Free Access
Issue
ESAIM: M2AN
Volume 36, Number 5, September/October 2002
Special issue on Programming
Page(s) 747 - 771
DOI https://doi.org/10.1051/m2an:2002035
Published online 15 October 2002
  1. M.A. Akgun, J.H. Garcelon and R.T. Haftka, Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas. Int. J. Numer. Methods Engrg. 50 (2001) 1587-1606. [CrossRef] [Google Scholar]
  2. E. Allgower and K. Georg, Simplicial and continuation methods for approximating fixed-points and solutions to systems of equations. SIAM Rev. 22 (1980) 28-85. [CrossRef] [MathSciNet] [Google Scholar]
  3. B.O. Almroth, P. Stern and F.A. Brogan, Automatic choice of global shape functions in structural analysis. AIAA Journal 16 (1978) 525-528. [CrossRef] [Google Scholar]
  4. A. Barrett and G. Reddien, On the reduced basis method. Z. Angew. Math. Mech. 75 (1995) 543-549. [MathSciNet] [Google Scholar]
  5. T.F. Chan and W.L. Wan, Analysis of projection methods for solving linear systems with multiple right-hand sides. SIAM J. Sci. Comput. 18 (1997) 1698-1721. [CrossRef] [MathSciNet] [Google Scholar]
  6. A.G. Evans, J.W. Hutchinson, N.A. Fleck, M.F. Ashby and H.N.G. Wadley, The topological design of multifunctional cellular metals. Prog. Mater. Sci. 46 (2001) 309-327. [CrossRef] [Google Scholar]
  7. C. Farhat, L. Crivelli and F.X. Roux, Extending substructure based iterative solvers to multiple load and repeated analyses. Comput. Methods Appl. Mech. Engrg. 117 (1994) 195-209. [CrossRef] [Google Scholar]
  8. J.P. Fink and W.C. Rheinboldt, On the error behavior of the reduced basis technique for nonlinear finite element approximations. Z. Angew. Math. Mech. 63 (1983) 21-28. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Machiels, J. Peraire and A.T. Patera, A posteriori finite element output bounds for the incompressible Navier-Stokes equations; Application to a natural convection problem. J. Comput. Phys. 172 (2001) 401-425. [Google Scholar]
  10. Y. Maday, L. Machiels, A.T. Patera and D.V. Rovas, Blackbox reduced-basis output bound methods for shape optimization, in Proceedings 12th International Domain Decomposition Conference, Chiba, Japan (2000) 429-436. [Google Scholar]
  11. 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 Sér. I Math. 328 (1999) 823-828. [Google Scholar]
  12. Y. Maday, A.T. Patera and G. Turinici, Global a priori convergence theory for reduced-basis approximation of single-parameter symmetric coercive elliptic partial differential equations. C. R. Acad. Sci. Paris Sér. I Math. 335 (2002) 1-6. [Google Scholar]
  13. A.K. Noor and J.M. Peters, Reduced basis technique for nonlinear analysis of structures. AIAA Journal 18 (1980) 455-462. [CrossRef] [Google Scholar]
  14. A.T. Patera and E.M. Rønquist, A general output bound result: Application to discretization and iteration error estimation and control. Math. Models Methods Appl. Sci. 11 (2001) 685-712. [CrossRef] [MathSciNet] [Google Scholar]
  15. A.T. Patera and E.M. Rønquist, A general output bound result: Application to discretization and iteration error estimation and control. Math. Models Methods Appl. Sci. (2000). MIT FML Report 98-12-1. [Google Scholar]
  16. J.S. Peterson, The reduced basis method for incompressible viscous flow calculations. SIAM J. Sci. Stat. Comput. 10 (1989) 777-786. [CrossRef] [Google Scholar]
  17. T.A. Porsching, Estimation of the error in the reduced basis method solution of nonlinear equations. Math. Comp. 45 (1985) 487-496. [CrossRef] [MathSciNet] [Google Scholar]
  18. C. Prud'homme, A Framework for Reliable Real-Time Web-Based Distributed Simulations. MIT (to appear). [Google Scholar]
  19. 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 Engrg. 124 (2002) 70-80. [CrossRef] [Google Scholar]
  20. W.C. Rheinboldt, Numerical analysis of continuation methods for nonlinear structural problems. Comput. Structures 13 (1981) 103-113. [CrossRef] [MathSciNet] [Google Scholar]
  21. W.C. Rheinboldt, On the theory and error estimation of the reduced basis method for multi-parameter problems. Nonlinear Anal. 21 (1993) 849-858. [CrossRef] [MathSciNet] [Google Scholar]
  22. D. Rovas, Reduced-Basis Output Bound Methods for Partial Differential Equations. Ph.D. thesis, MIT (in progress). [Google Scholar]
  23. K. Veroy, Reduced Basis Methods Applied to Problems in Elasticity: Analysis and Applications. Ph.D. thesis, MIT (in progress). [Google Scholar]
  24. N. Wicks and J. W. Hutchinson, Optimal truss plates. Internat. J. Solids Structures 38 (2001) 5165-5183. [CrossRef] [Google Scholar]
  25. E.L. Yip, A note on the stability of solving a rank-p modification of a linear system by the Sherman-Morrison-Woodbury formula. SIAM J. Sci. Stat. Comput. 7 (1986) 507-513. [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