Volume 47, Number 1, January-February 2013
|Page(s)||213 - 251|
|Published online||23 November 2012|
- H. Antil, M. Heinkenschloss, R.H.W. Hoppe and D.C. Sorensen, Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables. Comput. Visualization Sci. 13 (2010) 249–264. [CrossRef] [MathSciNet]
- H. Antil, M. Heinkenschloss and R.H.W. Hoppe, Domain decomposition and balanced truncation model reduction for shape optimization of the Stokes system. Optim. Methods Softw. 26 (2011) 643–669, doi: 10.1080/10556781003767904. [CrossRef]
- J.K. Bennighof and R.B. Lehoucq. An automated multilevel substructuring method for eigenspace computation in linear elastodynamics. SIAM J. Sci. Comput. 25 (2004) 2084–2106. [CrossRef] [MathSciNet]
- A. Bermúdez and F. Pena, Galerkin lumped parameter methods for transient problems. Int. J. Numer. Methods Eng. 87 (2011) 943–961, doi: 10.1002/nme.3140. [CrossRef]
- P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova and P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods. Technical Report, Aachen Institute for Advanced Study in Computational Engineering Science, preprint : AICES-2010/05-2 (2010).
- F. Bourquin, Component mode synthesis and eigenvalues of second order operators : discretization and algorithm. ESAIM : M2AN 26 (1992) 385–423.
- S.C. Brenner, The condition number of the Schur complement in domain decompostion. Numer. Math. 83 (1999) 187–203. [CrossRef] [MathSciNet]
- 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. To appear in ESAIM : M2AN (2010).
- Y. Chen, J.S. Hesthaven and Y. Maday, A Seamless Reduced Basis Element Methods for 2D Maxwell’s Problem : An Introduction, edited by J. Hesthaven and E.M. Rønquist, in Spectral and High Order Methods for Partial Differential Equations-Selected papers from the ICASOHOM’09 Conference 76 (2011).
- R. Craig and M. Bampton, Coupling of substructures for dynamic analyses. AIAA J. 6 (1968) 1313–1319. [CrossRef]
- J.L. Eftang, D.B.P. Huynh, D.J. Knezevic, E.M. Rønquist and A.T. Patera, Adaptive port reduction in static condensation, in MATHMOD 2012 – 7th Vienna International Conference on Mathematical Modelling (2012) (Submitted).
- M. Ganesh, J.S. Hesthaven and B. Stamm, A reduced basis method for multiple electromagnetic scattering in three dimensions. Technical Report 2011-9, Scientific Computing Group, Brown University, Providence, RI, USA (2011).
- G. Golub and C. van Loan, Matrix Computations. Johns Hopkins University Press (1996).
- B. Haggblad and L. Eriksson, Model reduction methods for dynamic analyses of large structures. Comput. Struct. 47 (1993) 735–749. [CrossRef]
- U.L. Hetmaniuk and R.B. Lehoucq, A special finite element method based on component mode synthesis. ESAIM : M2AN 44 (2010) 401–420. [CrossRef] [EDP Sciences]
- T.Y. Hou and X.-H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169–189. [CrossRef] [MathSciNet]
- W.C. Hurty, On the dynamic analysis of structural systems using component modes, in First AIAA Annual Meeting. Washington, DC, AIAA paper, No. 64-487 (1964).
- 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. 345 (2007) 473–478. [CrossRef] [MathSciNet]
- L. Iapichino, Quarteroni and G.A., Rozza, A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks. Comput. Methods Appl. Mech. Eng. 221-222 (2012) 63–82. [CrossRef]
- H. Jakobsson, F. Beingzon and M.G. Larson, Adaptive component mode synthesis in linear elasticity. Int. J. Numer. Methods Eng. 86 (2011) 829–844. [CrossRef]
- S. Kaulmann, M. Ohlberger and B. Haasdonk, A new local reduced basis discontinuous galerkin approach for heterogeneous multiscale problems. C. R. Math. 349 (2011) 1233–1238. [CrossRef] [MathSciNet]
- B.S. Kirk, J.W. Peterson, R.H. Stogner and G.F. Carey, libMesh : A C++ library for Parallel adaptive mesh refinement/coarsening simulations. Eng. Comput. 22 (2006) 237–254. [CrossRef]
- D.J. Knezevic and J.W. Peterson, A high-performance parallel implementation of the certified reduced basis method. Comput. Methods Appl. Mech. Eng. 200 (2011) 1455–1466. [CrossRef]
- Y Maday and EM Rønquist, The reduced basis element method : Application to a thermal fin problem. SIAM J. Sci. Comput. 26 (2004) 240–258. [CrossRef] [MathSciNet]
- Y. Maday, A.T. Patera and G. Turinici, A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. J. Sci. Comput. 17 (2002) 437–446. [CrossRef] [MathSciNet]
- N.C. Nguyen, A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales. J. Comput. Phys. 227 (2007) 9807–9822. [CrossRef]
- 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 Eng. 124 (2002) 70–80. [CrossRef]
- G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15 (2008) 229–275. [CrossRef] [MathSciNet]
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