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:

On the computation of intrinsic Proper Generalized Decomposition modes of parametric symmetric elliptic problems on Grassmann manifolds

Alejandro Bandera, Soledad Fernández-García and Macarena Gómez-Mármol
Applied Mathematics and Computation 470 128579 (2024)
https://doi.org/10.1016/j.amc.2024.128579

Automatic Proper Orthogonal Block Decomposition method for network dynamical systems with multiple timescales

A. Bandera, S. Fernández-García, M. Gómez-Mármol and A. Vidal
Communications in Nonlinear Science and Numerical Simulation 131 107844 (2024)
https://doi.org/10.1016/j.cnsns.2024.107844

Dual-grid mapping method for the advection-diffusion-reaction equation in a heterogeneous medium

Dylan J. Oliver, Ian W. Turner and Elliot J. Carr
Computers & Mathematics with Applications 154 78 (2024)
https://doi.org/10.1016/j.camwa.2023.11.021

A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE

Fabian Hoppe and Ira Neitzel
Computational Optimization and Applications 87 (3) 755 (2024)
https://doi.org/10.1007/s10589-021-00299-y

Data driven three-dimensional temperature and salinity anomaly reconstruction of the northwest Pacific Ocean

Yuanhong Chen, Li Liu, Xueen Chen, et al.
Frontiers in Marine Science 10 (2023)
https://doi.org/10.3389/fmars.2023.1121334

A new approach to proper orthogonal decomposition with difference quotients

Sarah Locke Eskew and John R. Singler
Advances in Computational Mathematics 49 (2) (2023)
https://doi.org/10.1007/s10444-023-10011-9

POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution

Bosco García-Archilla, Volker John and Julia Novo
SIAM Journal on Numerical Analysis 61 (3) 1340 (2023)
https://doi.org/10.1137/22M1503853

A multiple timescale network model of intracellular calcium concentrations in coupled neurons: Insights from ROM simulations

A. Bandera, S. Fernández-García, M. Gómez-Mármol, et al.
Mathematical Modelling of Natural Phenomena 17 11 (2022)
https://doi.org/10.1051/mmnp/2022016

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)
https://doi.org/10.1137/20M1371798

A cure for instabilities due to advection-dominance in POD solution to advection-diffusion-reaction equations

Mejdi Azaïez, Tomás Chacón Rebollo and Samuele Rubino
Journal of Computational Physics 425 109916 (2021)
https://doi.org/10.1016/j.jcp.2020.109916

New Proper Orthogonal Decomposition Approximation Theory for PDE Solution Data

Sarah Locke and John Singler
SIAM Journal on Numerical Analysis 58 (6) 3251 (2020)
https://doi.org/10.1137/19M1297002

HDG–POD reduced order model of the heat equation

Jiguang Shen, John R. Singler and Yangwen Zhang
Journal of Computational and Applied Mathematics 362 663 (2019)
https://doi.org/10.1016/j.cam.2018.09.031

Numerical analysis of the Leray reduced order model

Xuping Xie, David Wells, Zhu Wang and Traian Iliescu
Journal of Computational and Applied Mathematics 328 12 (2018)
https://doi.org/10.1016/j.cam.2017.06.026

Mathematical and Numerical Modeling of the Cardiovascular System and Applications

Andrea Manzoni, Diana Bonomi and Alfio Quarteroni
SEMA SIMAI Springer Series, Mathematical and Numerical Modeling of the Cardiovascular System and Applications 16 115 (2018)
https://doi.org/10.1007/978-3-319-96649-6_6

Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method

Stefano Pagani, Andrea Manzoni and Alfio Quarteroni
Computer Methods in Applied Mechanics and Engineering 340 530 (2018)
https://doi.org/10.1016/j.cma.2018.06.003

On Structure-Preserving Model Reduction for Damped Wave Propagation in Transport Networks

H. Egger, T. Kugler, B. Liljegren-Sailer, N. Marheineke and V. Mehrmann
SIAM Journal on Scientific Computing 40 (1) A331 (2018)
https://doi.org/10.1137/17M1125303

Model reduction of dynamical systems by proper orthogonal decomposition: Error bounds and comparison of methods using snapshots from the solution and the time derivatives

Tanya Kostova-Vassilevska and Geoffrey M. Oxberry
Journal of Computational and Applied Mathematics 330 553 (2018)
https://doi.org/10.1016/j.cam.2017.09.001

Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation

Shengfeng Zhu, Luca Dedè and Alfio Quarteroni
ESAIM: Mathematical Modelling and Numerical Analysis 51 (4) 1197 (2017)
https://doi.org/10.1051/m2an/2016056

An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier--Stokes Equations

Max Gunzburger, Nan Jiang and Michael Schneier
SIAM Journal on Numerical Analysis 55 (1) 286 (2017)
https://doi.org/10.1137/16M1056444

Isogeometric analysis and proper orthogonal decomposition for parabolic problems

Shengfeng Zhu, Luca Dedè and Alfio Quarteroni
Numerische Mathematik 135 (2) 333 (2017)
https://doi.org/10.1007/s00211-016-0802-5

Error Analysis for POD Approximations of Infinite Horizon Problems via the Dynamic Programming Approach

A. Alla, M. Falcone and S. Volkwein
SIAM Journal on Control and Optimization 55 (5) 3091 (2017)
https://doi.org/10.1137/15M1039596

Energy balance and mass conservation in reduced order models of fluid flows

Muhammad Mohebujjaman, Leo G. Rebholz, Xuping Xie and Traian Iliescu
Journal of Computational Physics 346 262 (2017)
https://doi.org/10.1016/j.jcp.2017.06.019

Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology

Cesare Corrado, Jamila Lassoued, Moncef Mahjoub and Néjib Zemzemi
Mathematical Biosciences 272 81 (2016)
https://doi.org/10.1016/j.mbs.2015.12.005

A posteriori error 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)
https://doi.org/10.1002/nme.4753

Recent Trends in Computational Engineering - CE2014

Eva Grimm, Martin Gubisch and Stefan Volkwein
Lecture Notes in Computational Science and Engineering, Recent Trends in Computational Engineering - CE2014 105 297 (2015)
https://doi.org/10.1007/978-3-319-22997-3_18

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)
https://doi.org/10.1002/num.21961

Uniform convergence of the POD method and applications to optimal control

Karl Kunisch and Markus Müller
Discrete & Continuous Dynamical Systems - A 35 (9) 4477 (2015)
https://doi.org/10.3934/dcds.2015.35.4477

New POD Error Expressions, Error Bounds, and Asymptotic Results for Reduced Order Models of Parabolic PDEs

John R. Singler
SIAM Journal on Numerical Analysis 52 (2) 852 (2014)
https://doi.org/10.1137/120886947

Fluid-Structure Interaction and Biomedical Applications

Luca Bertagna, Marta D’Elia, Mauro Perego and Alessandro Veneziani
Advances in Mathematical Fluid Mechanics, Fluid-Structure Interaction and Biomedical Applications 395 (2014)
https://doi.org/10.1007/978-3-0348-0822-4_6

Variational multiscale proper orthogonal decomposition: Navier‐stokes equations

Traian Iliescu and Zhu Wang
Numerical Methods for Partial Differential Equations 30 (2) 641 (2014)
https://doi.org/10.1002/num.21835

Are the Snapshot Difference Quotients Needed in the Proper Orthogonal Decomposition?

Traian Iliescu and Zhu Wang
SIAM Journal on Scientific Computing 36 (3) A1221 (2014)
https://doi.org/10.1137/130925141

Trends in PDE Constrained Optimization

Peter Benner, Ekkehard Sachs and Stefan Volkwein
International Series of Numerical Mathematics, Trends in PDE Constrained Optimization 165 303 (2014)
https://doi.org/10.1007/978-3-319-05083-6_19

A Galerkin strategy with Proper Orthogonal Decomposition for parameter-dependent problems – Analysis, assessments and applications to parameter estimation

D. Chapelle, A. Gariah, P. Moireau and J. Sainte-Marie
ESAIM: Mathematical Modelling and Numerical Analysis 47 (6) 1821 (2013)
https://doi.org/10.1051/m2an/2013090

Derivative-Extended POD Reduced-Order Modeling for Parameter Estimation

A. Schmidt, A. Potschka, S. Körkel and H. G. Bock
SIAM Journal on Scientific Computing 35 (6) A2696 (2013)
https://doi.org/10.1137/120896694