ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

An adaptive GMsFEM for high-contrast flow problems

Eric T. Chung, Yalchin Efendiev and Guanglian Li
Journal of Computational Physics 273 54 (2014)
DOI: 10.1016/j.jcp.2014.05.007
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Port reduction in parametrized component static condensation: approximation and a posteriori error estimation

Jens L. Eftang and Anthony T. Patera
International Journal for Numerical Methods in Engineering 96 (5) 269 (2013)
DOI: 10.1002/nme.4543
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Progress in Industrial Mathematics at ECMI 2014

Laura Iapichino, Alfio Quarteroni, Gianluigi Rozza and Stefan Volkwein
Mathematics in Industry, Progress in Industrial Mathematics at ECMI 2014 22 647 (2016)
DOI: 10.1007/978-3-319-23413-7_89
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Proper orthogonal decomposition‐based reduced basis element thermal modeling of integrated circuits

Daniel S. Meyer, Brian T. Helenbrook and Ming‐C. Cheng
International Journal for Numerical Methods in Engineering 112 (5) 479 (2017)
DOI: 10.1002/nme.5529
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Data‐driven physics‐based digital twins via a library of component‐based reduced‐order models

M.G. Kapteyn, D.J. Knezevic, D.B.P. Huynh, M. Tran and K.E. Willcox
International Journal for Numerical Methods in Engineering (2020)
DOI: 10.1002/nme.6423
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Proper generalized decomposition solutions within a domain decomposition strategy

Antonio Huerta, Enrique Nadal and Francisco Chinesta
International Journal for Numerical Methods in Engineering 113 (13) 1972 (2018)
DOI: 10.1002/nme.5729
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A reduced basis method with exact-solution certificates for steady symmetric coercive equations

Masayuki Yano
Computer Methods in Applied Mechanics and Engineering 287 290 (2015)
DOI: 10.1016/j.cma.2015.01.003
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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
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Numerical Mathematics and Advanced Applications - ENUMATH 2013

Immanuel Martini and Bernard Haasdonk
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications - ENUMATH 2013 103 437 (2015)
DOI: 10.1007/978-3-319-10705-9_43
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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
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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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A port-reduced static condensation reduced basis element method for large component-synthesized structures: approximation and A Posteriori error estimation

Jens L Eftang and Anthony T Patera
Advanced Modeling and Simulation in Engineering Sciences 1 (1) 3 (2014)
DOI: 10.1186/2213-7467-1-3
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Model reduction in elastoplasticity: proper orthogonal decomposition combined with adaptive sub-structuring

Annika Radermacher and Stefanie Reese
Computational Mechanics 54 (3) 677 (2014)
DOI: 10.1007/s00466-014-1020-6
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A static condensation reduced basis element method: Complex problems

D.B.P. Huynh, D.J. Knezevic and A.T. Patera
Computer Methods in Applied Mechanics and Engineering 259 197 (2013)
DOI: 10.1016/j.cma.2013.02.013
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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
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A new certification framework for the port reduced static condensation reduced basis element method

Kathrin Smetana
Computer Methods in Applied Mechanics and Engineering 283 352 (2015)
DOI: 10.1016/j.cma.2014.09.020
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Model Reduction of Parametrized Systems

Andreas Buhr, Christian Engwer, Mario Ohlberger and Stephan Rave
MS&A, Model Reduction of Parametrized Systems 17 137 (2017)
DOI: 10.1007/978-3-319-58786-8_9
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Approximate partitioned method of snapshots for POD

Zhu Wang, Brian McBee and Traian Iliescu
Journal of Computational and Applied Mathematics 307 374 (2016)
DOI: 10.1016/j.cam.2015.11.023
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Simulation-Based Classification; a Model-Order-Reduction Approach for Structural Health Monitoring

T. Taddei, J. D. Penn, M. Yano and A. T. Patera
Archives of Computational Methods in Engineering 25 (1) 23 (2018)
DOI: 10.1007/s11831-016-9185-0
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Reduced Basis’ Acquisition by a Learning Process for Rapid On-line Approximation of Solution to PDE’s: Laminar Flow Past a Backstep

Patrick Gallinari, Yvon Maday, Maxime Sangnier, Olivier Schwander and Tommaso Taddei
Archives of Computational Methods in Engineering 25 (1) 131 (2018)
DOI: 10.1007/s11831-017-9238-z
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Model order reduction for large-scale structures with local nonlinearities

Zhenying Zhang, Mengwu Guo and Jan S. Hesthaven
Computer Methods in Applied Mechanics and Engineering 353 491 (2019)
DOI: 10.1016/j.cma.2019.04.042
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A reduced-order representation of the Poincaré-Steklov operator: an application to coupled multi-physics problems

Matteo Aletti and Damiano Lombardi
International Journal for Numerical Methods in Engineering 111 (6) 581 (2017)
DOI: 10.1002/nme.5490
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A Domain Decomposition Model Reduction Method for Linear Convection-Diffusion Equations with Random Coefficients

Lin Mu and Guannan Zhang
SIAM Journal on Scientific Computing 41 (3) A1984 (2019)
DOI: 10.1137/18M1170601
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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
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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
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IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018

Kathrin Smetana
IUTAM Bookseries, IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018 36 1 (2020)
DOI: 10.1007/978-3-030-21013-7_1
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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
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Component-based reduced basis for parametrized symmetric eigenproblems

Sylvain Vallaghé, Phuong Huynh, David J Knezevic, Loi Nguyen and Anthony T Patera
Advanced Modeling and Simulation in Engineering Sciences 2 (1) (2015)
DOI: 10.1186/s40323-015-0021-0
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An Adaptive Model Order Reduction Method Based on the Damage Evolution for Nonlinear Seismic Analysis

Jian Wang, Ming Fang and Hui Li
Advances in Civil Engineering 2020 1 (2020)
DOI: 10.1155/2020/8865255
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The Static Condensation Reduced Basis Element Method for a Mixed-Mean Conjugate Heat Exchanger Model

Sylvain Vallaghé and Anthony T. Patera
SIAM Journal on Scientific Computing 36 (3) B294 (2014)
DOI: 10.1137/120887709
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Optimal Local Approximation Spaces for Component-Based Static Condensation Procedures

Kathrin Smetana and Anthony T. Patera
SIAM Journal on Scientific Computing 38 (5) A3318 (2016)
DOI: 10.1137/15M1009603
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A STATIC CONDENSATION REDUCED BASIS ELEMENT APPROXIMATION: APPLICATION TO THREE-DIMENSIONAL ACOUSTIC MUFFLER ANALYSIS

D. B. P. HUYNH
International Journal of Computational Methods 11 (03) 1343010 (2014)
DOI: 10.1142/S021987621343010X
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Randomized Local Model Order Reduction

Andreas Buhr and Kathrin Smetana
SIAM Journal on Scientific Computing 40 (4) A2120 (2018)
DOI: 10.1137/17M1138480
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Systematic sensor placement for structural anomaly detection in the absence of damaged states

Caterina Bigoni, Zhenying Zhang and Jan S. Hesthaven
Computer Methods in Applied Mechanics and Engineering 371 113315 (2020)
DOI: 10.1016/j.cma.2020.113315
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Spectral based Discontinuous Galerkin Reduced Basis Element method for parametrized Stokes problems

Paolo Pacciarini, Paola Gervasio and Alfio Quarteroni
Computers & Mathematics with Applications 72 (8) 1977 (2016)
DOI: 10.1016/j.camwa.2016.01.030
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An Adaptive Generalized Multiscale Discontinuous Galerkin Method for High-Contrast Flow Problems

Eric T. Chung, Yalchin Efendiev and Wing Tat Leung
Multiscale Modeling & Simulation 16 (3) 1227 (2018)
DOI: 10.1137/140986189
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A Localization Strategy for Data Assimilation; Application to State Estimation and Parameter Estimation

Tommaso Taddei and Anthony T. Patera
SIAM Journal on Scientific Computing 40 (2) B611 (2018)
DOI: 10.1137/17M1116830
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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
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ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications

Andreas Buhr, Christian Engwer, Mario Ohlberger and Stephan Rave
SIAM Journal on Scientific Computing 39 (4) A1435 (2017)
DOI: 10.1137/15M1054213
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Numerical Mathematics and Advanced Applications ENUMATH 2017

Jonas Ballani, Phuong Huynh, David Knezevic, Loi Nguyen and Anthony T. Patera
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications ENUMATH 2017 126 3 (2019)
DOI: 10.1007/978-3-319-96415-7_1
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Domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) nonlinear model reduction

Chi Hoang, Youngsoo Choi and Kevin Carlberg
Computer Methods in Applied Mechanics and Engineering 384 113997 (2021)
DOI: 10.1016/j.cma.2021.113997
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Windowed space–time least-squares Petrov–Galerkin model order reduction for nonlinear dynamical systems

Yukiko S. Shimizu and Eric J. Parish
Computer Methods in Applied Mechanics and Engineering 386 114050 (2021)
DOI: 10.1016/j.cma.2021.114050
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An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media

Eric T. Chung, Yalchin Efendiev and Wing Tat Leung
Communications in Computational Physics 21 (2) 401 (2017)
DOI: 10.4208/cicp.230815.090516a
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A Static Condensation Reduced Basis Element Approach for the Reynolds Lubrication Equation

Eduard Bader, Martin A. Grepl and Siegfried Müller
Communications in Computational Physics 21 (1) 126 (2017)
DOI: 10.4208/cicp.130815.180416a
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Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

Qifeng Liao and Guang Lin
Journal of Computational Physics 317 148 (2016)
DOI: 10.1016/j.jcp.2016.04.029
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An adaptive model order reduction method for nonlinear seismic analysis of civil structures based on the elastic–plastic states

Ming Fang, Jian Wang and Hui Li
International Journal for Numerical Methods in Engineering 122 (15) 3985 (2021)
DOI: 10.1002/nme.6689
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A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures

F. Vidal-Codina, N.-C. Nguyen, C. Ciracì, S.-H. Oh and J. Peraire
Journal of Computational Physics 429 110000 (2021)
DOI: 10.1016/j.jcp.2020.110000
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Rare event simulation for large-scale structures with local nonlinearities

Zhenying Zhang and Jan S. Hesthaven
Computer Methods in Applied Mechanics and Engineering 366 113051 (2020)
DOI: 10.1016/j.cma.2020.113051
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Hyper‐reduced direct numerical simulation of voids in welded joints via image‐based modeling

Laurent Lacourt, David Ryckelynck, Samuel Forest, Victor Rancourt and Sylvain Flouriot
International Journal for Numerical Methods in Engineering 121 (11) 2581 (2020)
DOI: 10.1002/nme.6320
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Uncertainty quantification of bladed disc systems using data driven stochastic reduced order models

Rahul Kumar, Shaikh Faruque Ali, Sankarkumar Jeyaraman and Sayan Gupta
International Journal of Mechanical Sciences 190 106011 (2021)
DOI: 10.1016/j.ijmecsci.2020.106011
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Interactive Simulations Using Localized Reduced Basis Methods

Andreas Buhr and Mario Ohlberger
IFAC-PapersOnLine 48 (1) 729 (2015)
DOI: 10.1016/j.ifacol.2015.05.134
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A component-based hybrid reduced basis/finite element method for solid mechanics with local nonlinearities

J. Ballani, D.B.P. Huynh, D.J. Knezevic, L. Nguyen and A.T. Patera
Computer Methods in Applied Mechanics and Engineering 329 498 (2018)
DOI: 10.1016/j.cma.2017.09.014
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Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Laura Iapichino, Alfio Quarteroni and Gianluigi Rozza
Computers & Mathematics with Applications 71 (1) 408 (2016)
DOI: 10.1016/j.camwa.2015.12.001
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Data Augmentation and Feature Selection for Automatic Model Recommendation in Computational Physics

Thomas Daniel, Fabien Casenave, Nissrine Akkari and David Ryckelynck
Mathematical and Computational Applications 26 (1) 17 (2021)
DOI: 10.3390/mca26010017
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A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals

F. Vidal-Codina, J. Saà-Seoane, N.-C. Nguyen and J. Peraire
Journal of Computational Physics: X 2 100016 (2019)
DOI: 10.1016/j.jcpx.2019.100016
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Component-wise reduced order model lattice-type structure design

Sean McBane and Youngsoo Choi
Computer Methods in Applied Mechanics and Engineering 381 113813 (2021)
DOI: 10.1016/j.cma.2021.113813
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Michael G. Kapteyn, David J. Knezevic and Karen Willcox
(2020)
DOI: 10.2514/6.2020-0418
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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
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A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation

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