Free Access
Volume 47, Number 6, November-December 2013
Page(s) 1821 - 1843
Published online 07 October 2013
  1. D. Amsallem and C. Farhat, An online method for interpolating linear parametric reduced-order models. SIAM J. Sci. Comput. 33 (2011) 2169. [CrossRef] [Google Scholar]
  2. H.T. Banks, M.L. Joyner, B. Winchesky and W.P. Winfree, Nondestructive evaluation using a reduced-order computational methodology. Inverse Problems 16 (2000) 1–17. [CrossRef] [Google Scholar]
  3. G. Berkooz, P. Holmes and J.L. Lumley, The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1993) 539–575. [Google Scholar]
  4. A. Buffa, Y. Maday, A.T. Patera, C. Prud’homme and G. Turinici, A priori convergence of the greedy algorithm for the parametrized reduced basis method. ESAIM: M2AN 46 (2012) 595–603. [CrossRef] [EDP Sciences] [Google Scholar]
  5. R. Chabiniok, P. Moireau, P.-F. Lesault, A. Rahmouni, J.-F. Deux and D. Chapelle, Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model. Biomech. Model. Mechanobiol. 11 (2012) 609–630. [CrossRef] [PubMed] [Google Scholar]
  6. D. Chapelle and K.J. Bathe, The inf-sup test. Comput. Struct. 47 (1993) 537–545. [CrossRef] [Google Scholar]
  7. D. Chapelle, A. Gariah and J. Sainte-Marie, Galerkin approximation with Proper Orthogonal Decomposition: new error estimates and illustrative examples. ESAIM: M2AN 46 (2012) 731–757. [CrossRef] [EDP Sciences] [Google Scholar]
  8. D. Chapelle, P. Le Tallec, P. Moireau and M. Sorine, An energy-preserving muscle tissue model: formulation and compatible discretizations. J. Multiscale Comput. Engrg. 10 (2012) 189–211. [CrossRef] [Google Scholar]
  9. G. Chavent, Nonlinear Least Squares for Inverse Problems: Theoretical foundations and step-by-step guide for applications. Scientific Computation. Springer, New York (2009). [Google Scholar]
  10. P.G. Ciarlet and P.A. Raviart, General Lagrange and Hermite interpolation in R with applications to finite element methods. Arch. Rational Mech. Anal. 46 (1972) 177–199. [CrossRef] [MathSciNet] [Google Scholar]
  11. R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1 (1961) 445–466. [CrossRef] [PubMed] [Google Scholar]
  12. D. Galbally, K. Fidkowski, K. Willcox and O. Ghattas, Non-linear model reduction for uncertainty quantification in large-scale inverse problems. International J. Numer. Methods Engrg. 81 (2010) 1581—1608. [MathSciNet] [Google Scholar]
  13. B. Haasdonk, Convergence rates of the POD-greedy method. ESAIM: M2AN 47 (2012) 859–873. [Google Scholar]
  14. S. Julier, J. Uhlmann and H. Durrant-Whyte, A new method for the nonlinear transformation of means and covariances in filter and estimators. IEEE Trans. Automat. Contr. 45 (2000) 447–482. [Google Scholar]
  15. K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J. Numer. Anal. 40 (2002) 492–515. [Google Scholar]
  16. A. Manzoni, A. Quarteroni and G. Rozza, Shape optimization for viscous flows by reduced basis methods and free form deformation. Int. J. Numer. Methods in Fluids 70 (2012) 646–670. [Google Scholar]
  17. P. Moireau and D. Chapelle, Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems. ESAIM: COCV 17 (2011) 380–405. [CrossRef] [EDP Sciences] [Google Scholar]
  18. P. Moireau, D. Chapelle and P. Le Tallec, Joint state and parameter estimation for distributed mechanical systems. Comput. Methods Appl. Mechanics Engrg. 197 (2008) 659–677. [Google Scholar]
  19. P. Moireau, D. Chapelle and P. Le Tallec, Filtering for distributed mechanical systems using position measurements: Perspectives in medical imaging. Inverse Problems 25 (2009) 035010. [Google Scholar]
  20. J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon. Proc. of IRE 50 (1962) 2061–2070. [Google Scholar]
  21. D.-T. Pham, J. Verron and L. Gourdeau, Filtres de Kalman singuliers évolutifs pour l’assimilation de données en océanographie. C.R. l’Acad. Sci. – Series IIA 326 (1998) 255–260. [Google Scholar]
  22. 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 Engrg. 124 (2002) 70–80. [Google Scholar]
  23. J. Sainte-Marie, D. Chapelle, R. Cimrman and M. Sorine, Modeling and estimation of the cardiac electromechanical activity. Comput. Struct. 84 (2006) 1743–1759. [Google Scholar]
  24. D. Simon, Optimal State Estimation: Kalman, H, and Nonlinear Approaches. Wiley-Interscience (2006). [Google Scholar]
  25. S.A. Smolyak. Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR 4 (1963) 240–243. [Google Scholar]
  26. K. Veroy and A.T. Patera, Certified real-time solution of the parametrized steady incompressible navier-stokes equations. Internat. J. Numer. Methods Fluids 47 (2004) 773–788. [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