A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems
ESAIM: M2AN, 48 6 (2014) 1777-1806
Published online: 2014-10-03
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 low-rank solver for conforming multipatch Isogeometric Analysis
Monica Montardini, Giancarlo Sangalli and Mattia TaniComputers & Mathematics with Applications 189 86 (2025)
https://doi.org/10.1016/j.camwa.2025.03.036
Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning
Luis Mandl, Somdatta Goswami, Lena Lambers and Tim RickenComputer Methods in Applied Mechanics and Engineering 434 117586 (2025)
https://doi.org/10.1016/j.cma.2024.117586
PGD reduced-order modeling for structural dynamics applications
Clément Vella and Serge PrudhommeComputer Methods in Applied Mechanics and Engineering 402 115736 (2022)
https://doi.org/10.1016/j.cma.2022.115736
Stable and Efficient Petrov--Galerkin Methods for a Kinetic Fokker--Planck Equation
Julia Brunken and Kathrin SmetanaSIAM Journal on Numerical Analysis 60 (1) 157 (2022)
https://doi.org/10.1137/20M1374857
Modified Iterations for Data-Sparse Solution of Linear Systems
Wolfgang Hackbusch and André UschmajewVietnam Journal of Mathematics 49 (2) 493 (2021)
https://doi.org/10.1007/s10013-021-00504-9
Data-free likelihood-informed dimension reduction of Bayesian inverse problems
Tiangang Cui and Olivier ZahmInverse Problems 37 (4) 045009 (2021)
https://doi.org/10.1088/1361-6420/abeafb
Randomized residual‐based error estimators for the proper generalized decomposition approximation of parametrized problems
Kathrin Smetana and Olivier ZahmInternational Journal for Numerical Methods in Engineering 121 (23) 5153 (2020)
https://doi.org/10.1002/nme.6339
Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods
Ignacio Muga and Kristoffer G. van der ZeeSIAM Journal on Numerical Analysis 58 (6) 3406 (2020)
https://doi.org/10.1137/20M1324338
HT-AWGM: a hierarchical Tucker–adaptive wavelet Galerkin method for high-dimensional elliptic problems
Mazen Ali and Karsten UrbanAdvances in Computational Mathematics 46 (4) (2020)
https://doi.org/10.1007/s10444-020-09797-9
Tensor Representation of Non-linear Models Using Cross Approximations
José V. Aguado, Domenico Borzacchiello, Kiran S. Kollepara, Francisco Chinesta and Antonio HuertaJournal of Scientific Computing 81 (1) 22 (2019)
https://doi.org/10.1007/s10915-019-00917-2
On a Goal-Oriented Version of the Proper Generalized Decomposition Method
Kenan Kergrene, Ludovic Chamoin, Marc Laforest and Serge PrudhommeJournal of Scientific Computing 81 (1) 92 (2019)
https://doi.org/10.1007/s10915-019-00918-1
Advances in Computational Plasticity
P. Ladevèze, Ch. Paillet and D. NéronComputational Methods in Applied Sciences, Advances in Computational Plasticity 46 201 (2018)
https://doi.org/10.1007/978-3-319-60885-3_10
Reduced-order model of optimal temperature control for the automated fibre placement process
Nicolas Bur, Pierre Joyot and Pierre VillonComptes Rendus. Mécanique 346 (7) 556 (2018)
https://doi.org/10.1016/j.crme.2018.04.007
The Optimization Landscape for Fitting a Rank-2 Tensor with a Rank-1 Tensor
Xue Gong, Martin J. Mohlenkamp and Todd R. YoungSIAM Journal on Applied Dynamical Systems 17 (2) 1432 (2018)
https://doi.org/10.1137/17M112213X
A parametric and non-intrusive reduced order model of car crash simulation
Y. Le Guennec, J.-P. Brunet, F.-Z. Daim, M. Chau and Y. TourbierComputer Methods in Applied Mechanics and Engineering 338 186 (2018)
https://doi.org/10.1016/j.cma.2018.03.005
A door to model reduction in high-dimensional parameter space
Charles Paillet, David Néron and Pierre LadevèzeComptes Rendus. Mécanique 346 (7) 524 (2018)
https://doi.org/10.1016/j.crme.2018.04.009
1 (2017)
https://doi.org/10.1002/9781119176817.ecm2110
Least-Squares Proper Generalized Decompositions for Weakly Coercive Elliptic Problems
Thomas L. D. Croft and Timothy N. PhillipsSIAM Journal on Scientific Computing 39 (4) A1366 (2017)
https://doi.org/10.1137/15M1049269
Iterative Methods Based on Soft Thresholding of Hierarchical Tensors
Markus Bachmayr and Reinhold SchneiderFoundations of Computational Mathematics 17 (4) 1037 (2017)
https://doi.org/10.1007/s10208-016-9314-z
Adaptive Low-Rank Methods: Problems on Sobolev Spaces
Markus Bachmayr and Wolfgang DahmenSIAM Journal on Numerical Analysis 54 (2) 744 (2016)
https://doi.org/10.1137/140978223
Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations
Markus Bachmayr, Reinhold Schneider and André UschmajewFoundations of Computational Mathematics 16 (6) 1423 (2016)
https://doi.org/10.1007/s10208-016-9317-9
Calculating vibrational spectra of molecules using tensor train decomposition
Maxim Rakhuba and Ivan OseledetsThe Journal of Chemical Physics 145 (12) (2016)
https://doi.org/10.1063/1.4962420
Adaptive low-rank methods for problems on Sobolev spaces with error control in L2
M. Bachmayr and W. DahmenESAIM: Mathematical Modelling and Numerical Analysis 50 (4) 1107 (2016)
https://doi.org/10.1051/m2an/2015071
Application of PGD on Parametric Modeling of a Piezoelectric Energy Harvester
Zhi Qin, Hakeim Talleb, Shuai Yan, Xiaoyu Xu and Zhuoxiang RenIEEE Transactions on Magnetics 52 (11) 1 (2016)
https://doi.org/10.1109/TMAG.2016.2591001