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Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations
Joan Baiges, Ramon Codina and Sergio Idelsohn International Journal for Numerical Methods in Fluids 72(12) 1219 (2013) https://doi.org/10.1002/fld.3777
Fast Evaluation of Time–Harmonic Maxwell's Equations Using the Reduced Basis Method
Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values
Alexandre Janon, Maëlle Nodet and Clémentine Prieur ESAIM: Mathematical Modelling and Numerical Analysis 47(2) 317 (2013) https://doi.org/10.1051/m2an/2012029
Efficient finite-element computation of far-fields of phased arrays by order reduction
Alexander Sommer, Oszkár Bíró, David A. Lowther and Piergiorgio Alotto, Ortwin Farle and Romanus Dyczij-Edlinger COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 32(5) 1721 (2013) https://doi.org/10.1108/COMPEL-04-2013-0120
Efficient surrogate construction by combining response surface methodology and reduced order modeling
The reduced basis method applied to transport equations of a lithium-ion battery
Stefan Volkwein, Prof. Oszkár Bíró, Prof. David A. Lowther and Andrea Wesche COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 32(5) 1760 (2013) https://doi.org/10.1108/COMPEL-04-2013-0115
Non-linear Petrov–Galerkin methods for reduced order modelling of the Navier–Stokes equations using a mixed finite element pair
Nonintrusive reduced‐order modeling of parametrized time‐dependent partial differential equations
Christophe Audouze, Florian De Vuyst and Prasanth B. Nair Numerical Methods for Partial Differential Equations 29(5) 1587 (2013) https://doi.org/10.1002/num.21768
Approximation of Parametric Derivatives by the Empirical Interpolation Method
Jens L. Eftang, Martin A. Grepl, Anthony T. Patera and Einar M. Rønquist Foundations of Computational Mathematics 13(5) 763 (2013) https://doi.org/10.1007/s10208-012-9125-9
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows
Reduced‐order modeling for cardiac electrophysiology. Application to parameter identification
M. Boulakia, E. Schenone and J‐F. Gerbeau International Journal for Numerical Methods in Biomedical Engineering 28(6-7) 727 (2012) https://doi.org/10.1002/cnm.2465
Jens L. Eftang and Benjamin Stamm International Journal for Numerical Methods in Engineering 90(4) 412 (2012) https://doi.org/10.1002/nme.3327
Certified reduced basis methods for parametrized parabolic partial differential equations with non-affine source terms
Dirk Klindworth, Martin A. Grepl and Georg Vossen Computer Methods in Applied Mechanics and Engineering 209-212 144 (2012) https://doi.org/10.1016/j.cma.2011.10.010
Shape optimization for viscous flows by reduced basis methods and free‐form deformation
Andrea Manzoni, Alfio Quarteroni and Gianluigi Rozza International Journal for Numerical Methods in Fluids 70(5) 646 (2012) https://doi.org/10.1002/fld.2712
Constrained Optimization and Optimal Control for Partial Differential Equations
Thomas Franke, Ronald H. W. Hoppe, Christopher Linsenmann and Achim Wixforth International Series of Numerical Mathematics, Constrained Optimization and Optimal Control for Partial Differential Equations 160 75 (2012) https://doi.org/10.1007/978-3-0348-0133-1_5
On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition
Toni Lassila, Andrea Manzoni and Gianluigi Rozza ESAIM: Mathematical Modelling and Numerical Analysis 46(6) 1555 (2012) https://doi.org/10.1051/m2an/2012016
Model order reduction of parametrized nonlinear reaction–diffusion systems
Certified reduced basis method for electromagnetic scattering and radar cross section estimation
Yanlai Chen, Jan S. Hesthaven, Yvon Maday, Jerónimo Rodríguez and Xueyu Zhu Computer Methods in Applied Mechanics and Engineering 233-236 92 (2012) https://doi.org/10.1016/j.cma.2012.04.013
Local–global multiscale model reduction for flows in high-contrast heterogeneous media
Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations
Kevin Carlberg, Charbel Bou‐Mosleh and Charbel Farhat International Journal for Numerical Methods in Engineering 86(2) 155 (2011) https://doi.org/10.1002/nme.3050
Spectral and High Order Methods for Partial Differential Equations
Yanlai Chen, Jan S. Hesthaven and Yvon Maday Lecture Notes in Computational Science and Engineering, Spectral and High Order Methods for Partial Differential Equations 76 141 (2011) https://doi.org/10.1007/978-3-642-15337-2_11
Kevin Carlberg, David Amsallem, Phil Avery, Matthew Zahr and Charbel Farhat (2011) https://doi.org/10.2514/6.2011-3112
Interpolatory Projection Methods for Parameterized Model Reduction
Ulrike Baur, Christopher Beattie, Peter Benner and Serkan Gugercin SIAM Journal on Scientific Computing 33(5) 2489 (2011) https://doi.org/10.1137/090776925
REDUCED BASIS APPROXIMATION AND A POSTERIORI ERROR ESTIMATION FOR THE PARAMETRIZED UNSTEADY BOUSSINESQ EQUATIONS
DAVID J. KNEZEVIC, NGOC-CUONG NGUYEN and ANTHONY T. PATERA Mathematical Models and Methods in Applied Sciences 21(07) 1415 (2011) https://doi.org/10.1142/S0218202511005441
Certified reduced basis approximation for parametrized partial differential equations and applications
An "$hp$" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations
Jens L. Eftang, Anthony T. Patera and Einar M. Rønquist SIAM Journal on Scientific Computing 32(6) 3170 (2010) https://doi.org/10.1137/090780122
Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
Yanlai Chen, Jan S. Hesthaven, Yvon Maday and Jerónimo Rodríguez SIAM Journal on Scientific Computing 32(2) 970 (2010) https://doi.org/10.1137/09075250X
Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems
D. Galbally, K. Fidkowski, K. Willcox and O. Ghattas International Journal for Numerical Methods in Engineering 81(12) 1581 (2010) https://doi.org/10.1002/nme.2746
A posteriori error bounds for the empirical interpolation method
A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient
Sébastien Boyaval, Claude Le Bris, Yvon Maday, Ngoc Cuong Nguyen and Anthony T. Patera Computer Methods in Applied Mechanics and Engineering 198(41-44) 3187 (2009) https://doi.org/10.1016/j.cma.2009.05.019
Improved successive constraint method baseda posteriorierror estimate for reduced basis approximation of 2D Maxwell's problem
Yanlai Chen, Jan S. Hesthaven, Yvon Maday and Jerónimo Rodríguez ESAIM: Mathematical Modelling and Numerical Analysis 43(6) 1099 (2009) https://doi.org/10.1051/m2an/2009037
Reliable Fast Frequency Sweep for Microwave Devices via the Reduced-Basis Method
A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations