Free Access
Issue
ESAIM: M2AN
Volume 48, Number 1, January-February 2014
Page(s) 207 - 229
DOI https://doi.org/10.1051/m2an/2013097
Published online 10 January 2014
  1. Z. Bai and D. Skoogh, Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl. Numer. Math. 43 (2002) 9–44. [CrossRef] [MathSciNet] [Google Scholar]
  2. M.A. Bahayou, Sur le problème de Helmholtz. Rendiconti del Seminario matematico della Università e Politecnico di Torino (2007) 427–450. [Google Scholar]
  3. M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. Acad. Sci. Paris 339 (2004) 667–672. [Google Scholar]
  4. A. Björck and C.C. Paige, Loss and recapture of orthogonality in the modified Gram–Schmidt algorithm. SIAM J. Matrix Anal. Appl. 13 (1992) 176–190. [CrossRef] [MathSciNet] [Google Scholar]
  5. S. Boyaval, Mathematical modelling and numerical simulation in materials science. Ph.D. thesis, Université Paris-Est (2009). [Google Scholar]
  6. A. Buffa and R. Hiptmair, Regularized combined field integral equations. Numer. Math. 100 (2005) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  7. R.L. Burden and J.D. Faires, Numerical Analysis. PWS Publishing Company (1993). [Google Scholar]
  8. E. Cancès, V. Ehrlacher and T. Lelièvre, Convergence of a greedy algorithm for high-dimensional convex nonlinear problems. Math. Models Methods Appl. Sci. 21 (2011) 2433–2467. [Google Scholar]
  9. F. Casenave, Accurate a posteriori error evaluation in the reduced basis method. C. R. Math. Acad. Sci. Paris 350 (2012) 539–542. [CrossRef] [MathSciNet] [Google Scholar]
  10. F. Casenave, Ph.D. thesis, in preparation (2013). [Google Scholar]
  11. F. Casenave, M. Ghattassi and R. Joubaud, A multiscale problem in thermal science. ESAIM: Proceedings 38 (2012) 202–219. [CrossRef] [EDP Sciences] [Google Scholar]
  12. A. Chatterjee, An introduction to the proper orthogonal decomposition. Curr. Sci. 78 (2000) 808–817. [Google Scholar]
  13. Y. Chen, J.S. Hesthaven, Y. Maday, J. Rodriguez and X. Zhu, Certified reduced basis method for electromagnetic scattering and radar cross section estimation. Technical Report 2011-28, Scientific Computing Group, Brown University, Providence, RI, USA (2011). [Google Scholar]
  14. Y. Chen, J.S. Hesthaven, Y. Maday and J. Rodríguez, Improved successive constraint method based a posteriori error estimate for reduced basis approximation of 2D Maxwell’s problem. ESAIM: M2AN 43 (2009) 1099–1116. [CrossRef] [EDP Sciences] [Google Scholar]
  15. F. Chinesta, P. Ladeveze and C. Elías, A short review on model order reduction based on proper generalized decomposition. Arch. Comput. Methods Eng. 18 (2011) 395–404. [Google Scholar]
  16. A. Delnevo, I. Terrasse, Code ACTI3S harmonique : Justifications Mathématiques : Partie I. Technical report, EADS CCR (2001). [Google Scholar]
  17. A. Delnevo, I. Terrasse, Code ACTI3S, Justifications Mathématiques : Partie II, présence d’un écoulement uniforme. Technical report, EADS CCR (2002). [Google Scholar]
  18. A. Ern and J.L. Guermond, Theory and Practice of Finite Elements, in vol. 159 of Applied Mathematical Sciences. Springer (2004). [Google Scholar]
  19. M. Fares, J.S. Hesthaven, Y. Maday and B. Stamm, The reduced basis method for the electric field integral equation. J. Comput. Phys. 230 (2011) 5532–5555. [Google Scholar]
  20. L. Giraud and J. Langou, When modified Gram–Schmidt generates a well-conditioned set of vectors. IMA J. Numer. Anal. 22 (2002) 521–528. [CrossRef] [MathSciNet] [Google Scholar]
  21. D. Goldberg, What every computer scientist should know about floating point arithmetic. ACM Computing Surveys 23 (1991) 5–48. [Google Scholar]
  22. G.H. Golub and C.F. Van Loan, Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press (1996). [Google Scholar]
  23. R.J. Guyan, Reduction of stiffness and mass matrices. AIAA J. 3 (1965) 380. [CrossRef] [Google Scholar]
  24. R. Hiptmair, Coercive combined field integral equations. J. Numer. Math. 11 (2003) 115–134. [CrossRef] [MathSciNet] [Google Scholar]
  25. R. Hiptmair and P. Meury, Stable FEM-BEM Coupling for Helmholtz Transmission Problems. ETH, Seminar für Angewandte Mathematik (2005). [Google Scholar]
  26. G.C. Hsiao and W.L. Wendland, Boundary Element Methods: Foundation and Error Analysis. John Wiley & Sons, Ltd (2004). [Google Scholar]
  27. D.B.P. Huynh, G. Rozza, S. Sen and A.T. Patera, A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants. C. R. Math. Acad. Sci. Paris 345 (2007) 473–478. [Google Scholar]
  28. P. Langlois, S. Graillat and N. Louvet, Compensated Horner scheme. Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006). [Google Scholar]
  29. L. Machiels, Y. Maday, I.B. Oliveira, A.T. Patera and D.V. Rovas, Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. C. R. Math. Acad. Sci. Paris 331 (2000) 153–158. [Google Scholar]
  30. Y. Maday, N.C. Nguyen, A.T. Patera and S. Pau, A general multipurpose interpolation procedure: the magic points. Commun. Pure Appl. Anal. 8 (2008) 383–404. [Google Scholar]
  31. W.C.H. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press (2000). [Google Scholar]
  32. A. Nouy and O.P. Le Maître, Generalized spectral decomposition for stochastic nonlinear problems. J. Comput. Phys. 228 (2009) 202–235. [CrossRef] [Google Scholar]
  33. A.T. Patera, Private communication (2012). [Google Scholar]
  34. A.T. Patera and G. Rozza, Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations. MIT Pappalardo Graduate Monographs in Mechanical Engineering (2007). [Google Scholar]
  35. M. Paz, Dynamic condensation. AIAA J. 22 (1984) 724–727. [CrossRef] [Google Scholar]
  36. C. Prud’homme, D.V. Rovas, K. Veroy, L. Machiels, Y. Maday, A.T. Patera and G. Turinici, Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods. J. Fluids Eng. 124 (2002) 70–80. [Google Scholar]
  37. S.A. Sauter and C. Schwab, Boundary Element Methods. Springer Series in Computational Mathematics. Springer (2010). [Google Scholar]
  38. I.E. Shparlinski, Sparse polynomial approximation in finite fields. In Proceedings of the thirty-third annual ACM symposium on Theory of computing, STOC ’01. ACM, New York, USA (2001) 209–215. [Google Scholar]
  39. K. Veroy and A.T. Patera, Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. Int. J. Numer. Methods Fluids 47 (2005) 773–788. [CrossRef] [MathSciNet] [Google Scholar]
  40. K. Veroy, C. Prud’homme and A.T. Patera, Reduced-basis approximation of the viscous Burgers equation: rigorous a posteriori error bounds. C. R. Math. Acad. Sci. Paris 337 (2003) 619–624. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you