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We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases.
The structure of inhomogeneous turbulent flows
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A linearized method for the frequency analysis of three-dimensional fluid/structure interaction problems in all flow regimes
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A reduced-basis element method
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Reliable real-time solution of parametrised partial differential equations: reduced basis output bound methods
C. Prud’homme, D.V. Rovas, K. Veroy, L. Machiels, Y. Maday, A.T. Patera, and G. Turicini · 2002
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Model reduction for compressible flow using POD and Galerkin projection
C.W. Rowley, T. Colonius, and R.M. Murray · 2004
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An "empirical interpolation" method: Application to efficient reduced-basis discretization of partial differential equations
M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera · 2004
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Certified real-time solution of the parametrized steady incompressible navier stokes equations: rigorous reduced-basis a posteriori error bounds
K. Veroy and A.T. Patera · 2005
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A priori hyperreduction: an adaptive approach
D. Ryckelynck · 2005
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Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition
K. Willcox · 2006
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Numerical optimization
Jorge Nocedal and S J Wright · 2006
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Parametric reduced-order models for probabilistic analysis of unsteady aerodynamic applications
T Bui-Thanh, K Willcox, and O Ghattas · 2008
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Interpolation method for adapting reduced-order models and application to aeroelasticity
D Amsallem and C Farhat · 2008
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Galerkin reduced order models for compressible flow with structural interaction
M.F. Barone, D.J. Segalman, and H.K. Thornquistand I. Kalashn ikova · 2008
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A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations
Robust Statistics
Peter J Huber and Elvezio M Ronchetti · 2011
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Efficient non-linear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations
K Carlberg, C Bou-Mosleh, and C Farhat · 2011
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Model reduction of parametrized evolution problems using the reduced basis method with adaptive time-partitioning
M Dihlmann, M Drohmann, and B Haasdonk · 2011
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A priori
A. Buffa, Y. Maday, A. T. Patera, C. Prud’homme, and G. Turinici · 2012
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Nonlinear model order reduction based on local reduced-order bases
D Amsallem, M J Zahr, and C Farhat · 2012
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The GNAT method for non linear model reduction: effective implementation and application to cpmputational fluid dynamics and turbulent flows
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L 1 L^{1} -approximation of stationnary Hamilton-Jacobi equations
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Stable galerkin reduced order models for linearized compressible gfows
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Toward real-time computational-fluid-dynamics-based aeroelastic computations using a database of reduced-order information
D Amsallem, J Cortial, and C Farhat · 2010
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Nonlinear model reduction via discrete empirical interpolation
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K. Carlberg, C. Farhat, J. Cortal, and D. Amsallem · 2013
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Locally adaptive greedy approximations for anisotropic parameter reduced basis spaces
Yvon Maday and Benjamin Stamm · 2013
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Online Greedy Reduced Basis Construction Using Dictionaries
S Kaulmann and B Haasdonk · 2013
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Design Optimization Using Hyper-Reduced-Order Models
D Amsallem, M J Zahr, Y Choi, and C Farhat · 2014
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Fast Local Reduced Basis Updates for the Efficient Reduction of Nonlinear Systems with Hyper-Reduction
D Amsallem, M J Zahr, and K Washabaugh · 2014
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An adaptive and efficient greedy procedure for the optimal training of parametric reduced-order models
A Paul-Dubois-Taine and D Amsallem · 2014
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