A method for computing guided waves in integrated optics. Part II: Numerical approximation and error analysis

SIAM Journal on Numerical Analysis

Volumn 39, Issue 5, 2001, Pages 1684-1711

  Gómez Pedreira, Dolores ^a   Joly, Patrick ^b  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b INRIA ROCQUENCOURT   (France)

Author keywords

Eigenvalue problems; Error estimates; Integrated optics; Transparent boundary conditions

Indexed keywords

EID: 0036414995     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900377711     Document Type: Article

References (15)

1. I. BABUŠKA AND J. OSBORN, Eigenvalue problems, in Handbook of Numerical Analysis, Vol. II, P. G. Ciarlet, ed., North-Holland, Amsterdam, 1991, pp. 641-787.
2. A. BERMÚDEZ, D. GÓMEZ PEDREIRA, AND P. JOLY, An hybrid approach for the computation of guided modes in integrated optics, Adv. Comput. Math., to appear.
3. A. S. BONNET-BENDHIA, Analyse mathématique de la propagation de modes guidés dans les fibres optiques, Technical report 229, Ecole Nationale Supérieure de Techniques Avancées, Paris, France, 1989.
4. A. S. BONNET-BENDHIA, G. CALOZ, AND F. MAHÉ, Guided modes of integrated optical guides. A mathematical study, IMA J. Appl. Math., 60 (1998), pp. 225-261.
5. N. DUNFORD AND J. T. SCHWARTZ, Linear Operators, Part II, Interscience Publishers, New York, 1963.
6. D. GÓMEZ PEDREIRA AND P. JOLY, A method for computing guided waves in integrated optics. Part I: Mathematical analysis, SIAM J. Numer. Anal., 39 (2001), pp. 596-623.
7. M. D. GÓMEZ PEDREIRA, A Numerical Method for the Computation of Guided Waves in Integrated Optics, Ph.D. thesis, Universidad de Santiago de Compostela, Santiago, Spain, 1999.
8. P. GRISVARD, Caractérisation de quelques spaces d'interpolation, Arch. Ration. Mech. Anal., 25 (1967), pp. 40-63.
9. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985.
10. P. JOLY AND C. POIRIER, A numerical method for the computation of electromagnetic modes in optical fibres, Math. Methods Appl. Sci., 22 (1999), pp. 389-447.
11. M. LENOIR AND A. TOUNSI, The localized finite element method and its application to the two-dimensional sea-keeping problem, SIAM J. Numer. Anal., 25 (1988), pp. 729-752.
12. J. L. LIONS AND E. MAGENES, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris, 1968.
13. J. E. OSBORN, Spectral approximation for compact operators, Math. Comp., 29 (1975), pp. 712-725.
14. J. RAZAFIARIVELO, Optimisation de la forme de transitions entre guides électromagnétiques par une méthode intégrale d'élements finis, Ph.D. thesis, Université de Paris VI, Paris, France, 1995.
15. C. VASSALLO, Optical Waveguide Concepts, Elsevier Science, Amsterdam, 1991.