorial finite-element solution of the three dimensional cavities and wave guides. IEEE Trans. Microwave Theory Techn.MTT-34, n. 2, 224-227 · doi:10.1109/TMTT.1986.1133315
[13] Koshiba, M., Suzuki, M. (1986): Vectorial finite-element method without any spurious solutions for dielectric waveguiding problems using transverse magnetic-field component. IEEE Trans. Microwave Theory TechnMTT-34, n. 11, 1120-1124 · doi:10.1109/TMTT.1986.1133508
[14] Nedelec, J.C. (1980): Mixed finite elements in ?3. Numer. Math.35, 315-341 · Zbl 0419.65069 · doi:10.1007/BF01396415
[15] Nedelec, J.C. (1986): A new family of mixed finite elements in ?3. Numer. Math.50, 57-81 · Zbl 0625.65107 · doi:10.1007/BF01389668
[16] Neittaanmäki, P., Picard, R. (1981): On the convergence of the finite element approximation of eigenfrequencies and eigenvectors to Maxwell’s boundary value problem. Ann. Acad. Sci. Fenn. Ser. A I Math.6, 255-271 · Zbl 0489.65068
[17] Rahman, M.A., Davies, J.B. (1984): Penalty function improvement of waveguide solution by finite elements. IEEE Trans. Microwave Theory Tech.MTT-32, n. 8, pp. 922-928 · doi:10.1109/TMTT.1984.1132789
[18] Rappaz, J. (1977): Approximation of the spectrum of a non-compact operator given by the magnetohydrodynamic stability of a plasma. Numer. Math.28, 15-24 · Zbl 0341.65044 · doi:10.1007/BF01403854
[19] Raviart, P.A., Thomas, J.M. (1983): Introduction à l’analyse numérique des équations aux dérivées partielles. Masson, Paris · Zbl 0561.65069
[20] Raviart, P.A., Thomas, J.M. (1977): A mixed finite element method for 2nd order elliptic problems. In: A. Dold, B. Eckman, eds., Mathematical aspects of finite element methods. Lecture notes Math. 606. Springer, Berlin Heidelberg New York, pp. 292-315 · Zbl 0362.65089
[21] Roberts, J.E., Thomas, J.M. (1991): Mixed and Hybrid Methods. In: P.G. Ciarlet, J.L. Lions, eds., Handbook of Numerical Analysis, Vol. 2, Finite Element Methods. North Holland, Amsterdam · Zbl 0875.65090
[22] Reitz, J.R., Mildorf, F.J. (1966): Foundations of the electromagnetic theory. Addison Wesley, New York
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