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DOI: 10.1016/j.jcp.2016.02.055
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A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains

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Journal of Scientific Computing 66 (1) 67 (2016)
DOI: 10.1007/s10915-015-0013-8
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Reduced Basis Methods: From Low-Rank Matrices to Low-Rank Tensors

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SIAM Journal on Scientific Computing 38 (4) A2045 (2016)
DOI: 10.1137/15M1042784
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Interpolatory Projection Methods for Parameterized Model Reduction

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DOI: 10.1137/090776925
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Automatic model reduction of differential algebraic systems by proper orthogonal decomposition

Dmytro Khlopov and Michael Mangold
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DOI: 10.1016/j.compchemeng.2016.11.004
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A Goal-Oriented Reduced Basis Methods-Accelerated Generalized Polynomial Chaos Algorithm

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DOI: 10.1137/16M1055736
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A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations

N.C. Nguyen
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DOI: 10.1016/j.jcp.2007.08.031
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Accelerated mesh sampling for the hyper reduction of nonlinear computational models

Todd Chapman, Philip Avery, Pat Collins and Charbel Farhat
International Journal for Numerical Methods in Engineering 109 (12) 1623 (2017)
DOI: 10.1002/nme.5332
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Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation

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Optimization and Engineering 19 (3) 663 (2018)
DOI: 10.1007/s11081-018-9389-2
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A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems

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SIAM Journal on Scientific Computing 36 (2) A311 (2014)
DOI: 10.1137/120899042
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Dimensional hyper-reduction of nonlinear finite element models via empirical cubature

J.A. Hernández, M.A. Caicedo and A. Ferrer
Computer Methods in Applied Mechanics and Engineering 313 687 (2017)
DOI: 10.1016/j.cma.2016.10.022
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Assessment of self-adapting local projection-based solvers for laminar and turbulent industrial flows

Tomás Chacón Rebollo, Enrique Delgado Ávila, Macarena Gómez Mármol and Samuele Rubino
Journal of Mathematics in Industry 8 (1) (2018)
DOI: 10.1186/s13362-018-0045-4
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Reduced-basis boundary element method for fast electromagnetic field computation

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DOI: 10.1364/JOSAA.34.002231
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Mathematical and numerical results on the parametric sensitivity of a ROM-POD of the Burgers equation

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European Journal of Computational Mechanics 23 (1-2) 78 (2014)
DOI: 10.1080/17797179.2014.912410
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Reduction procedure for parametrized fluid dynamics problems based on proper orthogonal decomposition and calibration

Mykhaylo Krasnyk, Michael Mangold and Achim Kienle
Chemical Engineering Science 65 (23) 6238 (2010)
DOI: 10.1016/j.ces.2010.09.005
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3D-VAR for parameterized partial differential equations: a certified reduced basis approach

Nicole Aretz-Nellesen, Martin A. Grepl and Karen Veroy
Advances in Computational Mathematics 45 (5-6) 2369 (2019)
DOI: 10.1007/s10444-019-09713-w
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Discontinuous Galerkin reduced basis empirical quadrature procedure for model reduction of parametrized nonlinear conservation laws

Masayuki Yano
Advances in Computational Mathematics 45 (5-6) 2287 (2019)
DOI: 10.1007/s10444-019-09710-z
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Non-intrusive reduced-order modeling for fluid problems: A brief review

Jian Yu, Chao Yan and Mengwu Guo
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 095441001989072 (2019)
DOI: 10.1177/0954410019890721
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Toni Lassila, Andrea Manzoni and Gianluigi Rozza
ESAIM: Mathematical Modelling and Numerical Analysis 46 (6) 1555 (2012)
DOI: 10.1051/m2an/2012016
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Development of a coupling between a system thermal–hydraulic code and a reduced order CFD model

S. Kelbij Star, Giuseppe Spina, Francesco Belloni and Joris Degroote
Annals of Nuclear Energy 153 108056 (2021)
DOI: 10.1016/j.anucene.2020.108056
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Certified reduced-basis solutions of viscous Burgers equation parametrized by initial and boundary values

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ESAIM: Mathematical Modelling and Numerical Analysis 47 (2) 317 (2013)
DOI: 10.1051/m2an/2012029
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Modeling and Quantification of Model-Form Uncertainties in Eigenvalue Computations Using a Stochastic Reduced Model

Charbel Farhat, Adrien Bos, Philip Avery and Christian Soize
AIAA Journal 56 (3) 1198 (2018)
DOI: 10.2514/1.J056314
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A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics

Diana Bonomi, Andrea Manzoni and Alfio Quarteroni
Computer Methods in Applied Mechanics and Engineering 324 300 (2017)
DOI: 10.1016/j.cma.2017.06.011
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MLACE-MLFMA Combined With Reduced Basis Method for Efficient Wideband Electromagnetic Scattering From Metallic Targets

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IEEE Transactions on Antennas and Propagation 67 (7) 4738 (2019)
DOI: 10.1109/TAP.2019.2911352
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Progress in Industrial Mathematics at ECMI 2016

Tomás Chacón Rebollo, Enrique Delgado Ávila, Macarena Gómez Mármol and Samuele Rubino
Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2016 26 561 (2017)
DOI: 10.1007/978-3-319-63082-3_87
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Reduced-basis method for band structure calculations

George S. H. Pau
Physical Review E 76 (4) 046704 (2007)
DOI: 10.1103/PhysRevE.76.046704
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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
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Nonlinear model reduction based on the finite element method with interpolated coefficients: Semilinear parabolic equations

Zhu Wang
Numerical Methods for Partial Differential Equations 31 (6) 1713 (2015)
DOI: 10.1002/num.21961
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Certified Reduced Basis Methods for Parametrized Saddle Point Problems

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SIAM Journal on Scientific Computing 34 (5) A2812 (2012)
DOI: 10.1137/110854084
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Computational Reduction for Parametrized PDEs: Strategies and Applications

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Milan Journal of Mathematics 80 (2) 283 (2012)
DOI: 10.1007/s00032-012-0182-y
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A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient

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Computer Methods in Applied Mechanics and Engineering 198 (41-44) 3187 (2009)
DOI: 10.1016/j.cma.2009.05.019
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Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

Romain Guibert, Kristin McLeod, Alfonso Caiazzo, et al.
Medical Image Analysis 18 (1) 63 (2014)
DOI: 10.1016/j.media.2013.09.003
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Reduced-Basis Approach for Homogenization beyond the Periodic Setting

Sébastien Boyaval
Multiscale Modeling & Simulation 7 (1) 466 (2008)
DOI: 10.1137/070688791
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Optimal snapshot location for computing POD basis functions

Karl Kunisch and Stefan Volkwein
ESAIM: Mathematical Modelling and Numerical Analysis 44 (3) 509 (2010)
DOI: 10.1051/m2an/2010011
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A fast certified parametric near-field-to-far-field transformation technique for electrically large antenna arrays

Alexander Sommer, Ortwin Farle and Romanus Dyczij-Edlinger
Advances in Computational Mathematics 41 (5) 1015 (2015)
DOI: 10.1007/s10444-014-9373-0
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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)
DOI: 10.1016/j.cma.2012.04.013
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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
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POD-Galerkin approximations in PDE-constrained optimization

Ekkehard W. Sachs and Stefan Volkwein
GAMM-Mitteilungen 33 (2) 194 (2010)
DOI: 10.1002/gamm.201010015
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Principal interval decomposition framework for POD reduced-order modeling of convective Boussinesq flows

O. San and J. Borggaard
International Journal for Numerical Methods in Fluids 78 (1) 37 (2015)
DOI: 10.1002/fld.4006
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Reduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils

Andrea Manzoni, Filippo Salmoiraghi and Luca Heltai
Computer Methods in Applied Mechanics and Engineering 284 1147 (2015)
DOI: 10.1016/j.cma.2014.11.037
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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
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Virtual charts of solutions for parametrized nonlinear equations

Matthieu Vitse, David Néron and Pierre-Alain Boucard
Computational Mechanics 54 (6) 1529 (2014)
DOI: 10.1007/s00466-014-1073-6
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Galerkin lumped parameter methods for transient problems

A. Bermúdez and F. Pena
International Journal for Numerical Methods in Engineering 87 (10) 943 (2011)
DOI: 10.1002/nme.3140
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Dennis Beermann, Michael Dellnitz, Sebastian Peitz and Stefan Volkwein
Reduced-Order Modeling (ROM) for Simulation and Optimization 47 (2018)
DOI: 10.1007/978-3-319-75319-5_3
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DOI: 10.1007/978-3-030-51264-4_10
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A POD–EIM reduced two-scale model for precipitation in porous media

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DOI: 10.1080/13873954.2016.1198384
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An empirical interpolation approach to reduced basis approximations for variational inequalities

E. Bader, Z. Zhang and K. Veroy
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DOI: 10.1080/13873954.2016.1198388
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A-posteriori error analysis for lithium-ion concentrations in batteries utilizing the reduced-basis method

L. Iapichino, S. Volkwein and A. Wesche
Mathematical and Computer Modelling of Dynamical Systems 22 (4) 362 (2016)
DOI: 10.1080/13873954.2016.1198387
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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
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Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability

Davide Pradovera
SIAM Journal on Numerical Analysis 58 (4) 2265 (2020)
DOI: 10.1137/19M1269695
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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
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Multi-fidelity aerodynamic design trade-off exploration using point-by-point Pareto set identification

Anand Amrit, Leifur Leifsson and Slawomir Koziel
Aerospace Science and Technology 79 399 (2018)
DOI: 10.1016/j.ast.2018.05.023
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Local–global model reduction method for stochastic optimal control problems constrained by partial differential equations

Lingling Ma, Qiuqi Li and Lijian Jiang
Computer Methods in Applied Mechanics and Engineering 339 514 (2018)
DOI: 10.1016/j.cma.2018.05.012
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A Multiscale Neural Network Based on Hierarchical Matrices

Yuwei Fan, Lin Lin, Lexing Ying and Leonardo Zepeda-Nún͂ez
Multiscale Modeling & Simulation 17 (4) 1189 (2019)
DOI: 10.1137/18M1203602
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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
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REDUCED BASIS A POSTERIORI ERROR BOUNDS FOR THE STOKES EQUATIONS IN PARAMETRIZED DOMAINS: A PENALTY APPROACH

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Mathematical Models and Methods in Applied Sciences 21 (10) 2103 (2011)
DOI: 10.1142/S0218202511005672
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CERTIFIED REDUCED BASIS METHODS FOR NONAFFINE LINEAR TIME-VARYING AND NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

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Mathematical Models and Methods in Applied Sciences 22 (03) 1150015 (2012)
DOI: 10.1142/S0218202511500151
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A hybrid model reduction method for stochastic parabolic optimal control problems

Lijian Jiang and Lingling Ma
Computer Methods in Applied Mechanics and Engineering 370 113244 (2020)
DOI: 10.1016/j.cma.2020.113244
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A reduced-order shifted boundary method for parametrized incompressible Navier–Stokes equations

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Computer Methods in Applied Mechanics and Engineering 370 113273 (2020)
DOI: 10.1016/j.cma.2020.113273
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A new bi‐fidelity model reduction method for Bayesian inverse problems

Na Ou, Lijian Jiang and Guang Lin
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DOI: 10.1002/nme.6079
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An offline/online procedure for dual norm calculations of parameterized functionals: empirical quadrature and empirical test spaces

Tommaso Taddei
Advances in Computational Mathematics 45 (5-6) 2429 (2019)
DOI: 10.1007/s10444-019-09721-w
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Fast and accurate two-field reduced basis approximation for parametrized thermoelasticity problems

Khac Chi Hoang, Tae-Yeon Kim and Jeong-Hoon Song
Finite Elements in Analysis and Design 141 96 (2018)
DOI: 10.1016/j.finel.2017.12.004
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EVALUATION OF FLUX INTEGRAL OUTPUTS FOR THE REDUCED BASIS METHOD

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Mathematical Models and Methods in Applied Sciences 20 (03) 351 (2010)
DOI: 10.1142/S021820251000426X
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An hp -proper orthogonal decomposition–moving least squares approach for molecular dynamics simulation

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Computer Methods in Applied Mechanics and Engineering 298 548 (2016)
DOI: 10.1016/j.cma.2015.10.003
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The Reference Point Method, a “hyperreduction” technique: Application to PGD-based nonlinear model reduction

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Computer Methods in Applied Mechanics and Engineering 322 483 (2017)
DOI: 10.1016/j.cma.2017.04.033
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Accelerating optimization and uncertainty quantification of nonlinear SMB chromatography using reduced-order models

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Computers & Chemical Engineering 96 237 (2017)
DOI: 10.1016/j.compchemeng.2016.09.017
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Projection-based reduced order models for a cut finite element method in parametrized domains

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DOI: 10.1016/j.camwa.2019.08.003
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DOI: 10.1016/j.euromechsol.2016.08.005
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Certified dual-corrected radiation patterns of phased antenna arrays by offline–online order reduction of finite-element models

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DOI: 10.1016/j.jcp.2015.06.024
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Gaussian functional regression for output prediction: Model assimilation and experimental design

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DOI: 10.1016/j.jcp.2015.12.035
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Computational Vibroacoustics in Low- and Medium- Frequency Bands: Damping, ROM, and UQ Modeling

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Applied Sciences 7 (12) 586 (2017)
DOI: 10.3390/app7060586
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Fast solution of the linearized Poisson–Boltzmann equation with nonaffine parametrized boundary conditions using the reduced basis method

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Computing and Visualization in Science 23 (1-4) (2020)
DOI: 10.1007/s00791-020-00336-z
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Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling

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Acta Applicandae Mathematicae 161 (1) 171 (2019)
DOI: 10.1007/s10440-018-0209-7
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A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow

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Computer Methods in Applied Mechanics and Engineering 347 568 (2019)
DOI: 10.1016/j.cma.2018.12.040
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A LATIN-based model reduction approach for the simulation of cycling damage

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Computational Mechanics 62 (4) 725 (2018)
DOI: 10.1007/s00466-017-1523-z
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The Discrete Empirical Interpolation Method: Canonical Structure and Formulation in Weighted Inner Product Spaces

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SIAM Journal on Matrix Analysis and Applications 39 (3) 1152 (2018)
DOI: 10.1137/17M1129635
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Stability of Discrete Empirical Interpolation and Gappy Proper Orthogonal Decomposition with Randomized and Deterministic Sampling Points

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DOI: 10.1137/19M1307391
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Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling

Benjamin Peherstorfer
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DOI: 10.1137/19M1257275
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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
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A Progressive Reduced Basis/Empirical Interpolation Method for Nonlinear Parabolic Problems

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SIAM Journal on Scientific Computing 40 (5) A2930 (2018)
DOI: 10.1137/17M1149638
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Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces

Virginie Ehrlacher, Damiano Lombardi, Olga Mula and François-Xavier Vialard
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DOI: 10.1051/m2an/2020013
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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
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Adaptive greedy algorithms based on parameter‐domain decomposition and reconstruction for the reduced basis method

Jiahua Jiang and Yanlai Chen
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DOI: 10.1002/nme.6544
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Dealing with a nonlinear material behavior and its variability through PGD models: Application to reinforced concrete structures

M. Vitse, D. Néron and P.-A. Boucard
Finite Elements in Analysis and Design 153 22 (2019)
DOI: 10.1016/j.finel.2018.05.006
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On a Certified Smagorinsky Reduced Basis Turbulence Model

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SIAM Journal on Numerical Analysis 55 (6) 3047 (2017)
DOI: 10.1137/17M1118233
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Efficient Reduced Basis Methods for Saddle Point Problems with Applications in Groundwater Flow

Craig J. Newsum and Catherine E. Powell
SIAM/ASA Journal on Uncertainty Quantification 5 (1) 1248 (2017)
DOI: 10.1137/16M1108856
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Reduced Basis Methods for Uncertainty Quantification

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DOI: 10.1137/151004550
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SIAM Review 60 (3) 550 (2018)
DOI: 10.1137/16M1082469
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Data Driven Modal Decompositions: Analysis and Enhancements

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SIAM Journal on Scientific Computing 40 (4) A2253 (2018)
DOI: 10.1137/17M1144155
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Data-Driven Reduced Model Construction with Time-Domain Loewner Models

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SIAM Journal on Scientific Computing 39 (5) A2152 (2017)
DOI: 10.1137/16M1094750
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Model order reduction for parametrized nonlinear hyperbolic problems as an application to uncertainty quantification

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Journal of Computational and Applied Mathematics 348 466 (2019)
DOI: 10.1016/j.cam.2018.09.018
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Fast divergence-conforming reduced basis methods for steady Navier–Stokes flow

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Computer Methods in Applied Mechanics and Engineering 346 486 (2019)
DOI: 10.1016/j.cma.2018.11.038
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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
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An LP empirical quadrature procedure for reduced basis treatment of parametrized nonlinear PDEs

Masayuki Yano and Anthony T. Patera
Computer Methods in Applied Mechanics and Engineering 344 1104 (2019)
DOI: 10.1016/j.cma.2018.02.028
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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
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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
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Primal-Dual Reduced Basis Methods for Convex Minimization Variational Problems: Robust True Solution a Posteriori Error Certification and Adaptive Greedy Algorithms

Shun Zhang
SIAM Journal on Scientific Computing 42 (6) A3638 (2020)
DOI: 10.1137/19M1281551
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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
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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
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Non-linear model reduction for uncertainty quantification in large-scale inverse problems

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DOI: 10.1002/nme.2746
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DOI: 10.1137/16M1091320
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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
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Non-intrusive Sparse Subspace Learning for Parametrized Problems

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SIAM Journal on Scientific Computing 41 (6) A3552 (2019)
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