EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 46 3 (2012) 595-603 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:

A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations

Lewin Ernst and Karsten Urban
IMA Journal of Numerical Analysis 45 (1) 494 (2025)
https://doi.org/10.1093/imanum/drae011

A Priori Analysis of a Tensor ROM for Parameter Dependent Parabolic Problems

Alexander V. Mamonov and Maxim A. Olshanskii
SIAM Journal on Numerical Analysis 63 (1) 239 (2025)
https://doi.org/10.1137/23M1616844

Reduced basis method for the elastic scattering by multiple shape-parametric open arcs in two dimensions

José Pinto and Fernando Henríquez
ESAIM: Mathematical Modelling and Numerical Analysis 59 (1) 201 (2025)
https://doi.org/10.1051/m2an/2024078

Deflation-based certified greedy algorithm and adaptivity for bifurcating nonlinear PDEs

Federico Pichi and Maria Strazzullo
Communications in Nonlinear Science and Numerical Simulation 149 108941 (2025)
https://doi.org/10.1016/j.cnsns.2025.108941

An ensemble-based efficient iterative method for uncertainty quantification of partial differential equations with random inputs

Yuming Ba, Qiuqi Li, Zehua Li and Lingling Ma
Computers & Mathematics with Applications 182 256 (2025)
https://doi.org/10.1016/j.camwa.2025.02.001

The Kolmogorov N-width for linear transport: exact representation and the influence of the data

Florian Arbes, Constantin Greif and Karsten Urban
Advances in Computational Mathematics 51 (2) (2025)
https://doi.org/10.1007/s10444-025-10224-0

POD-Galerkin reduced order model coupled with neural networks to solve flow in porous media

C. Allery, C. Béghein, C. Dubot and F. Dubot
Journal of Computational Science 84 102471 (2025)
https://doi.org/10.1016/j.jocs.2024.102471

Ruminated Tensor Decomposition algorithm for solving inviscid Burgers' equation

Shaoqiang Tang and Hongjian Xu
Journal of Computational Physics 523 113663 (2025)
https://doi.org/10.1016/j.jcp.2024.113663

A greedy sensor selection algorithm for hyperparameterized linear Bayesian inverse problems with correlated noise models

Nicole Aretz, Peng Chen, Denise Degen and Karen Veroy
Journal of Computational Physics 498 112599 (2024)
https://doi.org/10.1016/j.jcp.2023.112599

Model order reduction and sensitivity analysis for complex heat transfer simulations inside the human eyeball

Thomas Saigre, Christophe Prud'homme and Marcela Szopos
International Journal for Numerical Methods in Biomedical Engineering 40 (11) (2024)
https://doi.org/10.1002/cnm.3864

Reduced basis homogenization of thermal and elastic properties for periodic composite materials

Quang Xuan Pham and Kyunghoon Lee
International Journal of Mechanical Sciences 109801 (2024)
https://doi.org/10.1016/j.ijmecsci.2024.109801

A Reduced Conjugate Gradient Basis Method for Fractional Diffusion

Yuwen Li, Ludmil Zikatanov and Cheng Zuo
SIAM Journal on Scientific Computing 46 (5) S68 (2024)
https://doi.org/10.1137/23M1575913

A locally adaptive non-intrusive block reduced basis method for scattering applications using the boundary element method

P. Edel and J. Simon
Computer Methods in Applied Mechanics and Engineering 421 116830 (2024)
https://doi.org/10.1016/j.cma.2024.116830

TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs

Yanlai Chen, Yajie Ji, Akil Narayan and Zhenli Xu
Computer Methods in Applied Mechanics and Engineering 430 117198 (2024)
https://doi.org/10.1016/j.cma.2024.117198

Influence of sampling on the convergence rates of greedy algorithms for parameter-dependent random variables

Mohamed-Raed Blel, Virginie Ehrlacher and Tony Lelièvre
Mathematics of Computation (2024)
https://doi.org/10.1090/mcom/3979

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Francesco Regazzoni, Stefano Pagani, Matteo Salvador, Luca Dede’ and Alfio Quarteroni
Nature Communications 15 (1) (2024)
https://doi.org/10.1038/s41467-024-45323-x

A reduced basis method for frictional contact problems formulated with Nitsche’s method

Idrissa Niakh, Guillaume Drouet, Virginie Ehrlacher and Alexandre Ern
The SMAI Journal of computational mathematics 10 29 (2024)
https://doi.org/10.5802/smai-jcm.105

A probabilistic reduced basis method for parameter-dependent problems

Marie Billaud-Friess, Arthur Macherey, Anthony Nouy and Clémentine Prieur
Advances in Computational Mathematics 50 (2) (2024)
https://doi.org/10.1007/s10444-024-10114-x

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Niccolò Discacciati and Jan S. Hesthaven
Computer Methods in Applied Mechanics and Engineering 420 116770 (2024)
https://doi.org/10.1016/j.cma.2024.116770

A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems

Francesca Bonizzoni, Moritz Hauck and Daniel Peterseim
Journal of Computational Physics 499 112698 (2024)
https://doi.org/10.1016/j.jcp.2023.112698

A projection‐based reduced‐order model for parametric quasi‐static nonlinear mechanics using an open‐source industrial code

Eki Agouzal, Jean‐Philippe Argaud, Michel Bergmann, Guilhem Ferté and Tommaso Taddei
International Journal for Numerical Methods in Engineering 125 (4) (2024)
https://doi.org/10.1002/nme.7385

Data-driven structure-preserving model reduction for stochastic Hamiltonian systems

Tomasz M. Tyranowski
Journal of Computational Dynamics (2024)
https://doi.org/10.3934/jcd.2024010

Accurate error estimation for model reduction of nonlinear dynamical systems via data-enhanced error closure

Sridhar Chellappa, Lihong Feng and Peter Benner
Computer Methods in Applied Mechanics and Engineering 420 116712 (2024)
https://doi.org/10.1016/j.cma.2023.116712

Reduced order modeling for elliptic problems with high contrast diffusion coefficients

Albert Cohen, Wolfgang Dahmen, Matthieu Dolbeault and Agustin Somacal
ESAIM: Mathematical Modelling and Numerical Analysis 57 (5) 2775 (2023)
https://doi.org/10.1051/m2an/2023013

An automated parameter domain decomposition approach for gravitational wave surrogates using hp-greedy refinement

Franco Cerino, J Andrés Diaz-Pace and Manuel Tiglio
Classical and Quantum Gravity 40 (20) 205003 (2023)
https://doi.org/10.1088/1361-6382/acf4e7

An Adaptive Model Reduction Method Leveraging Locally Supported Basis Functions

Han Gao and Matthew J. Zahr
International Journal of Computational Fluid Dynamics 37 (6) 451 (2023)
https://doi.org/10.1080/10618562.2024.2326553

Evaluation of the iterative method of task distribution in a swarm of unmanned aerial vehicles in a clustered field of targets

Vyacheslav Petrenko, Fariza Tebueva, Vladimir Antonov, Sergey Ryabtsev, Artur Sakolchik and Dina Satybaldina
Journal of King Saud University - Computer and Information Sciences 35 (3) 283 (2023)
https://doi.org/10.1016/j.jksuci.2023.02.022

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)
https://doi.org/10.1016/j.jcp.2022.111739

Optimal Reduced Basis Method for Aeroacoustics with Impedance Boundary Conditions

Rémi Roncen, Philip Edel and Christophe Peyret
AIAA Journal 61 (2) 640 (2023)
https://doi.org/10.2514/1.J062138

Stabilization of Generalized Empirical Interpolation Method (GEIM) in presence of noise: A novel approach based on Tikhonov regularization

Carolina Introini, Simone Cavalleri, Stefano Lorenzi, Stefano Riva and Antonio Cammi
Computer Methods in Applied Mechanics and Engineering 404 115773 (2023)
https://doi.org/10.1016/j.cma.2022.115773

Error estimate of the Non-Intrusive Reduced Basis (NIRB) two-grid method with parabolic equations

Elise Grosjean and Yvon Maday
The SMAI Journal of computational mathematics 9 227 (2023)
https://doi.org/10.5802/smai-jcm.100

Localized model order reduction and domain decomposition methods for coupled heterogeneous systems

Niccolò Discacciati and Jan S. Hesthaven
International Journal for Numerical Methods in Engineering 124 (18) 3964 (2023)
https://doi.org/10.1002/nme.7295

An iterative multi‐fidelity approach for model order reduction of multidimensional input parametric PDE systems

Manisha Chetry, Domenico Borzacchiello, Lucas Lestandi and Luisa Rocha Da Silva
International Journal for Numerical Methods in Engineering 124 (22) 4941 (2023)
https://doi.org/10.1002/nme.7333

Multi‐fidelity error estimation accelerates greedy model reduction of complex dynamical systems

Lihong Feng, Luigi Lombardi, Giulio Antonini and Peter Benner
International Journal for Numerical Methods in Engineering 124 (23) 5312 (2023)
https://doi.org/10.1002/nme.7348

Bayes goes fast: Uncertainty quantification for a covariant energy density functional emulated by the reduced basis method

Pablo Giuliani, Kyle Godbey, Edgard Bonilla, Frederi Viens and Jorge Piekarewicz
Frontiers in Physics 10 (2023)
https://doi.org/10.3389/fphy.2022.1054524

Exponential tractability of L2-approximation with function values

David Krieg, Paweł Siedlecki, Mario Ullrich and Henryk Woźniakowski
Advances in Computational Mathematics 49 (2) (2023)
https://doi.org/10.1007/s10444-023-10021-7

Evaluation of dual-weighted residual and machine learning error estimation for projection-based reduced-order models of steady partial differential equations

Patrick J. Blonigan and Eric J. Parish
Computer Methods in Applied Mechanics and Engineering 409 115988 (2023)
https://doi.org/10.1016/j.cma.2023.115988

A learning-based projection method for model order reduction of transport problems

Zhichao Peng, Min Wang and Fengyan Li
Journal of Computational and Applied Mathematics 418 114560 (2023)
https://doi.org/10.1016/j.cam.2022.114560

Projection-tree reduced-order modeling for fast N-body computations

Steven N. Rodriguez, Athanasios P. Iliopoulos, Kevin T. Carlberg, et al.
Journal of Computational Physics 459 111141 (2022)
https://doi.org/10.1016/j.jcp.2022.111141

An Efficient QSC Approximation of Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations with Variably Diffusive Coefficients

Jun Liu and Hongfei Fu
Journal of Scientific Computing 93 (2) (2022)
https://doi.org/10.1007/s10915-022-02007-2

Quadratic approximation manifold for mitigating the Kolmogorov barrier in nonlinear projection-based model order reduction

Joshua Barnett and Charbel Farhat
Journal of Computational Physics 464 111348 (2022)
https://doi.org/10.1016/j.jcp.2022.111348

AMS-Net: Adaptive Multiscale Sparse Neural Network with Interpretable Basis Expansion for Multiphase Flow Problems

Yating Wang, Wing Tat Leung and Guang Lin
Multiscale Modeling & Simulation 20 (2) 618 (2022)
https://doi.org/10.1137/21M1405289

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, et al.
Advances in Water Resources 166 104260 (2022)
https://doi.org/10.1016/j.advwatres.2022.104260

Linear/Ridge expansions: enhancing linear approximations by ridge functions

Constantin Greif, Philipp Junk and Karsten Urban
Advances in Computational Mathematics 48 (3) (2022)
https://doi.org/10.1007/s10444-022-09936-4

State Estimation with Model Reduction and Shape Variability. Application to biomedical problems

Felipe Galarce, Damiano Lombardi and Olga Mula
SIAM Journal on Scientific Computing 44 (3) B805 (2022)
https://doi.org/10.1137/21M1430480

Recent Advances in Industrial and Applied Mathematics

Albert Cohen, Wolfgang Dahmen and Ron DeVore
SEMA SIMAI Springer Series, Recent Advances in Industrial and Applied Mathematics 1 57 (2022)
https://doi.org/10.1007/978-3-030-86236-7_4

Non-Smooth and Complementarity-Based Distributed Parameter Systems

Stefan Banholzer, Bennet Gebken, Michael Dellnitz, Sebastian Peitz and Stefan Volkwein
International Series of Numerical Mathematics, Non-Smooth and Complementarity-Based Distributed Parameter Systems 172 43 (2022)
https://doi.org/10.1007/978-3-030-79393-7_3

Optimal and fast field reconstruction with reduced basis and limited observations: Application to reactor core online monitoring

Helin Gong, Zhang Chen, Yvon Maday and Qing Li
Nuclear Engineering and Design 377 111113 (2021)
https://doi.org/10.1016/j.nucengdes.2021.111113

On the stability and accuracy of the empirical interpolation method and gravitational wave surrogates

Manuel Tiglio and Aarón Villanueva
Classical and Quantum Gravity 38 (13) 135011 (2021)
https://doi.org/10.1088/1361-6382/abf894

A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence

Christopher Jelich, Suhaib Koji Baydoun, Matthias Voigt and Steffen Marburg
International Journal for Numerical Methods in Engineering 122 (24) 7409 (2021)
https://doi.org/10.1002/nme.6835

Generalization of the Neville–Aitken interpolation algorithm on Grassmann manifolds: Applications to reduced order model

Rolando Mosquera, Abdallah El Hamidi, Aziz Hamdouni and Antoine Falaize
International Journal for Numerical Methods in Fluids 93 (7) 2421 (2021)
https://doi.org/10.1002/fld.4981

Error estimate of the non-intrusive reduced basis method with finite volume schemes

Elise Grosjean and Yvon Maday
ESAIM: Mathematical Modelling and Numerical Analysis 55 (5) 1941 (2021)
https://doi.org/10.1051/m2an/2021044

Hierarchical Model Reduction Techniques for Flow Modeling in a Parametrized Setting

Matteo Zancanaro, Francesco Ballarin, Simona Perotto and Gianluigi Rozza
Multiscale Modeling & Simulation 19 (1) 267 (2021)
https://doi.org/10.1137/19M1285330

An Automatic Krylov subspaces Recycling technique for the construction of a global solution basis of non-affine parametric linear systems

Dionysios Panagiotopoulos, Wim Desmet and Elke Deckers
Computer Methods in Applied Mechanics and Engineering 373 113510 (2021)
https://doi.org/10.1016/j.cma.2020.113510

Application of ANN for prediction of chloride penetration resistance and concrete compressive strength

Osama Mohamed, Manish Kewalramani, Modafar Ati and Waddah Al Hawat
Materialia 17 101123 (2021)
https://doi.org/10.1016/j.mtla.2021.101123

A novel class of stabilized greedy kernel approximation algorithms: Convergence, stability and uniform point distribution

Tizian Wenzel, Gabriele Santin and Bernard Haasdonk
Journal of Approximation Theory 262 105508 (2021)
https://doi.org/10.1016/j.jat.2020.105508

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

Suhaib Koji Baydoun, Matthias Voigt, Christopher Jelich and Steffen Marburg
International Journal for Numerical Methods in Engineering 121 (2) 187 (2020)
https://doi.org/10.1002/nme.6205

Reduced Basis Greedy Selection Using Random Training Sets

Albert Cohen, Wolfgang Dahmen, Ronald DeVore and James Nichols
ESAIM: Mathematical Modelling and Numerical Analysis 54 (5) 1509 (2020)
https://doi.org/10.1051/m2an/2020004

Integration of moment equations in a reduced-order modeling strategy for Monte Carlo simulations of groundwater flow

Chuan-An Xia, Damiano Pasetto, Bill X. Hu, Mario Putti and Alberto Guadagnini
Journal of Hydrology 590 125257 (2020)
https://doi.org/10.1016/j.jhydrol.2020.125257

A Variable-Separation Method for Nonlinear Partial Differential Equations With Random Inputs

Qiuqi Li and Pingwen Zhang
SIAM Journal on Scientific Computing 42 (2) A723 (2020)
https://doi.org/10.1137/19M1262486

Optimal Reduced Model Algorithms for Data-Based State Estimation

Albert Cohen, Wolfgang Dahmen, Ronald DeVore, et al.
SIAM Journal on Numerical Analysis 58 (6) 3355 (2020)
https://doi.org/10.1137/19M1255185

Reduced basis approximations of the solutions to spectral fractional diffusion problems

Andrea Bonito, Diane Guignard and Ashley R. Zhang
Journal of Numerical Mathematics 28 (3) 147 (2020)
https://doi.org/10.1515/jnma-2019-0053

Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

Olena Burkovska and Max Gunzburger
SIAM Journal on Numerical Analysis 58 (3) 1469 (2020)
https://doi.org/10.1137/19M124321X

Multilevel a posteriori error estimator for greedy reduced basis algorithms

Marta Čertíková, Liya Gaynutdinova and Ivana Pultarová
SN Applied Sciences 2 (4) (2020)
https://doi.org/10.1007/s42452-020-2409-9

Gaussian Process Landmarking on Manifolds

Tingran Gao, Shahar Z. Kovalsky and Ingrid Daubechies
SIAM Journal on Mathematics of Data Science 1 (1) 208 (2019)
https://doi.org/10.1137/18M1184035

Nonintrusive approximation of parametrized limits of matrix power algorithms – application to matrix inverses and log-determinants

Fabien Casenave, Nissrine Akkari, Alexandre Charles and Christian Rey
ESAIM: Mathematical Modelling and Numerical Analysis 53 (1) 219 (2019)
https://doi.org/10.1051/m2an/2018048

Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

Qian Wang, Jan S. Hesthaven and Deep Ray
Journal of Computational Physics 384 289 (2019)
https://doi.org/10.1016/j.jcp.2019.01.031

A hierarchical a posteriori error estimator for the Reduced Basis Method

Stefan Hain, Mario Ohlberger, Mladjan Radic and Karsten Urban
Advances in Computational Mathematics 45 (5-6) 2191 (2019)
https://doi.org/10.1007/s10444-019-09675-z

A Reduced Generalized Multiscale Basis Method for Parametrized Groundwater Flow Problems in Heterogeneous Porous Media

Xinguang He, Qiuqi Li and Lijian Jiang
Water Resources Research 55 (3) 2390 (2019)
https://doi.org/10.1029/2018WR023954

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)
https://doi.org/10.1007/s41980-019-00210-w

Greedy optimal control for elliptic problems and its application to turnpike problems

Víctor Hernández-Santamaría, Martin Lazar and Enrique Zuazua
Numerische Mathematik 141 (2) 455 (2019)
https://doi.org/10.1007/s00211-018-1005-z

A non-intrusive reduced basis approach for parametrized heat transfer problems

R. Chakir, Y. Maday and P. Parnaudeau
Journal of Computational Physics 376 617 (2019)
https://doi.org/10.1016/j.jcp.2018.10.001