Free Access
Volume 50, Number 6, November-December 2016
Page(s) 1857 - 1885
Published online 21 October 2016
  1. A. Ammar and F. Chinesta, Circumventing curse of dimensionality in the solution of highly multidimensional models encountered in quantum mechanics using meshfree finite sums decomposition. In Meshfree Methods for Partial Differential Equations IV, edited by M. Griebel and M. Schweitzer. Vol. 65 of Lect. Notes Comput. Sci. Eng. Springer, Berlin, Heidelberg (2008) 1–17. [Google Scholar]
  2. 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]
  3. R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. 10 (2001) 1–102. [CrossRef] [MathSciNet] [Google Scholar]
  4. L. Beirão da Veiga and M. Verani, A posteriori boundary control for FEM approximation of elliptic eigenvalue problems. Numer. Methods Partial Differential Equations 28 (2012) 369–388. [CrossRef] [MathSciNet] [Google Scholar]
  5. P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods. SIAM J. Math. Anal. 43 (2011) 1457–1472. [CrossRef] [MathSciNet] [Google Scholar]
  6. 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]
  7. E. Cancès, V. Ehrlacher and T. Lelièvre, Greedy algorithms for high-dimensional eigenvalue problems. Constructive Approximation 40 (2013) 387–423. [Google Scholar]
  8. A. Cohen and R. DeVore, Approximation of high-dimensional parametric PDEs. Acta Numerica, 1–159 (2015). [Google Scholar]
  9. L. Dedè, Reduced basis method and a posteriori error estimation for parametrized linear-quadratic optimal control problems. SIAM J. Sci. Comput. 32 (2010) 997–1019. [CrossRef] [Google Scholar]
  10. T. Dickopf, T. Horger and B. Wohlmuth, Simultaneous reduced basis approximation of parameterized eigenvalue problems. Preprint arXiv:1506.09200 (2015). [Google Scholar]
  11. D.C. Dobson and F. Santosa, Optimal localization of eigenfunctions in an inhomogeneous medium. SIAM J. Appl. Math. 64 (2004) 762–774. [CrossRef] [Google Scholar]
  12. L. Evans, Partial differential equations. Vol. 19 of Graduate Studies in Mathematics, 2nd edition. American Mathematical Society, Providence, RI (2010). [Google Scholar]
  13. M. Fares, J. Hesthaven, Y. Maday and B. Stamm, The reduced basis method for the electric field integral equation. J. Comp. Phys. 230 (2011) 5532–5555. [CrossRef] [Google Scholar]
  14. G.H. Golub and C.F. Van Loan, Matrix Computations, 4th edition. The John Hopkins University Press, Baltimore (2013). [Google Scholar]
  15. J.S. Hesthaven, G. Rozza and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations. Springer Briefs in Mathematics. Springer (2016). [Google Scholar]
  16. V. Heuveline and R. Rannacher, A posteriori error control for finite approximations of elliptic eigenvalue problems. Adv. Comput. Math. 15 (2001) 107–138. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Hintermüller, C.-Y. Kao and A. Laurain, Principal eigenvalue minimization for an elliptic problem with indefinite weight and Robin boundary conditions. Appl. Math. Optim. 65 (2012) 111–146. [CrossRef] [Google Scholar]
  18. D.B.P. Huynh, D.J. Knezevic and A.T. Patera. A static condensation reduced basis element method: approximation and a posteriori error estimation. ESAIM: M2AN 47 (2013) 213–251. [CrossRef] [EDP Sciences] [Google Scholar]
  19. T. Lassila and G. Rozza, Parametric free-form shape design with PDE models and reduced basis method. Comput. Meth. Appl. Mech. Engrg. 199 (2010) 1583–1592. [CrossRef] [Google Scholar]
  20. T. Lassila, A. Manzoni, A. Quarteroni and G. Rozza, Model order reduction in fluid dynamics: challenges and perspectives. In Reduced order methods for modeling and computational reduction, edited by A. Quarteroni and G. Rozza. Vol. 9. Springer, MS&A Series (2013) 235–274. [Google Scholar]
  21. L. Machiels, Y. Maday, I. Oliveira, A.T. Patera and D. Rovas, Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 153–158. [Google Scholar]
  22. Y. Maday, A.T. Patera and J. Peraire, A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem. C. R. Acad. Sci. Paris, Série I 327 (1998) 823–828. [CrossRef] [Google Scholar]
  23. A. Manzoni, An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows. ESAIM: M2AN 48 (2014) 1199–1226. [CrossRef] [EDP Sciences] [Google Scholar]
  24. A. Manzoni, A. Quarteroni and G. Rozza, Shape optimization of cardiovascular geometries by reduced basis methods and free-form deformation techniques. Int. J. Numer. Meth. Fluids 70 (2012) 646–670. [Google Scholar]
  25. A. Manzoni and F. Negri, Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs. Adv. Comput. Math. 41 (2015) 1255–1288. [CrossRef] [Google Scholar]
  26. J.A. Méndez-Bermùdez and F.M. Izrailev, Transverse localization in quasi-1d corrugated waveguides (2008) 1376–1378. [Google Scholar]
  27. J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson et Cie, Paris; Academia, Prague (1967). [Google Scholar]
  28. F. Negri, G. Rozza, A. Manzoni and A. Quarteroni, Reduced basis method for parametrized elliptic optimal control problems. SIAM J. Sci. Comput. 35 (2013) A2316–A2340. [Google Scholar]
  29. N.C. Nguyen, K. Veroy and A.T. Patera, Certified real-time solution of parametrized partial differential equations. In Handbook of Materials Modeling, edited by S. Yip (2005) 1523–1558. [Google Scholar]
  30. S.J. Osher and F. Santosa, Level set methods for optimization problems involving geometry and constraints i. frequencies of a two-density inhomogeneous drum. J. Comput. Phys. 171 (2001) 272–288. [CrossRef] [MathSciNet] [Google Scholar]
  31. G.S.H. Pau, Reduced Basis Method for Quantum Models of Crystalline Solids. Ph.D. thesis, Massachusetts Institute of Technology (2007). [Google Scholar]
  32. C. Prud’homme, D. Rovas, K. Veroy, Y. Maday, A.T. Patera and G. Turinici, Reliable real-time solution of parametrized partial differential equations: reduced-basis output bounds methods. J. Fluids. Engng. 124 (2002) 70–80. [Google Scholar]
  33. A. Quarteroni, G. Rozza and A. Manzoni, Certified reduced basis approximation for parametrized partial differential equations in industrial applications. J. Math. Ind. 1 (2011). [Google Scholar]
  34. A. Quarteroni, A. Manzoni and F. Negri, Reduced Basis Methods for Partial Differential Equations. An Introduction. Vol. 92 of Unitext Series. Springer (2016). [Google Scholar]
  35. D.V. Rovas, Reduced-Basis Output Bound Methods for Parametrized Partial Differential Equations. Ph.D. thesis, Massachusetts Institute of Technology (2003). [Google Scholar]
  36. G. Rozza, D.B.P. Huynh and A. Manzoni, Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants. Numer. Math. 125 (2013) 115–152. [CrossRef] [MathSciNet] [Google Scholar]
  37. B. Sapoval, O. Haeberlé and S. Russ. Acoustical properties of irregular and fractal cavities. Acoust. Soc. Am. J. 102 (1997) 2014–2019. [CrossRef] [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