Free access
Issue
ESAIM: M2AN
Volume 36, Number 5, September/October 2002
Special issue on Programming
Page(s) 747 - 771
DOI http://dx.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]
  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]
  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]
  4. A. Barrett and G. Reddien, On the reduced basis method. Z. Angew. Math. Mech. 75 (1995) 543-549. [MathSciNet]
  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]
  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]
  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]
  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]
  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.
  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.
  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.
  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.
  13. A.K. Noor and J.M. Peters, Reduced basis technique for nonlinear analysis of structures. AIAA Journal 18 (1980) 455-462. [CrossRef]
  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]
  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.
  16. J.S. Peterson, The reduced basis method for incompressible viscous flow calculations. SIAM J. Sci. Stat. Comput. 10 (1989) 777-786. [CrossRef]
  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]
  18. C. Prud'homme, A Framework for Reliable Real-Time Web-Based Distributed Simulations. MIT (to appear).
  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]
  20. W.C. Rheinboldt, Numerical analysis of continuation methods for nonlinear structural problems. Comput. Structures 13 (1981) 103-113. [CrossRef] [MathSciNet]
  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]
  22. D. Rovas, Reduced-Basis Output Bound Methods for Partial Differential Equations. Ph.D. thesis, MIT (in progress).
  23. K. Veroy, Reduced Basis Methods Applied to Problems in Elasticity: Analysis and Applications. Ph.D. thesis, MIT (in progress).
  24. N. Wicks and J. W. Hutchinson, Optimal truss plates. Internat. J. Solids Structures 38 (2001) 5165-5183. [CrossRef]
  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]

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