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A reduced basis approach for rapid and reliable computation of structural linear elasticity problems using mixed interpolation of tensorial components element
F Lei, YL Ma, YC Bai and HB Yang Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227(5) 905 (2013) https://doi.org/10.1177/0954406212456794
A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data
Peng Chen, Alfio Quarteroni and Gianluigi Rozza SIAM Journal on Numerical Analysis 51(6) 3163 (2013) https://doi.org/10.1137/130905253
Wave Equation Simulation Using a Compressed Modeler
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
Certified Reduced Basis Methods for Parametrized Saddle Point Problems
Adaptive Hessian-Based Nonstationary Gaussian Process Response Surface Method for Probability Density Approximation with Application to Bayesian Solution of Large-Scale Inverse Problems
Tan Bui-Thanh, Omar Ghattas and David Higdon SIAM Journal on Scientific Computing 34(6) A2837 (2012) https://doi.org/10.1137/110851419
Constrained Optimization and Optimal Control for Partial Differential Equations
Thomas Franke, Ronald H. W. Hoppe, Christopher Linsenmann and Achim Wixforth Constrained Optimization and Optimal Control for Partial Differential Equations 75 (2012) https://doi.org/10.1007/978-3-0348-0133-1_5
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
Certified reduced basis model validation: A frequentistic uncertainty framework
Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis
Joris Degroote, Jan Vierendeels and Karen Willcox International Journal for Numerical Methods in Fluids 63(2) 207 (2010) https://doi.org/10.1002/fld.2089
POD‐Galerkin approximations in PDE‐constrained optimization
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
Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation
An efficient reduced‐order modeling approach for non‐linear parametrized partial differential equations
N. C. Nguyen and J. Peraire International Journal for Numerical Methods in Engineering 76(1) 27 (2008) https://doi.org/10.1002/nme.2309
Hessian‐based model reduction for large‐scale systems with initial‐condition inputs
O. Bashir, K. Willcox, O. Ghattas, B. van Bloemen Waanders and J. Hill International Journal for Numerical Methods in Engineering 73(6) 844 (2008) https://doi.org/10.1002/nme.2100
Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
G. Rozza, D. B. P. Huynh and A. T. Patera Archives of Computational Methods in Engineering 15(3) 1 (2007) https://doi.org/10.1007/BF03024948
A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations
Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
Max D. Gunzburger, Janet S. Peterson and John N. Shadid Computer Methods in Applied Mechanics and Engineering 196(4-6) 1030 (2007) https://doi.org/10.1016/j.cma.2006.08.004
Reduced basis approximation and a posteriori error estimation for stress intensity factors
D. B. P. Huynh and A. T. Patera International Journal for Numerical Methods in Engineering 72(10) 1219 (2007) https://doi.org/10.1002/nme.2090
Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
Martin A. Grepl, Yvon Maday, Ngoc C. Nguyen and Anthony T. Patera ESAIM: Mathematical Modelling and Numerical Analysis 41(3) 575 (2007) https://doi.org/10.1051/m2an:2007031
Reduced basis approximation and a posteriori error estimation for a Boltzmann model