EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 39 1 (2005) 157-181 Article references

Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

This article has been cited by the following article(s):

A space-time certified reduced basis method for quasilinear parabolic partial differential equations

Michael Hinze and Denis Korolev
Advances in Computational Mathematics 47 (3) (2021)
DOI: 10.1007/s10444-021-09860-z
See this article

Encyclopedia of Computational Mechanics Second Edition

Francisco Chinesta, Antonio Huerta, Gianluigi Rozza and Karen Willcox
Encyclopedia of Computational Mechanics Second Edition 1 (2017)
DOI: 10.1002/9781119176817.ecm2110
See this article

Multivariate predictions of local reduced-order-model errors and dimensions

Azam Moosavi, Răzvan Ştefănescu and Adrian Sandu
International Journal for Numerical Methods in Engineering 113 (3) 512 (2018)
DOI: 10.1002/nme.5624
See this article

A reduced-order stochastic finite element approach for design optimization under uncertainty

Kurt Maute, Gary Weickum and Mike Eldred
Structural Safety 31 (6) 450 (2009)
DOI: 10.1016/j.strusafe.2009.06.004
See this article

Adaptive training of local reduced bases for unsteady incompressible Navier-Stokes flows

Yuqi Wu and Ulrich Hetmaniuk
International Journal for Numerical Methods in Engineering 103 (3) 183 (2015)
DOI: 10.1002/nme.4883
See this article

Model Reduction of Parametrized Systems

Robert O’Connor and Martin Grepl
MS&A, Model Reduction of Parametrized Systems 17 121 (2017)
DOI: 10.1007/978-3-319-58786-8_8
See this article

The reduced‐order hybrid Monte Carlo sampling smoother

Ahmed Attia, Răzvan Ştefănescu and Adrian Sandu
International Journal for Numerical Methods in Fluids 83 (1) 28 (2017)
DOI: 10.1002/fld.4255
See this article

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Wenrui Hao, Jan Hesthaven, Guang Lin and Bin Zheng
Journal of Scientific Computing 82 (1) (2020)
DOI: 10.1007/s10915-020-01123-1
See this article

Reduced Order Methods for Modeling and Computational Reduction

Harbir Antil, Matthias Heinkenschloss and Danny C. Sorensen
Reduced Order Methods for Modeling and Computational Reduction 101 (2014)
DOI: 10.1007/978-3-319-02090-7_4
See this article

Reduced Order Methods for Modeling and Computational Reduction

Toni Lassila, Andrea Manzoni, Alfio Quarteroni and Gianluigi Rozza
Reduced Order Methods for Modeling and Computational Reduction 235 (2014)
DOI: 10.1007/978-3-319-02090-7_9
See this article

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)
DOI: 10.1137/130905253
See this article

An efficient goal-oriented sampling strategy using reduced basis method for parametrized elastodynamic problems

K. C. Hoang, P. Kerfriden, B. C. Khoo and S. P. A. Bordas
Numerical Methods for Partial Differential Equations 31 (2) 575 (2015)
DOI: 10.1002/num.21932
See this article

An adaptive and efficient greedy procedure for the optimal training of parametric reduced-order models

A. Paul-Dubois-Taine and D. Amsallem
International Journal for Numerical Methods in Engineering 102 (5) 1262 (2015)
DOI: 10.1002/nme.4759
See this article

Verifying Calculations - Forty Years On

Yvon Maday
SpringerBriefs in Applied Sciences and Technology, Verifying Calculations - Forty Years On 1 (2016)
DOI: 10.1007/978-3-319-20553-3_1
See this article

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Jan S. Hesthaven, Gianluigi Rozza and Benjamin Stamm
SpringerBriefs in Mathematics, Certified Reduced Basis Methods for Parametrized Partial Differential Equations 1 (2016)
DOI: 10.1007/978-3-319-22470-1_1
See this article

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Jan S. Hesthaven, Gianluigi Rozza and Benjamin Stamm
SpringerBriefs in Mathematics, Certified Reduced Basis Methods for Parametrized Partial Differential Equations 87 (2016)
DOI: 10.1007/978-3-319-22470-1_6
See this article

A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space

Bernard Haasdonk, Markus Dihlmann and Mario Ohlberger
Mathematical and Computer Modelling of Dynamical Systems 17 (4) 423 (2011)
DOI: 10.1080/13873954.2011.547674
See this article

PEBL-ROM: Projection-error based local reduced-order models

David Amsallem and Bernard Haasdonk
Advanced Modeling and Simulation in Engineering Sciences 3 (1) (2016)
DOI: 10.1186/s40323-016-0059-7
See this article

Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems

Peng Chen, Alfio Quarteroni and Gianluigi Rozza
Journal of Scientific Computing 59 (1) 187 (2014)
DOI: 10.1007/s10915-013-9764-2
See this article

A Dirichlet–Neumann reduced basis method for homogeneous domain decomposition problems

I. Maier and B. Haasdonk
Applied Numerical Mathematics 78 31 (2014)
DOI: 10.1016/j.apnum.2013.12.001
See this article

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

Kevin Carlberg, Ray Tuminaro and Paul Boggs
SIAM Journal on Scientific Computing 37 (2) B153 (2015)
DOI: 10.1137/140959602
See this article

The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows

Kevin Carlberg, Charbel Farhat, Julien Cortial and David Amsallem
Journal of Computational Physics 242 623 (2013)
DOI: 10.1016/j.jcp.2013.02.028
See this article

The localized reduced basis multiscale method for two-phase flows in porous media

S. Kaulmann, B. Flemisch, B. Haasdonk, K. -A. Lie and M. Ohlberger
International Journal for Numerical Methods in Engineering 102 (5) 1018 (2015)
DOI: 10.1002/nme.4773
See this article

A Two-Step Certified Reduced Basis Method

J. L. Eftang, D. B. P. Huynh, D. J. Knezevic and A. T. Patera
Journal of Scientific Computing 51 (1) 28 (2012)
DOI: 10.1007/s10915-011-9494-2
See this article

Double greedy algorithms: Reduced basis methods for transport dominated problems

Wolfgang Dahmen, Christian Plesken and Gerrit Welper
ESAIM: Mathematical Modelling and Numerical Analysis 48 (3) 623 (2014)
DOI: 10.1051/m2an/2013103
See this article

2D Burgers equation with large Reynolds number using POD/DEIM and calibration

Yuepeng Wang, Ionel M. Navon, Xinyue Wang and Yue Cheng
International Journal for Numerical Methods in Fluids 82 (12) 909 (2016)
DOI: 10.1002/fld.4249
See this article

A Certified Reduced Basis Method for the Fokker–Planck Equation of Dilute Polymeric Fluids: FENE Dumbbells in Extensional Flow

David J. Knezevic and Anthony T. Patera
SIAM Journal on Scientific Computing 32 (2) 793 (2010)
DOI: 10.1137/090759239
See this article

A Space-Time Petrov--Galerkin Certified Reduced Basis Method: Application to the Boussinesq Equations

Masayuki Yano
SIAM Journal on Scientific Computing 36 (1) A232 (2014)
DOI: 10.1137/120903300
See this article

Reduced Basis Method and Error Estimation for Parametrized Optimal Control Problems with Control Constraints

Luca Dedè
Journal of Scientific Computing 50 (2) 287 (2012)
DOI: 10.1007/s10915-011-9483-5
See this article

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)
DOI: 10.1016/j.cma.2011.10.010
See this article

Certified reduced basis model validation: A frequentistic uncertainty framework

D.B.P. Huynh, D.J. Knezevic and A.T. Patera
Computer Methods in Applied Mechanics and Engineering 201-204 13 (2012)
DOI: 10.1016/j.cma.2011.09.011
See this article

A posteriorierror estimators for linear reduced-order models using Krylov-based integrators

D. Amsallem and U. Hetmaniuk
International Journal for Numerical Methods in Engineering 102 (5) 1238 (2015)
DOI: 10.1002/nme.4753
See this article

Efficient reduced models anda posteriorierror estimation for parametrized dynamical systems by offline/online decomposition

Bernard Haasdonk and Mario Ohlberger
Mathematical and Computer Modelling of Dynamical Systems 17 (2) 145 (2011)
DOI: 10.1080/13873954.2010.514703
See this article

Proper orthogonal decomposition for optimality systems

Karl Kunisch and Stefan Volkwein
ESAIM: Mathematical Modelling and Numerical Analysis 42 (1) 1 (2008)
DOI: 10.1051/m2an:2007054
See this article

An Efficient Output Error Estimation for Model Order Reduction of Parametrized Evolution Equations

Yongjin Zhang, Lihong Feng, Suzhou Li and Peter Benner
SIAM Journal on Scientific Computing 37 (6) B910 (2015)
DOI: 10.1137/140998603
See this article

Comparison and combination of reduced-order modelling techniques in 3D parametrized heat transfer problems

Fabrizio Gelsomino and Gianluigi Rozza
Mathematical and Computer Modelling of Dynamical Systems 17 (4) 371 (2011)
DOI: 10.1080/13873954.2011.547672
See this article

Reduced Basis Method and A Posteriori Error Estimation for Parametrized Linear-Quadratic Optimal Control Problems

Luca Dedè
SIAM Journal on Scientific Computing 32 (2) 997 (2010)
DOI: 10.1137/090760453
See this article

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)
DOI: 10.1016/j.cma.2009.05.019
See this article

Reduced Basis Methods for Parameterized Partial Differential Equations with Stochastic Influences Using the Karhunen--Loève Expansion

Bernard Haasdonk, Karsten Urban and Bernhard Wieland
SIAM/ASA Journal on Uncertainty Quantification 1 (1) 79 (2013)
DOI: 10.1137/120876745
See this article

A high-performance parallel implementation of the certified reduced basis method

David J. Knezevic and John W. Peterson
Computer Methods in Applied Mechanics and Engineering 200 (13-16) 1455 (2011)
DOI: 10.1016/j.cma.2010.12.026
See this article

H2,α -norm optimal model reduction for optimal control problems subject to parabolic and hyperbolic evolution equations

G. Vossen
Optimal Control Applications and Methods 35 (5) 501 (2014)
DOI: 10.1002/oca.2084
See this article

A reduced-order model for groundwater flow equation with random hydraulic conductivity: Application to Monte Carlo methods

Damiano Pasetto, Mario Putti and William W-G. Yeh
Water Resources Research 49 (6) 3215 (2013)
DOI: 10.1002/wrcr.20136
See this article

Parametric free-form shape design with PDE models and reduced basis method

Toni Lassila and Gianluigi Rozza
Computer Methods in Applied Mechanics and Engineering 199 (23-24) 1583 (2010)
DOI: 10.1016/j.cma.2010.01.007
See this article

Large-Scale Inverse Problems and Quantification of Uncertainty

M. Frangos, Y. Marzouk, K. Willcox and B. van Bloemen Waanders
Large-Scale Inverse Problems and Quantification of Uncertainty 123 (2010)
DOI: 10.1002/9780470685853.ch7
See this article

Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system

Immanuel Martini, Gianluigi Rozza and Bernard Haasdonk
Advances in Computational Mathematics 41 (5) 1131 (2015)
DOI: 10.1007/s10444-014-9396-6
See this article

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)
DOI: 10.1016/j.cma.2006.08.004
See this article

Reduced Basis Methods for Pricing Options with the Black--Scholes and Heston Models

O. Burkovska, B. Haasdonk, J. Salomon and B. Wohlmuth
SIAM Journal on Financial Mathematics 6 (1) 685 (2015)
DOI: 10.1137/140981216
See this article

Reduced Basis Approaches in Time-Dependent Non-Coercive Settings for Modelling the Movement of Nuclear Reactor Control Rods

Alberto Sartori, Antonio Cammi, Lelio Luzzi and Gianluigi Rozza
Communications in Computational Physics 20 (1) 23 (2016)
DOI: 10.4208/cicp.120914.021115a
See this article

Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media

Saifon Chaturantabut and Danny C. Sorensen
Mathematical and Computer Modelling of Dynamical Systems 17 (4) 337 (2011)
DOI: 10.1080/13873954.2011.547660
See this article

Goal-Oriented Error Estimation for the Reduced Basis Method, with Application to Sensitivity Analysis

Alexandre Janon, Maëlle Nodet and Clémentine Prieur
Journal of Scientific Computing 68 (1) 21 (2016)
DOI: 10.1007/s10915-015-0127-z
See this article

A PosterioriError Estimation for Reduced Order Solutions of Parametrized Parabolic Optimal Control Problems

Mark Kärcher and Martin A. Grepl
ESAIM: Mathematical Modelling and Numerical Analysis 48 (6) 1615 (2014)
DOI: 10.1051/m2an/2014012
See this article

A new error bound for reduced basis approximation of parabolic partial differential equations

Karsten Urban and Anthony T. Patera
Comptes Rendus Mathematique 350 (3-4) 203 (2012)
DOI: 10.1016/j.crma.2012.01.026
See this article

Model order reduction of parametrized nonlinear reaction–diffusion systems

Martin A. Grepl
Computers & Chemical Engineering 43 33 (2012)
DOI: 10.1016/j.compchemeng.2012.03.013
See this article

“Natural norm” a posteriori error estimators for reduced basis approximations

S. Sen, K. Veroy, D.B.P. Huynh, et al.
Journal of Computational Physics 217 (1) 37 (2006)
DOI: 10.1016/j.jcp.2006.02.012
See this article

Rapid inverse parameter estimation using reduced-basis approximation with asymptotic error estimation

G.R. Liu, Khin Zaw and Y.Y. Wang
Computer Methods in Applied Mechanics and Engineering 197 (45-48) 3898 (2008)
DOI: 10.1016/j.cma.2008.03.012
See this article

Certified Reduced Basis Methods for Parametrized Saddle Point Problems

Anna-Lena Gerner and Karen Veroy
SIAM Journal on Scientific Computing 34 (5) A2812 (2012)
DOI: 10.1137/110854084
See this article

Rapid identification of elastic modulus of the interface tissue on dental implants surfaces using reduced-basis method and a neural network

Khin Zaw, G.R. Liu, B. Deng and K.B.C. Tan
Journal of Biomechanics 42 (5) 634 (2009)
DOI: 10.1016/j.jbiomech.2008.12.001
See this article

Local–global multiscale model reduction for flows in high-contrast heterogeneous media

Yalchin Efendiev, Juan Galvis and Eduardo Gildin
Journal of Computational Physics 231 (24) 8100 (2012)
DOI: 10.1016/j.jcp.2012.07.032
See this article

Large-Scale Inverse Problems and Quantification of Uncertainty

N. C. Nguyen, G. Rozza, D. B. P. Huynh and A. T. Patera
Large-Scale Inverse Problems and Quantification of Uncertainty 151 (2010)
DOI: 10.1002/9780470685853.ch8
See this article

Effiziente und gesicherte Modellreduktion für parametrisierte dynamische Systeme

Bernard Haasdonk
at - Automatisierungstechnik 58 (8) 468 (2010)
DOI: 10.1524/auto.2010.0861
See this article

Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space

T. Bui-Thanh, K. Willcox and O. Ghattas
SIAM Journal on Scientific Computing 30 (6) 3270 (2008)
DOI: 10.1137/070694855
See this article

Adaptive POD-based low-dimensional modeling supported by residual estimates

M.-L. Rapún, F. Terragni and J. M. Vega
International Journal for Numerical Methods in Engineering 104 (9) 844 (2015)
DOI: 10.1002/nme.4947
See this article

POD-based Monte Carlo approach for the solution of regional scale groundwater flow driven by randomly distributed recharge

Damiano Pasetto, Alberto Guadagnini and Mario Putti
Advances in Water Resources 34 (11) 1450 (2011)
DOI: 10.1016/j.advwatres.2011.07.003
See this article

Reduced basis methods with adaptive snapshot computations

Mazen Ali, Kristina Steih and Karsten Urban
Advances in Computational Mathematics 43 (2) 257 (2017)
DOI: 10.1007/s10444-016-9485-9
See this article

Reduced Basis Techniques for Stochastic Problems

S. Boyaval, C. Le Bris, T. Lelièvre, et al.
Archives of Computational Methods in Engineering 17 (4) 435 (2010)
DOI: 10.1007/s11831-010-9056-z
See this article

Reduced basis method for finite volume approximations of parametrized linear evolution equations

Bernard Haasdonk and Mario Ohlberger
ESAIM: Mathematical Modelling and Numerical Analysis 42 (2) 277 (2008)
DOI: 10.1051/m2an:2008001
See this article

A reduced-order model for Monte Carlo simulations of stochastic groundwater flow

Damiano Pasetto, Alberto Guadagnini and Mario Putti
Computational Geosciences 18 (2) 157 (2014)
DOI: 10.1007/s10596-013-9389-4
See this article

Implicit partitioning methods for unknown parameter sets

Bernhard Wieland
Advances in Computational Mathematics 41 (5) 1159 (2015)
DOI: 10.1007/s10444-015-9404-5
See this article

Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes

Filippo Salmoiraghi, Francesco Ballarin, Luca Heltai and Gianluigi Rozza
Advanced Modeling and Simulation in Engineering Sciences 3 (1) (2016)
DOI: 10.1186/s40323-016-0076-6
See this article

On the verification of model reduction methods based on the proper generalized decomposition

Pierre Ladevèze and Ludovic Chamoin
Computer Methods in Applied Mechanics and Engineering 200 (23-24) 2032 (2011)
DOI: 10.1016/j.cma.2011.02.019
See this article

Reduced basis approximation and a posteriori error estimation for a Boltzmann model

Anthony T. Patera and Einar M. Rønquist
Computer Methods in Applied Mechanics and Engineering 196 (29-30) 2925 (2007)
DOI: 10.1016/j.cma.2007.02.008
See this article

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)
DOI: 10.1051/m2an:2007031
See this article

Anhpcertified reduced basis method for parametrized parabolic partial differential equations

Jens L. Eftang, David J. Knezevic and Anthony T. Patera
Mathematical and Computer Modelling of Dynamical Systems 17 (4) 395 (2011)
DOI: 10.1080/13873954.2011.547670
See this article

Sampling Theory, a Renaissance

Wolfgang Dahmen
Applied and Numerical Harmonic Analysis, Sampling Theory, a Renaissance 403 (2015)
DOI: 10.1007/978-3-319-19749-4_11
See this article

Error modeling for surrogates of dynamical systems using machine learning

Sumeet Trehan, Kevin T. Carlberg and Louis J. Durlofsky
International Journal for Numerical Methods in Engineering 112 (12) 1801 (2017)
DOI: 10.1002/nme.5583
See this article

A reduced order model-based preconditioner for the efficient solution of transient diffusion equations

Damiano Pasetto, Massimiliano Ferronato and Mario Putti
International Journal for Numerical Methods in Engineering 109 (8) 1159 (2017)
DOI: 10.1002/nme.5320
See this article

Approximate optimal projection for reduced-order models

Assad A. Oberai and Jayanth Jagalur-Mohan
International Journal for Numerical Methods in Engineering 105 (1) 63 (2016)
DOI: 10.1002/nme.4963
See this article

Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems

Lihong Feng, Athanasios C. Antoulas and Peter Benner
ESAIM: Mathematical Modelling and Numerical Analysis 51 (6) 2127 (2017)
DOI: 10.1051/m2an/2017014
See this article

Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations

Răzvan Ştefănescu, Adrian Sandu and Ionel M. Navon
International Journal for Numerical Methods in Fluids 76 (8) 497 (2014)
DOI: 10.1002/fld.3946
See this article

Mathematical and numerical results on the parametric sensitivity of a ROM-POD of the Burgers equation

N. Akkari, A. Hamdouni and M. Jazar
European Journal of Computational Mechanics 23 (1-2) 78 (2014)
DOI: 10.1080/17797179.2014.912410
See this article

The ROMES Method for Statistical Modeling of Reduced-Order-Model Error

Martin Drohmann and Kevin Carlberg
SIAM/ASA Journal on Uncertainty Quantification 3 (1) 116 (2015)
DOI: 10.1137/140969841
See this article

Effects of transient processes for thermal simulations of the Central European Basin

Denise Degen and Mauro Cacace
Geoscientific Model Development 14 (3) 1699 (2021)
DOI: 10.5194/gmd-14-1699-2021
See this article

Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems

Markus A. Dihlmann and Bernard Haasdonk
Computational Optimization and Applications 60 (3) 753 (2015)
DOI: 10.1007/s10589-014-9697-1
See this article

Parametric Reduced Order Models Using Adaptive Sampling and Interpolation

Jeff Borggaard, Kevin R. Pond and Lizette Zietsman
IFAC Proceedings Volumes 47 (3) 7773 (2014)
DOI: 10.3182/20140824-6-ZA-1003.02664
See this article

Space-Time Reduced Basis Methods for Time-Periodic Partial Differential Equations

Kristina Steih and Karsten Urban
IFAC Proceedings Volumes 45 (2) 710 (2012)
DOI: 10.3182/20120215-3-AT-3016.00126
See this article

Reduced Basis A Posteriori Error Bounds for the Instationary Stokes Equations: A Penalty Approach

Anna-Lena Gerner and Karen Veroy
IFAC Proceedings Volumes 45 (2) 700 (2012)
DOI: 10.3182/20120215-3-AT-3016.00124
See this article

A reduced basis approach for the parametric low frequency response of submerged viscoelastic structures

C. Leblond and J.-F. Sigrist
Finite Elements in Analysis and Design 119 15 (2016)
DOI: 10.1016/j.finel.2016.05.002
See this article

A two-level parameterized Model-Order Reduction approach for time-domain elastodynamics

Mohamed Aziz Bhouri and Anthony T. Patera
Computer Methods in Applied Mechanics and Engineering 385 114004 (2021)
DOI: 10.1016/j.cma.2021.114004
See this article

A priorierror estimates for reduced order models in finance

Ekkehard W. Sachs and Matthias Schu
ESAIM: Mathematical Modelling and Numerical Analysis 47 (2) 449 (2013)
DOI: 10.1051/m2an/2012039
See this article

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)
DOI: 10.1051/m2an/2012029
See this article

A Component-Based Parametric Reduced-Order Modeling Method Combined with Substructural Matrix Interpolation and Automatic Sampling

Ying Liu, Hongguang Li, Yun Li and Huanyu Du
Shock and Vibration 2019 1 (2019)
DOI: 10.1155/2019/6407437
See this article

Global sensitivity analysis for the boundary control of an open channel

Alexandre Janon, Maëlle Nodet, Christophe Prieur and Clémentine Prieur
Mathematics of Control, Signals, and Systems 28 (1) (2016)
DOI: 10.1007/s00498-015-0151-4
See this article

A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains

Yanlai Chen, Sigal Gottlieb, Alfa Heryudono and Akil Narayan
Journal of Scientific Computing 66 (1) 67 (2016)
DOI: 10.1007/s10915-015-0013-8
See this article

Adaptive parametric sampling scheme for nonlinear model order reduction

Danish Rafiq and Mohammad Abid Bazaz
Nonlinear Dynamics 107 (1) 813 (2022)
DOI: 10.1007/s11071-021-07025-7
See this article

A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations

N.C. Nguyen
Journal of Computational Physics 227 (2) 983 (2007)
DOI: 10.1016/j.jcp.2007.08.031
See this article

Wave Equation Simulation Using a Compressed Modeler

Victor Pereyra
American Journal of Computational Mathematics 03 (03) 231 (2013)
DOI: 10.4236/ajcm.2013.33033
See this article

Stabilized reduced basis method for parametrized advection–diffusion PDEs

Paolo Pacciarini and Gianluigi Rozza
Computer Methods in Applied Mechanics and Engineering 274 1 (2014)
DOI: 10.1016/j.cma.2014.02.005
See this article

Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods

Jan S. Hesthaven, Benjamin Stamm and Shun Zhang
ESAIM: Mathematical Modelling and Numerical Analysis 48 (1) 259 (2014)
DOI: 10.1051/m2an/2013100
See this article

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

Francesco Rizzi, Eric J. Parish, Patrick J. Blonigan and John Tencer
Computer Methods in Applied Mechanics and Engineering 384 113973 (2021)
DOI: 10.1016/j.cma.2021.113973
See this article

An empirical interpolation approach to reduced basis approximations for variational inequalities

E. Bader, Z. Zhang and K. Veroy
Mathematical and Computer Modelling of Dynamical Systems 22 (4) 345 (2016)
DOI: 10.1080/13873954.2016.1198388
See this article

IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018

Efthymios N. Karatzas, Giovanni Stabile, Nabil Atallah, Guglielmo Scovazzi and Gianluigi Rozza
IUTAM Bookseries, IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 36 111 (2020)
DOI: 10.1007/978-3-030-21013-7_8
See this article

POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation

R. Ştefănescu, A. Sandu and I.M. Navon
Journal of Computational Physics 295 569 (2015)
DOI: 10.1016/j.jcp.2015.04.030
See this article

Parametric Reduced-Order Models for Probabilistic Analysis of Unsteady Aerodynamic Applications

T. Bui-Thanh, K. Willcox and O. Ghattas
AIAA Journal 46 (10) 2520 (2008)
DOI: 10.2514/1.35850
See this article

A review on design of experiments and surrogate models in aircraft real-time and many-query aerodynamic analyses

Raul Yondo, Esther Andrés and Eusebio Valero
Progress in Aerospace Sciences 96 23 (2018)
DOI: 10.1016/j.paerosci.2017.11.003
See this article

A two-step model order reduction method to simulate a compressible flow over an extended rough surface

G. Deolmi and S. Müller
Mathematics and Computers in Simulation 150 49 (2018)
DOI: 10.1016/j.matcom.2018.02.008
See this article

A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

Sebastian Peitz and Michael Dellnitz
Mathematical and Computational Applications 23 (2) 30 (2018)
DOI: 10.3390/mca23020030
See this article

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)
DOI: 10.1142/S0218202511005441
See this article

An improved error bound for reduced basis approximation of linear parabolic problems

Karsten Urban and Anthony Patera
Mathematics of Computation 83 (288) 1599 (2013)
DOI: 10.1090/S0025-5718-2013-02782-2
See this article

CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

MARTIN A. GREPL
Mathematical Models and Methods in Applied Sciences 22 (03) 1150015 (2012)
DOI: 10.1142/S0218202511500151
See this article

Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models

Immanuel Martini, Bernard Haasdonk and Gianluigi Rozza
Journal of Scientific Computing (2017)
DOI: 10.1007/s10915-017-0430-y
See this article

A space-time hp-interpolation-based certified reduced basis method for Burgers' equation

Masayuki Yano, Anthony T. Patera and Karsten Urban
Mathematical Models and Methods in Applied Sciences 24 (09) 1903 (2014)
DOI: 10.1142/S0218202514500110
See this article

A certified reduced basis method for parametrized elliptic optimal control problems

Mark Kärcher and Martin A. Grepl
ESAIM: Control, Optimisation and Calculus of Variations 20 (2) 416 (2014)
DOI: 10.1051/cocv/2013069
See this article

Accelerating optimization and uncertainty quantification of nonlinear SMB chromatography using reduced-order models

Yongjin Zhang, Lihong Feng, Andreas Seidel-Morgenstern and Peter Benner
Computers & Chemical Engineering 96 237 (2017)
DOI: 10.1016/j.compchemeng.2016.09.017
See this article

Physically based modeling in catchment hydrology at 50: Survey and outlook

Claudio Paniconi and Mario Putti
Water Resources Research 51 (9) 7090 (2015)
DOI: 10.1002/2015WR017780
See this article

Learning physics-based models from data: perspectives from inverse problems and model reduction

Omar Ghattas and Karen Willcox
Acta Numerica 30 445 (2021)
DOI: 10.1017/S0962492921000064
See this article

Model reduction using L 1 -norm minimization as an application to nonlinear hyperbolic problems

R. Abgrall and R. Crisovan
International Journal for Numerical Methods in Fluids 87 (12) 628 (2018)
DOI: 10.1002/fld.4507
See this article

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Peng Chen and Alfio Quarteroni
Computer Methods in Applied Mechanics and Engineering 267 233 (2013)
DOI: 10.1016/j.cma.2013.08.016
See this article

Reduced-order modelling for linear heat conduction with parametrised moving heat sources

Benjamin Brands, Julia Mergheim and Paul Steinmann
GAMM-Mitteilungen 39 (2) 170 (2016)
DOI: 10.1002/gamm.201610011
See this article

Efficient approximation of Sparse Jacobians for time-implicit reduced order models

Răzvan Ştefănescu and Adrian Sandu
International Journal for Numerical Methods in Fluids 83 (2) 175 (2017)
DOI: 10.1002/fld.4260
See this article

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Peter Benner, Serkan Gugercin and Karen Willcox
SIAM Review 57 (4) 483 (2015)
DOI: 10.1137/130932715
See this article

Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation

Martin Drohmann, Bernard Haasdonk and Mario Ohlberger
SIAM Journal on Scientific Computing 34 (2) A937 (2012)
DOI: 10.1137/10081157X
See this article

A Reduced Basis Model with Parametric Coupling for Fluid-Structure Interaction Problems

Toni Lassila, Alfio Quarteroni and Gianluigi Rozza
SIAM Journal on Scientific Computing 34 (2) A1187 (2012)
DOI: 10.1137/110819950
See this article

A Goal-Oriented Reduced Basis Methods-Accelerated Generalized Polynomial Chaos Algorithm

Jiahua Jiang, Yanlai Chen and Akil Narayan
SIAM/ASA Journal on Uncertainty Quantification 4 (1) 1398 (2016)
DOI: 10.1137/16M1055736
See this article

A proper-orthogonal-decomposition–based model for the wall layer of a turbulent channel flow

Bérengère Podvin
Physics of Fluids 21 (1) 015111 (2009)
DOI: 10.1063/1.3068759
See this article

A Reduced Basis Method for Parametrized Variational Inequalities

B. Haasdonk, J. Salomon and B. Wohlmuth
SIAM Journal on Numerical Analysis 50 (5) 2656 (2012)
DOI: 10.1137/110835372
See this article

Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems

Paul G. Constantine and Qiqi Wang
SIAM Journal on Scientific Computing 34 (4) A2118 (2012)
DOI: 10.1137/100816717
See this article

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)
DOI: 10.1137/110851419
See this article

A reduced basis Kalman filter for parametrized partial differential equations

Markus Dihlmann and Bernard Haasdonk
ESAIM: Control, Optimisation and Calculus of Variations 22 (3) 625 (2016)
DOI: 10.1051/cocv/2015019
See this article

Lyapunov-Based Error Bounds for the Reduced-Basis Method

Robert O’Connor
IFAC-PapersOnLine 49 (8) 1 (2016)
DOI: 10.1016/j.ifacol.2016.07.409
See this article

Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation

Mark Kärcher, Sébastien Boyaval, Martin A. Grepl and Karen Veroy
Optimization and Engineering 19 (3) 663 (2018)
DOI: 10.1007/s11081-018-9389-2
See this article

Recent Advances in Computational Engineering

Christopher Spannring, Sebastian Ullmann and Jens Lang
Lecture Notes in Computational Science and Engineering, Recent Advances in Computational Engineering 124 145 (2018)
DOI: 10.1007/978-3-319-93891-2_9
See this article

Adaptive non-intrusive reduced order modeling for compressible flows

Jian Yu, Chao Yan, Zhenhua Jiang, Wu Yuan and Shusheng Chen
Journal of Computational Physics 397 108855 (2019)
DOI: 10.1016/j.jcp.2019.07.053
See this article

Parameter estimation with model order reduction for elliptic differential equations

Axel Ariaan Lukassen and Martin Kiehl
Inverse Problems in Science and Engineering 26 (4) 479 (2018)
DOI: 10.1080/17415977.2017.1318873
See this article

Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method

K.C. Hoang, B.C. Khoo, G.R. Liu, N.C. Nguyen and A.T. Patera
Inverse Problems in Science and Engineering 21 (8) 1310 (2013)
DOI: 10.1080/17415977.2012.757315
See this article

A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods

Alberto Sartori, Antonio Cammi, Lelio Luzzi and Gianluigi Rozza
Journal of Nuclear Engineering and Radiation Science 2 (2) 021019 (2016)
DOI: 10.1115/1.4031945
See this article

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference

Benjamin Peherstorfer
SIAM Journal on Scientific Computing 42 (5) A3489 (2020)
DOI: 10.1137/19M1292448
See this article

Numerical Methods for PDEs

Dinh Bao Phuong Huynh, Federico Pichi and Gianluigi Rozza
SEMA SIMAI Springer Series, Numerical Methods for PDEs 15 203 (2018)
DOI: 10.1007/978-3-319-94676-4_8
See this article

Reduced order modeling of random linear dynamical systems based on a new a posteriori error bound

Md. Nurtaj Hossain and Debraj Ghosh
International Journal for Numerical Methods in Engineering 116 (12-13) 741 (2018)
DOI: 10.1002/nme.5942
See this article

Gradient-based constrained optimization using a database of linear reduced-order models

Youngsoo Choi, Gabriele Boncoraglio, Spenser Anderson, David Amsallem and Charbel Farhat
Journal of Computational Physics 423 109787 (2020)
DOI: 10.1016/j.jcp.2020.109787
See this article

Accelerated Solution of Discrete Ordinates Approximation to the Boltzmann Transport Equation for a Gray Absorbing–Emitting Medium Via Model Reduction

John Tencer, Kevin Carlberg, Marvin Larsen and Roy Hogan
Journal of Heat Transfer 139 (12) 122701 (2017)
DOI: 10.1115/1.4037098
See this article

Adaptive basis construction and improved error estimation for parametric nonlinear dynamical systems

Sridhar Chellappa, Lihong Feng and Peter Benner
International Journal for Numerical Methods in Engineering 121 (23) 5320 (2020)
DOI: 10.1002/nme.6462
See this article

A mathematical and numerical study of the sensitivity of a reduced order model by POD (ROM–POD), for a 2D incompressible fluid flow

N. Akkari, A. Hamdouni, E. Liberge and M. Jazar
Journal of Computational and Applied Mathematics 270 522 (2014)
DOI: 10.1016/j.cam.2013.11.025
See this article

Reduced Basis Methods for Uncertainty Quantification

Peng Chen, Alfio Quarteroni and Gianluigi Rozza
SIAM/ASA Journal on Uncertainty Quantification 5 (1) 813 (2017)
DOI: 10.1137/151004550
See this article

Projection-Based Model Order Reduction Methods for the Estimation of Vector-Valued Variables of Interest

Olivier Zahm, Marie Billaud-Friess and Anthony Nouy
SIAM Journal on Scientific Computing 39 (4) A1647 (2017)
DOI: 10.1137/16M106385X
See this article

Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems

Marie Billaud-Friess and Anthony Nouy
SIAM Journal on Scientific Computing 39 (4) A1766 (2017)
DOI: 10.1137/16M1071493
See this article

A Certified Trust Region Reduced Basis Approach to PDE-Constrained Optimization

Elizabeth Qian, Martin Grepl, Karen Veroy and Karen Willcox
SIAM Journal on Scientific Computing 39 (5) S434 (2017)
DOI: 10.1137/16M1081981
See this article

A nonintrusive reduced order modelling approach using Proper Orthogonal Decomposition and locally adaptive sparse grids

Fahad Alsayyari, Zoltán Perkó, Danny Lathouwers and Jan Leen Kloosterman
Journal of Computational Physics 399 108912 (2019)
DOI: 10.1016/j.jcp.2019.108912
See this article

Reduced basis approximation anda 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)
DOI: 10.1002/nme.2090
See this article

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)
DOI: 10.1002/nme.2100
See this article

Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations

Brian A. Freno and Kevin T. Carlberg
Computer Methods in Applied Mechanics and Engineering 348 250 (2019)
DOI: 10.1016/j.cma.2019.01.024
See this article

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)
DOI: 10.1002/nme.2309
See this article

Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems

Kuan Lu, Yulin Jin, Yushu Chen, et al.
Mechanical Systems and Signal Processing 123 264 (2019)
DOI: 10.1016/j.ymssp.2019.01.018
See this article

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) 229 (2008)
DOI: 10.1007/s11831-008-9019-9
See this article

A multi-point reduced-order modeling approach of transient structural dynamics with application to robust design optimization

G. Weickum, M. S. Eldred and K. Maute
Structural and Multidisciplinary Optimization 38 (6) 599 (2009)
DOI: 10.1007/s00158-008-0309-5
See this article

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)
DOI: 10.1007/BF03024948
See this article

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 n/a (2009)
DOI: 10.1002/fld.2089
See this article

Reduced basis approximation and a posteriori error estimation for the time-dependent viscous Burgers’ equation

Ngoc-Cuong Nguyen, Gianluigi Rozza and Anthony T. Patera
Calcolo 46 (3) 157 (2009)
DOI: 10.1007/s10092-009-0005-x
See this article

Experimental design for estimating unknown hydraulic conductivity in an aquifer using a genetic algorithm and reduced order model

Timothy T. Ushijima and William W-G. Yeh
Advances in Water Resources 86 193 (2015)
DOI: 10.1016/j.advwatres.2015.09.029
See this article

POD-Galerkin approximations in PDE-constrained optimization

Ekkehard W. Sachs and Stefan Volkwein
GAMM-Mitteilungen 33 (2) 194 (2010)
DOI: 10.1002/gamm.201010015
See this article

Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods

Benjamin Brands, Denis Davydov, Julia Mergheim and Paul Steinmann
Mathematical and Computational Applications 24 (1) 20 (2019)
DOI: 10.3390/mca24010020
See this article

Handbook of Materials Modeling

Nguyen Ngoc Cuong, Karen Veroy and Anthony T. Patera
Handbook of Materials Modeling 1529 (2005)
DOI: 10.1007/978-1-4020-3286-8_76
See this article

Real-time solution of linear computational problems using databases of parametric reduced-order models with arbitrary underlying meshes

David Amsallem, Radek Tezaur and Charbel Farhat
Journal of Computational Physics 326 373 (2016)
DOI: 10.1016/j.jcp.2016.08.025
See this article

Reduced-order controllers for control of flow past an airfoil

S. S. Ravindran
International Journal for Numerical Methods in Fluids 50 (5) 531 (2006)
DOI: 10.1002/fld.1053
See this article

Reduced Collocation Method for Time-Dependent Parametrized Partial Differential Equations

Rezvan Ghaffari and Farideh Ghoreishi
Bulletin of the Iranian Mathematical Society 45 (5) 1487 (2019)
DOI: 10.1007/s41980-019-00210-w
See this article

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)
DOI: 10.1108/COMPEL-04-2013-0115
See this article

Spectral and High Order Methods for Partial Differential Equations

Jens L. Eftang, Anthony T. Patera and Einar M. Rønquist
Lecture Notes in Computational Science and Engineering, Spectral and High Order Methods for Partial Differential Equations 76 179 (2011)
DOI: 10.1007/978-3-642-15337-2_15
See this article

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)
DOI: 10.1007/978-3-0348-0133-1_5
See this article

Sparse Grids and Applications

Benjamin Peherstorfer, Stefan Zimmer and Hans-Joachim Bungartz
Lecture Notes in Computational Science and Engineering, Sparse Grids and Applications 88 223 (2012)
DOI: 10.1007/978-3-642-31703-3_11
See this article

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

F. Vidal-Codina, N.C. Nguyen, M.B. Giles and J. Peraire
Journal of Computational Physics 297 700 (2015)
DOI: 10.1016/j.jcp.2015.05.041
See this article

An adaptive sampling procedure for parametric model order reduction by matrix interpolation

Ying Liu, Hongguang Li, Huanyu Du, Ningke Tong and Guang Meng
Journal of Low Frequency Noise, Vibration and Active Control 39 (4) 821 (2020)
DOI: 10.1177/1461348419851595
See this article

A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems

Ludovic Chamoin, Florent Pled, Pierre-Eric Allier and Pierre Ladevèze
Computer Methods in Applied Mechanics and Engineering 327 118 (2017)
DOI: 10.1016/j.cma.2017.08.047
See this article

Numerical Simulation-based Design

Xu Han and Jie Liu
Numerical Simulation-based Design 89 (2020)
DOI: 10.1007/978-981-10-3090-1_5
See this article

Certified reduced basis method in geosciences

Denise Degen, Karen Veroy and Florian Wellmann
Computational Geosciences 24 (1) 241 (2020)
DOI: 10.1007/s10596-019-09916-6
See this article

On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition

Birgul Koc, Samuele Rubino, Michael Schneier, John Singler and Traian Iliescu
SIAM Journal on Numerical Analysis 59 (4) 2163 (2021)
DOI: 10.1137/20M1371798
See this article

Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM

Vasileios Tsiolakis, Matteo Giacomini, Ruben Sevilla, Carsten Othmer and Antonio Huerta
Computer Physics Communications 249 107013 (2020)
DOI: 10.1016/j.cpc.2019.107013
See this article

Certified reduced basis approximation for parametrized partial differential equations and applications

Alfio Quarteroni, Gianluigi Rozza and Andrea Manzoni
Journal of Mathematics in Industry 1 (1) (2011)
DOI: 10.1186/2190-5983-1-3
See this article

Efficient geometrical parametrization for finite‐volume‐based reduced order methods

Giovanni Stabile, Matteo Zancanaro and Gianluigi Rozza
International Journal for Numerical Methods in Engineering 121 (12) 2655 (2020)
DOI: 10.1002/nme.6324
See this article

Reduced basis approximation of large scale parametric algebraic Riccati equations

Andreas Schmidt and Bernard Haasdonk
ESAIM: Control, Optimisation and Calculus of Variations 24 (1) 129 (2018)
DOI: 10.1051/cocv/2017011
See this article

A posteriori global error estimator based on the error in the constitutive relation for reduced basis approximation of parametrized linear elastic problems

L. Gallimard and D. Ryckelynck
Applied Mathematical Modelling 40 (7-8) 4271 (2016)
DOI: 10.1016/j.apm.2015.11.016
See this article

A Reduced Order Model for a Stable Embedded Boundary Parametrized Cahn–Hilliard Phase-Field System Based on Cut Finite Elements

Efthymios N. Karatzas and Gianluigi Rozza
Journal of Scientific Computing 89 (1) (2021)
DOI: 10.1007/s10915-021-01623-8
See this article

An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation

Yanlai Chen, Sigal Gottlieb, Lijie Ji and Yvon Maday
Journal of Computational Physics 444 110545 (2021)
DOI: 10.1016/j.jcp.2021.110545
See this article

Kolmogorov n-widths for linear dynamical systems

Benjamin Unger and Serkan Gugercin
Advances in Computational Mathematics 45 (5-6) 2273 (2019)
DOI: 10.1007/s10444-019-09701-0
See this article

Certified Offline-Free Reduced Basis (COFRB) Methods for Stochastic Differential Equations Driven by Arbitrary Types of Noise

Yong Liu, Tianheng Chen, Yanlai Chen and Chi-Wang Shu
Journal of Scientific Computing 81 (3) 1210 (2019)
DOI: 10.1007/s10915-019-00976-5
See this article

Adaptive reduced order modeling for nonlinear dynamical systems through a new a posteriori error estimator: Application to uncertainty quantification

Md. Nurtaj Hossain and Debraj Ghosh
International Journal for Numerical Methods in Engineering 121 (15) 3417 (2020)
DOI: 10.1002/nme.6365
See this article

Offline-Enhanced Reduced Basis Method Through Adaptive Construction of the Surrogate Training Set

Jiahua Jiang, Yanlai Chen and Akil Narayan
Journal of Scientific Computing 73 (2-3) 853 (2017)
DOI: 10.1007/s10915-017-0551-3
See this article

Time-series machine-learning error models for approximate solutions to parameterized dynamical systems

Eric J. Parish and Kevin T. Carlberg
Computer Methods in Applied Mechanics and Engineering 365 112990 (2020)
DOI: 10.1016/j.cma.2020.112990
See this article

Adaptive POD–DEIM basis construction and its application to a nonlinear population balance system

Lihong Feng, Michael Mangold and Peter Benner
AIChE Journal 63 (9) 3832 (2017)
DOI: 10.1002/aic.15749
See this article

Basis generation approaches for a reduced basis linear quadratic regulator

Andreas Schmidt, Markus Dihlmann and Bernard Haasdonk
IFAC-PapersOnLine 48 (1) 713 (2015)
DOI: 10.1016/j.ifacol.2015.05.016
See this article

Efficient structural reliability analysis by using a PGD model in an adaptive importance sampling schema

Annika Robens-Radermacher and Jörg F. Unger
Advanced Modeling and Simulation in Engineering Sciences 7 (1) (2020)
DOI: 10.1186/s40323-020-00168-z
See this article

Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process

Shane A. McQuarrie, Cheng Huang and Karen E. Willcox
Journal of the Royal Society of New Zealand 51 (2) 194 (2021)
DOI: 10.1080/03036758.2020.1863237
See this article

A Least-Squares Finite Element Reduced Basis Method

Jehanzeb H. Chaudhry, Luke N. Olson and Peter Sentz
SIAM Journal on Scientific Computing 43 (2) A1081 (2021)
DOI: 10.1137/20M1323552
See this article

Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

Federico Negri, Andrea Manzoni and David Amsallem
Journal of Computational Physics 303 431 (2015)
DOI: 10.1016/j.jcp.2015.09.046
See this article

A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow

Efthymios N. Karatzas, Giovanni Stabile, Leo Nouveau, Guglielmo Scovazzi and Gianluigi Rozza
Computer Methods in Applied Mechanics and Engineering 347 568 (2019)
DOI: 10.1016/j.cma.2018.12.040
See this article

Parametric domain decomposition for accurate reduced order models: Applications of MP-LROM methodology

Razvan Stefanescu, Azam Moosavi and Adrian Sandu
Journal of Computational and Applied Mathematics 340 629 (2018)
DOI: 10.1016/j.cam.2017.11.018
See this article

Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

Wayne Isaac Tan Uy and Benjamin Peherstorfer
ESAIM: Mathematical Modelling and Numerical Analysis 55 (3) 735 (2021)
DOI: 10.1051/m2an/2021010
See this article

A Review of Model Order Reduction Methods for Large-Scale Structure Systems

Kuan Lu, Kangyu Zhang, Haopeng Zhang, et al.
Shock and Vibration 2021 1 (2021)
DOI: 10.1155/2021/6631180
See this article

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)
DOI: 10.1177/0954406212456794
See this article

Model order reduction for the simulation of parametric interest rate models in financial risk analysis

Andreas Binder, Onkar Jadhav and Volker Mehrmann
Journal of Mathematics in Industry 11 (1) (2021)
DOI: 10.1186/s13362-021-00105-8
See this article

Limited‐memory adaptive snapshot selection for proper orthogonal decomposition

Geoffrey M. Oxberry, Tanya Kostova‐Vassilevska, William Arrighi and Kyle Chand
International Journal for Numerical Methods in Engineering 109 (2) 198 (2017)
DOI: 10.1002/nme.5283
See this article

Yi Wang, Kapil Pant, Martin J. Brenner and Jeffrey A. Ouellette
(2018)
DOI: 10.2514/6.2018-1210
See this article

Tan Bui-Thanh, Karen Willcox and Omar Ghattas
(2007)
DOI: 10.2514/6.2007-2049
See this article

Eduardo Gildin, Mohammadreza Ghasemi, Anastasiya Romanovskay and Yalchin Efendiev
(2013)
DOI: 10.2118/163618-MS
See this article

Alexandre Janon, Maelle Nodet, Christophe Prieur and Clementine Prieur
589 (2014)
DOI: 10.1109/CDC.2014.7039445
See this article

José M. Vega and Filippo Terragni
1060 (2015)
DOI: 10.3934/proc.2015.1060
See this article

Marcelo Buffoni and Karen Willcox
(2010)
DOI: 10.2514/6.2010-5008
See this article

Building a certified reduced basis for coupled thermo-hydro-mechanical systems with goal-oriented error estimation

Ygee Larion, Sergio Zlotnik, Thierry J. Massart and Pedro Díez
Computational Mechanics 66 (3) 559 (2020)
DOI: 10.1007/s00466-020-01865-7
See this article

Parametric Model Order Reduction of Guided Ultrasonic Wave Propagation in Fiber Metal Laminates with Damage

Nanda Kishore Bellam Muralidhar, Natalie Rauter, Andrey Mikhaylenko, Rolf Lammering and Dirk A. Lorenz
Modelling 2 (4) 591 (2021)
DOI: 10.3390/modelling2040031
See this article

A Training Set Subsampling Strategy for the Reduced Basis Method

Sridhar Chellappa, Lihong Feng and Peter Benner
Journal of Scientific Computing 89 (3) (2021)
DOI: 10.1007/s10915-021-01665-y
See this article

Reduced order modelling for a rotor-stator cavity using proper orthogonal decomposition

Michel Onori and Nicholas J. Hills
Computers & Fluids 216 104818 (2021)
DOI: 10.1016/j.compfluid.2020.104818
See this article

Goal-oriented model reduction for parametrized time-dependent nonlinear partial differential equations

Michael K. Sleeman and Masayuki Yano
Computer Methods in Applied Mechanics and Engineering 388 114206 (2022)
DOI: 10.1016/j.cma.2021.114206
See this article

A solution for fractional PDE constrained optimization problems using reduced basis method

A. Rezazadeh, M. Mahmoudi and M. Darehmiraki
Computational and Applied Mathematics 39 (2) (2020)
DOI: 10.1007/s40314-020-1092-1
See this article

Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms

Matteo Giacomini, Luca Borchini, Ruben Sevilla and Antonio Huerta
Finite Elements in Analysis and Design 196 103530 (2021)
DOI: 10.1016/j.finel.2021.103530
See this article

Stefan Banholzer, Bennet Gebken, Michael Dellnitz, Sebastian Peitz and Stefan Volkwein
172 43 (2022)
DOI: 10.1007/978-3-030-79393-7_3
See this article

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Jan S. Hesthaven, Cecilia Pagliantini and Nicolò Ripamonti
ESAIM: Mathematical Modelling and Numerical Analysis 56 (2) 617 (2022)
DOI: 10.1051/m2an/2022013
See this article

L1-Based Reduced Over Collocation and Hyper Reduction for Steady State and Time-Dependent Nonlinear Equations

Yanlai Chen, Lijie Ji, Akil Narayan and Zhenli Xu
Journal of Scientific Computing 87 (1) (2021)
DOI: 10.1007/s10915-021-01416-z
See this article

Accelerating PDE constrained optimization by the reducedbasis method: application to batch chromatography

Yongjin Zhang, Lihong Feng, Suzhou Li and Peter Benner
International Journal for Numerical Methods in Engineering 104 (11) 983 (2015)
DOI: 10.1002/nme.4950
See this article

Petar Mlinarić, Stephan Rave and Jens Saak
171 357 (2021)
DOI: 10.1007/978-3-030-72983-7_17
See this article

Online Reduced Basis Construction Procedure for Model Reduction of Parametrized Evolution Systems

Markus Dihlmann, Sven Kaulmann and Bernard Haasdonk
IFAC Proceedings Volumes 45 (2) 112 (2012)
DOI: 10.3182/20120215-3-AT-3016.00020
See this article

Research on the efficiency of reduced-basis approach in computations of structural problems and its improvements

F Lei, XP Xie, XW Wang and YG Wang
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227 (10) 2143 (2013)
DOI: 10.1177/0954406212470895
See this article

Interpolatory tensorial reduced order models for parametric dynamical systems

Alexander V. Mamonov and Maxim A. Olshanskii
Computer Methods in Applied Mechanics and Engineering 397 115122 (2022)
DOI: 10.1016/j.cma.2022.115122
See this article

Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations

Giovanni Stabile and Gianluigi Rozza
Computers & Fluids 173 273 (2018)
DOI: 10.1016/j.compfluid.2018.01.035
See this article

Reduced basis methods for time-dependent problems

Jan S. Hesthaven, Cecilia Pagliantini and Gianluigi Rozza
Acta Numerica 31 265 (2022)
DOI: 10.1017/S0962492922000058
See this article

A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations

Efthymios N. Karatzas, Giovanni Stabile, Leo Nouveau, Guglielmo Scovazzi and Gianluigi Rozza
Computer Methods in Applied Mechanics and Engineering 370 113273 (2020)
DOI: 10.1016/j.cma.2020.113273
See this article

Reduced Basis Approximation for a Spatial Lotka-Volterra Model

Peter Rashkov
Mathematics 10 (12) 1983 (2022)
DOI: 10.3390/math10121983
See this article

Inversion method of hydraulic conductivity for steady-state problem based on reduced-order model constructed by improved greedy sampling method

Wuwen Qian, Junrui Chai, Xinyu Zhao, JingTai Niu, Fang Xiao and Zhiping Deng
Advances in Water Resources 166 104260 (2022)
DOI: 10.1016/j.advwatres.2022.104260
See this article

Projection-based reduced order models for a cut finite element method in parametrized domains

Efthymios N. Karatzas, Francesco Ballarin and Gianluigi Rozza
Computers & Mathematics with Applications 79 (3) 833 (2020)
DOI: 10.1016/j.camwa.2019.08.003
See this article

A Reduced Order Cut Finite Element method for geometrically parametrized steady and unsteady Navier–Stokes problems

Efthymios N. Karatzas, Monica Nonino, Francesco Ballarin and Gianluigi Rozza
Computers & Mathematics with Applications 116 140 (2022)
DOI: 10.1016/j.camwa.2021.07.016
See this article

A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations

Yanlai Chen, Lijie Ji and Zhu Wang
Journal of Computational Physics 466 111412 (2022)
DOI: 10.1016/j.jcp.2022.111412
See this article

Using Reduced Basis Approximation for Efficient Surrogate-Based Inverse Identification of Thermo-Hydro-Mechanical Parameters from an In Situ Heating Test

Ygee Larion, Guangjing Chen, Sergio Zlotnik, Pedro Díez, Suresh Seetharam and Thierry J. Massart
Rock Mechanics and Rock Engineering 55 (9) 5739 (2022)
DOI: 10.1007/s00603-022-02925-5
See this article

Reduced Operator Inference for Nonlinear Partial Differential Equations

Elizabeth Qian, Ionuţ-Gabriel Farcaş and Karen Willcox
SIAM Journal on Scientific Computing 44 (4) A1934 (2022)
DOI: 10.1137/21M1393972
See this article

Parametric model-order-reduction development for unsteady convection

Ping-Hsuan Tsai and Paul Fischer
Frontiers in Physics 10 (2022)
DOI: 10.3389/fphy.2022.903169
See this article

Certified Reduced Basis Method for the Damped Wave Equations on Networks

Nadine Stahl, Björn Liljegren-Sailer and Nicole Marheineke
IFAC-PapersOnLine 55 (20) 289 (2022)
DOI: 10.1016/j.ifacol.2022.09.110
See this article

A POD-based ROM strategy for the prediction in time of advection-dominated problems

P. Solán-Fustero, J.L. Gracia, A. Navas-Montilla and P. García-Navarro
Journal of Computational Physics 471 111672 (2022)
DOI: 10.1016/j.jcp.2022.111672
See this article

Trust-Region RB Methods for PDE-Constrained Optimization and Optimal Input Design

Andrea Petrocchi, Matthias K. Scharrer and Stefan Volkwein
IFAC-PapersOnLine 55 (26) 149 (2022)
DOI: 10.1016/j.ifacol.2022.10.392
See this article

Model reduction of convection-dominated partial differential equations via optimization-based implicit feature tracking

Marzieh Alireza Mirhoseini and Matthew J. Zahr
Journal of Computational Physics 473 111739 (2023)
DOI: 10.1016/j.jcp.2022.111739
See this article