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All issues Volume 45 / No 1 (January-February 2011) ESAIM: M2AN, 45 1 (2011) 91-113 References
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Issue
ESAIM: M2AN
Volume 45, Number 1, January-February 2011
Page(s) 91 - 113
DOI https://doi.org/10.1051/m2an/2010032
Published online 15 April 2010
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. J.B. Apoung-Kamga and O. Pironneau, Numerical zoom for multiscale problems with an application to nuclear waste disposal. J. Comput. Phys. 224 (2007) 403–413. [CrossRef] [MathSciNet] [Google Scholar]
  3. F. Ben Belgacem, M. Fournié, N. Gmati, F. Jelassi, Handling boundary conditions at infinity for some exterior problems by the alternating Schwarz method. C. R. Acad. Sci., Sér. 1 Math. 336 (2003) 277–282. [Google Scholar]
  4. F. Ben Belgacem, M. Fournié, N. Gmati and F. Jelassi, On the Schwarz algorithms for the elliptic exterior boundary value problems. ESAIM: M2AN 39 (2005) 693–714. [CrossRef] [EDP Sciences] [Google Scholar]
  5. C. Bernardi, Y. Maday and A.T. Patera, A New Non Conforming Approach to Domain Decomposition: The Mortar Element Method, in Non-linear Partial Differential Equations and their Applications 11, H. Brezis and J.-L. Lions Eds., Pitman/Wiley, London/New York (1994) 13–51. [Google Scholar]
  6. S. Bertoluzza, M. Ismaïl and B. Maury, The Fat Boundary Method: Semi-Discrete Scheme and Some Numerical experiments, in Domain decomposition methods in science and engineering, Lect. Notes Comput. Sci. Eng. 40, Springer, Berlin (2005) 513–520. [Google Scholar]
  7. F. Brezzi, J.L. Lions and O. Pironneau, On the chimera method. C. R. Acad. Sci., Sér. 1 Math. 332 (2001) 655–660. [Google Scholar]
  8. H.D. Bui, Fracture Mechanics: Inverse Problems and Solutions, Solid Mechanics and Its Applications 139. Springer (2006). [Google Scholar]
  9. P.-G. Ciarlet, The Finite Element Method for Elliptic Problems, Studies in Mathematics and Its Applications 4. North Holland (1978). [Google Scholar]
  10. D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, Applied Mathematical Sciences 93. Springer (1992). [Google Scholar]
  11. R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques. Second edition, Masson, Paris (1988). [Google Scholar]
  12. G. Dolzmann and S. Müller, Estimates for Green's matrices of elliptic systems by Lp theory. Manuscripta Math. 88 (1995) 261–273. [CrossRef] [MathSciNet] [Google Scholar]
  13. V. Frayssé, L. Giraud, G. Gratton and J. Langou, A Set of GMRES Routines for Real and Complex Arithmeticcs on High Performance Computers. CERFACS Technical Report TR/PA/03/3 (2003). [Google Scholar]
  14. R. Glowinski, J. He, J. Rappaz and J. Wagner, Approximation of multi-scale elliptic problems using patches of finite elements. C. R. Acad. Sci., Sér. 1 Math. 337 (2003) 679–684. [Google Scholar]
  15. R. Glowinski, J. He, J. Rappaz and J. Wagner, A multi-domain method for solving numerically multi-scale elliptic problems. C.R., Math. 338 (2004) 741–746. [Google Scholar]
  16. N. Gmati and B. Philippe, Comments on the GMRES convergence for preconditioned systems, in 6th International Conference on Large-Scale Scientific Computations, June 5–9, 2007, I. Lirkov, S. Margenov and J. Waśniewski Eds., Lect. Notes Comput. Sci. 4818, Springer-Verlag (2008) 40–51. [Google Scholar]
  17. P. Grisvard, Boundary value problems in non-smooth domains, Monographs and Studies in Mathematics 24. Pitman, London (1985). [Google Scholar]
  18. M. Grüter and K.-O Widman, The Green function for uniformly elliptic equations. Manuscripta Math. 37 (1982) 303–342. [Google Scholar]
  19. J. He, A. Lozinski and J. Rappaz, Accelerating the method of finite element patches using approximately harmonic functions. C. R. Acad. Sci., Sér. 1 Math. 345 (2007) 107–112. [Google Scholar]
  20. F. Hecht, EMC2, Éditeur de Maillage et de Contours en 2 Dimensions. http://www-rocq1.inria.fr/gamma/cdrom/www/emc2. [Google Scholar]
  21. F. Hecht, A. Lozinski and O. Pironneau, Numerical Zoom and the Schwarz Algorithm, in Domain Decomposition Methods in Science and Engineering XVIII, Lecture Notes in Computational Science and Engineering 70, M. Bercovier, M.J. Gander, R. Kornhuber and O. Widlund Eds., Springer (2008). [Google Scholar]
  22. M. Ismaïl, The Fat Boundary Method for the Numerical Resolution of Elliptic Problems in Perforated Domains. Application to 3D Fluid Flows. Ph.D. thesis, Université UPMC, Paris VI, France (2004). [Google Scholar]
  23. F. Jelassi, Sur les méthodes de Schwarz pour les problèmes extérieurs. Application au calcul des courants de Foucault en électrotechnique. Ph.D. Thesis, Université Paul Sabatier, Toulouse III, France (2006). [Google Scholar]
  24. P.-L. Lions, On the alternating Schwarz method I., in First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Gowinski, G.H. Golub, G.A. Meurant and J. Périaux Eds., SIAM, Philadelphia (1988) 1–42. [Google Scholar]
  25. J. Liu and J.M. Jin, A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering and radiation problems. IEEE Trans. Antennas Propag. 49 (2001) 1794–1806. [Google Scholar]
  26. B. Lucquin and O. Pironneau, Introduction to Scientific Computing. John Wiley & Sons Ltd., Inc., New York (1998). [Google Scholar]
  27. D. Martin, MELINA, Guide de l'utilisateur. I.R.M.A.R., Université de Rennes I/E.N.S.T.A. Paris, France (2000). http://perso.univ-rennes1.fr/daniel.martin/melina. [Google Scholar]
  28. B. Maury, A fat boundary method for the Poisson equation in a domain with holes. J. Sci. Comp. 16 (2001) 319–339. [CrossRef] [Google Scholar]
  29. I. Moret, A note on the superlinear convergence of GMRES. SIAM J. Numer. Anal. 34 (1997) 513–516. [CrossRef] [MathSciNet] [Google Scholar]
  30. J.C. Nédélec, Acoustic and Electromagnetic Equations. Integral Representations for Harmonic Problems. Springer (2000). [Google Scholar]
  31. O. Pironneau, Numerical Zoom for Localized Multi-Scale Problems. Invited conference, MAFELAP, Brunel University, London (2009). [Google Scholar]
  32. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations. Oxford Science Publications (1999). [Google Scholar]
  33. A. Quarteroni, A Veneziani and P. Zunino, A domain decomposition method for advection-diffusion processes with application to blood solutes. SIAM J. Sci. Comput. 23 (2002) 1959–1980. [CrossRef] [MathSciNet] [Google Scholar]
  34. Y. Saad, Iterative methods for sparse linear systems. Second edition, SIAM (2003). [Google Scholar]
  35. R. Schinzinger and P.A.A. Laura, Conformal Mapping: Methods and Applications. Amsterdam: Elsevier Science Publishers (1991). [Google Scholar]
  36. A. Toselli and O.B. Widlund, Domain decomposition methods–algorithms and theory, Springer Series in Computational Mathematics 34. Springer-Verlag, Berlin (2005). [Google Scholar]
  37. H. Weyl, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung). Math. Ann. 71 (1912) 441–479. [CrossRef] [MathSciNet] [Google Scholar]

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