Une analyse de la méthode des domaines fictifs pour le problème de Helmholtz extérieur

C. Atamian; P. Joly

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1993)

  • Volume: 27, Issue: 3, page 251-288
  • ISSN: 0764-583X

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Atamian, C., and Joly, P.. "Une analyse de la méthode des domaines fictifs pour le problème de Helmholtz extérieur." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 27.3 (1993): 251-288. <http://eudml.org/doc/193703>.

@article{Atamian1993,
author = {Atamian, C., Joly, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {fictitious domain method; exterior Helmholtz problem; capacitance matrix method; numerical results; diffraction; harmonic wave; optimal control; Lagrange multiplier; potential theory; convergence; regularization- penalization method},
language = {fre},
number = {3},
pages = {251-288},
publisher = {Dunod},
title = {Une analyse de la méthode des domaines fictifs pour le problème de Helmholtz extérieur},
url = {http://eudml.org/doc/193703},
volume = {27},
year = {1993},
}

TY - JOUR
AU - Atamian, C.
AU - Joly, P.
TI - Une analyse de la méthode des domaines fictifs pour le problème de Helmholtz extérieur
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1993
PB - Dunod
VL - 27
IS - 3
SP - 251
EP - 288
LA - fre
KW - fictitious domain method; exterior Helmholtz problem; capacitance matrix method; numerical results; diffraction; harmonic wave; optimal control; Lagrange multiplier; potential theory; convergence; regularization- penalization method
UR - http://eudml.org/doc/193703
ER -

References

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  1. [Ad] R. ADAMS, Sobolev spaces, Academic Press, 1975. Zbl0314.46030MR450957
  2. [Ag] S. AGMON, Lectures on elliptic boundary value problems, Van Nostrand, 1965. Zbl0142.37401MR178246
  3. [AS] M. ABRAMOWITZ, I. STEGUN, Handbook of mathematical fonctions, Dover Publications, 1968. 
  4. [Ast 1] G. B. ASTRAKHANTSEV, Methods of fictitious domains for a second-order elliptic equation with natural boundary conditions, U.S.S.R. Comput. Math. and Math. Phys., vol. 18, n° 1, 1978, pp. 114-121. Zbl0394.35028
  5. [Ast 2] G. B. ASTRAKHANTSEV, Numerical solution of the Dirichlet problem using a discrete analogue of a double-layer potential, Soviet. J. Numer. Anal. Math. Modelling, 1, 1986, pp. 267-276. Zbl0825.65075MR897993
  6. [At] C. ATAMIAN, Résolution de problèmes de diffraction d'ondes acoustiques et électromagnétiques en régime fréquentiel par une méthode de domaines fictifs, Thèse de doctorat de l'université de Paris VI, 1991. 
  7. [BDGG] B. BUZBEE, F. DORR, J. GEORGE, G. GOLUB, The direct solution of the discrete Poisson equation on irregular regions, SIAM J. Numer. Anal., vol. 8, n° 4, 1970, pp. 722-736. Zbl0231.65083MR292316
  8. [Ben] A. BENDALI, Approximation par éléments finis de surface de problèmes de diffraction des ondes électromagnétiques, Thèse de doctorat d'état, Université de Paris VI, 1984. 
  9. [Ber] M. BERCOVIER, Perturbation of mixed variational problems. Application to mixed finite element methods, RAIRO Modél. Math. Anal. Numér., n° 12, 1978, pp. 211-236. Zbl0428.65059MR509973
  10. [Br] H. BREZIS, Analyse fonctionnelle. Théorie et applications, Masson, Paris 1983. Zbl0511.46001MR697382
  11. [BW] C. BÖRGERS, O. B. WIDLUND, Finite element capacitance matrix methods, Technical report 261, Computer Science Department, New York University, and LBL Report 22583, Lawrence Berkeley Laboratory, 1986. 
  12. [Ce] J. CEA, Optimisation, Théorie et algorithmes, Dunod, Paris, 1971. Zbl0211.17402MR298892
  13. [Ci] P. G. CIARLET, Introduction à l'analyse numérique matricielle et à l'optimisation, Masson, Paris, 1982. Zbl0488.65001MR680778
  14. [DL] R. DAUTRAY, J. L. LIONS, Analyse mathématique et calcul numérique pour les sciences et techniques, Masson, Paris, 1984. Zbl0642.35001
  15. [DS] N. DUNFORD, J. T. SCHWARTZ, Linear operators, Interscience, 1958. Zbl0084.10402
  16. [Fa] P. FAURRE, Notes d'optimisation, Cours du CMAP, Ecole Polytechnique, Palaiseau, 1984. 
  17. [FK] S. A. FINOGENOV, Y. A. KUZNETSOV, Two-stage fictitious component method for solving the Dirichlet boundary value problem, Sov. J. Num. Anal. Math. Modelling, 3, 1988, pp. 301-324. Zbl0825.65080MR953949
  18. [G] J. GIROIRE, Integral equations methods for exterior problems for the Helmholtz Integral equation, Rapport interne du CMAP, École polytechnique, n° 40, Palaiseau, 1978. 
  19. [H] L. HÖRMANDER, The analysis of linear partial differential operators, Springer, 1983. Zbl0521.35002
  20. [Li] J. L. LIONS, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles, Dunod, Paris, 1968. Zbl0179.41801MR244606
  21. [LM] J. L. LIONS, E. MAGENES, Problèmes aux limites non homogènes et applications, Dunod, Paris, 1968. Zbl0165.10801
  22. [Lu] D. G. LUENBERGER, Optimization by vector space methods, Wiley, 1969. Zbl0176.12701MR238472
  23. [MKM] G. I. MARCHUK, Y. A. KUZNETSOV, A. M. MATSOKIN, Fictitious domain and domain decomposition methods, Sov. J. Num. Anal. Math. Modelling, 1, 1986, pp. 3-36. Zbl0825.65027MR897996
  24. [Nec] J. NEČAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. MR227584
  25. [Ned] J. C. NEDELEC, Approximation des équations intégrales en mécanique et en physique, Cours de l'école d'été d'analyse numérique, EDF-CEA-INRIA, 1977. 
  26. [O] F. OLVER, Asymptotics and special functions, Academic Press, 1981. Zbl0303.41035
  27. [OW] D. P. O'LEARY, O. WIDLUND, Capacitance matrix methods for the Helmholtz equation on general three-dimensional regions, Math. Comp., vol. 33, n° 147, 1979, pp. 849-879. Zbl0407.65047MR528044
  28. [PW1] W. PROSKUROWSKI, O. WIDLUND, On the numerical solution of Helmholtz's equation by the capacitance matrix method, Math. Comp., vol. 30, n° 135, 1976, pp. 433-468. Zbl0332.65057MR421102
  29. [PW2] W. PROSKUROWSKI, O. WIDLUND, A finite element capacitance matrix method for the Neumann problem for the Laplace's equation, SIAM J, Sci. Comp., col. 1, n° 4, 1980, pp. 410-425. Zbl0458.65087MR610753
  30. [R] A. G. RAMM, Scattering by obstacles, Reidel Publishing Company, 1986. Zbl0607.35006MR847716
  31. [RT] J. E. ROBERTS, J. M. THOMAS, Mixed and hybrid methods, Handbook of numerical analysis, vol. II, Finite element methods (Part 1), North Holland, 1991. Zbl0875.65090MR1115239
  32. [RS] M. REED, B. SIMON, Methods of modern mathematical physics, Academic Press, 1981. Zbl0459.46001
  33. [Sc] L. SCHWARTZ, Théorie des distributions, Hermann, 1966. Zbl0149.09501MR209834
  34. [So] A. SOMMERFELD, Partial differential equations in physics, Academic Press, New York, 1964. Zbl0034.35702MR29463
  35. [TA] A. TYCHONOV, V. ARSENINE, Méthode de résolution de problèmes mal posés, Éditions Mir, Moscou, 1976. MR455367
  36. [W] C. H. WILCOX, Scattering theory for the d'Alembert equation in exterior domains, Lecture Notes in Maths., n° 442, Springer-Verlag, Berlin, 1975. Zbl0299.35002MR460927

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