Klein, R. B.; Sanderse, B. Energy-conserving hyper-reduction and temporal localization for reduced order models of the incompressible Navier-Stokes equations. (English) Zbl 07819050 J. Comput. Phys. 499, Article ID 112697, 33 p. (2024). MSC: 65Mxx 76Mxx 65Lxx PDFBibTeX XMLCite \textit{R. B. Klein} and \textit{B. Sanderse}, J. Comput. Phys. 499, Article ID 112697, 33 p. (2024; Zbl 07819050) Full Text: DOI
Wu, Zhizhang; Zhang, Cheng; Zhang, Zhiwen Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems. (English) Zbl 07797178 J. Comput. Appl. Math. 441, Article ID 115659, 17 p. (2024). MSC: 35R30 35J25 35R60 62F15 68T07 78M34 PDFBibTeX XMLCite \textit{Z. Wu} et al., J. Comput. Appl. Math. 441, Article ID 115659, 17 p. (2024; Zbl 07797178) Full Text: DOI
Fu, R.; Xiao, D.; Navon, I. M.; Fang, F.; Yang, L.; Wang, C.; Cheng, S. A non-linear non-intrusive reduced order model of fluid flow by auto-encoder and self-attention deep learning methods. (English) Zbl 1524.76277 Int. J. Numer. Methods Eng. 124, No. 13, 3087-3111 (2023). MSC: 76M22 PDFBibTeX XMLCite \textit{R. Fu} et al., Int. J. Numer. Methods Eng. 124, No. 13, 3087--3111 (2023; Zbl 1524.76277) Full Text: DOI
Pagliantini, Cecilia; Vismara, Federico Gradient-preserving hyper-reduction of nonlinear dynamical systems via discrete empirical interpolation. (English) Zbl 1526.65057 SIAM J. Sci. Comput. 45, No. 5, A2725-A2754 (2023). MSC: 65P10 37N30 65L99 PDFBibTeX XMLCite \textit{C. Pagliantini} and \textit{F. Vismara}, SIAM J. Sci. Comput. 45, No. 5, A2725--A2754 (2023; Zbl 1526.65057) Full Text: DOI arXiv
Abbaszadeh, Mostafa; Azis, Mohammad Ivan; Dehghan, Mehdi; Mohammadi-Arani, Reza Reduced order model for simulation of air pollution model and application in 2D urban street canyons via the meshfree gradient smoothing method. (English) Zbl 07692044 Comput. Math. Appl. 140, 195-210 (2023). MSC: 76M25 76D05 76M12 65M06 76M20 PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., Comput. Math. Appl. 140, 195--210 (2023; Zbl 07692044) Full Text: DOI
Stoter, Stein K. F.; Jessen, Etienne; Niedens, Viktor; Schillinger, Dominik A DEIM driven reduced basis method for the diffuse Stokes/Darcy model coupled at parametric phase-field interfaces. (English) Zbl 1502.86003 Comput. Geosci. 26, No. 6, 1465-1502 (2022). MSC: 86-10 86A32 76S05 PDFBibTeX XMLCite \textit{S. K. F. Stoter} et al., Comput. Geosci. 26, No. 6, 1465--1502 (2022; Zbl 1502.86003) Full Text: DOI arXiv
Li, Xi; Luo, Yan; Feng, Minfu An efficient Chorin-Temam projection proper orthogonal decomposition based reduced-order model for nonstationary Stokes equations. (English) Zbl 1503.65239 J. Sci. Comput. 93, No. 3, Paper No. 64, 26 p. (2022). MSC: 65M60 65M06 65N30 65M12 65M15 76D07 76M10 35Q30 PDFBibTeX XMLCite \textit{X. Li} et al., J. Sci. Comput. 93, No. 3, Paper No. 64, 26 p. (2022; Zbl 1503.65239) Full Text: DOI arXiv
Mohammadi, Vahid; Dehghan, Mehdi A POD-RBF-FD scheme for simulating chemotaxis models on surfaces. (English) Zbl 1521.92008 Eng. Anal. Bound. Elem. 143, 316-330 (2022). MSC: 92-08 65M06 35Q35 35Q92 65D12 92C17 PDFBibTeX XMLCite \textit{V. Mohammadi} and \textit{M. Dehghan}, Eng. Anal. Bound. Elem. 143, 316--330 (2022; Zbl 1521.92008) Full Text: DOI
Banagaaya, Nicodemus; Alì, Giuseppe; Grundel, Sara; Benner, Peter Index-aware model-order reduction for a special class of nonlinear differential-algebraic equations. (English) Zbl 1519.93041 J. Dyn. Differ. Equations 34, No. 3, 2465-2489 (2022). MSC: 93B11 93C10 93C15 34A09 34A34 76N15 PDFBibTeX XMLCite \textit{N. Banagaaya} et al., J. Dyn. Differ. Equations 34, No. 3, 2465--2489 (2022; Zbl 1519.93041) Full Text: DOI arXiv
MohammadiArani, Reza; Dehghan, Mehdi; Abbaszadeh, Mostafa Proper orthogonal decomposition-lattice Boltzmann method: simulating the air pollutant problem in street canyon areas. (English) Zbl 1492.76097 SIAM J. Sci. Comput. 44, No. 4, B885-B909 (2022). MSC: 76N15 65M22 76M28 PDFBibTeX XMLCite \textit{R. MohammadiArani} et al., SIAM J. Sci. Comput. 44, No. 4, B885--B909 (2022; Zbl 1492.76097) Full Text: DOI
Liljegren-Sailer, Björn; Marheineke, Nicole On snapshot-based model reduction under compatibility conditions for a nonlinear flow problem on networks. (English) Zbl 07568382 J. Sci. Comput. 92, No. 2, Paper No. 62, 30 p. (2022). MSC: 65-XX 35L60 35R02 65N12 PDFBibTeX XMLCite \textit{B. Liljegren-Sailer} and \textit{N. Marheineke}, J. Sci. Comput. 92, No. 2, Paper No. 62, 30 p. (2022; Zbl 07568382) Full Text: DOI arXiv
Saffarian, Marziyeh; Mohebbi, Akbar Reduced proper orthogonal decomposition spectral element method for the solution of 2D multi-term time fractional mixed diffusion and diffusion-wave equations in linear and nonlinear modes. (English) Zbl 1524.65681 Comput. Math. Appl. 117, 127-154 (2022). MSC: 65M70 65M06 35R11 65M12 65M60 26A33 65M99 65N35 PDFBibTeX XMLCite \textit{M. Saffarian} and \textit{A. Mohebbi}, Comput. Math. Appl. 117, 127--154 (2022; Zbl 1524.65681) Full Text: DOI
Bai, Feng; Wang, Yi A reduced order modeling method based on GNAT-embedded hybrid snapshot simulation. (English) Zbl 07538452 Math. Comput. Simul. 199, 100-132 (2022). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{F. Bai} and \textit{Y. Wang}, Math. Comput. Simul. 199, 100--132 (2022; Zbl 07538452) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi; Khodadadian, Amirreza; Noii, Nima; Heitzinger, Clemens; Wick, Thomas A reduced-order variational multiscale interpolating element free Galerkin technique based on proper orthogonal decomposition for solving Navier-Stokes equations coupled with a heat transfer equation: nonstationary incompressible Boussinesq equations. (English) Zbl 07510038 J. Comput. Phys. 426, Article ID 109875, 27 p. (2021). MSC: 80-XX 65-XX PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., J. Comput. Phys. 426, Article ID 109875, 27 p. (2021; Zbl 07510038) Full Text: DOI
Rungpitaxmana, Suchinthra; Chaturantabut, Saifon Model reduction for Fisher’s equation with an error bound. (English) Zbl 1482.65108 Thai J. Math. 19, No. 4, 1729-1762 (2021). MSC: 65L05 65L70 93B11 PDFBibTeX XMLCite \textit{S. Rungpitaxmana} and \textit{S. Chaturantabut}, Thai J. Math. 19, No. 4, 1729--1762 (2021; Zbl 1482.65108) Full Text: Link
Yildiz, Süleyman; Uzunca, Murat; Karasözen, Bülent Structure-preserving reduced-order modeling of non-traditional shallow water equation. (English) Zbl 1480.93068 Benner, Peter (ed.) et al., Model reduction of complex dynamical systems. Selected papers based on the presentations at the workshop, University of Graz, Graz, Austria, August 28–30, 2019. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 171, 327-345 (2021). MSC: 93B11 93C20 93C15 65M06 PDFBibTeX XMLCite \textit{S. Yildiz} et al., ISNM, Int. Ser. Numer. Math. 171, 327--345 (2021; Zbl 1480.93068) Full Text: DOI arXiv
Karasözen, Bülent; Mülayim, Gülden; Uzunca, Murat; Yıldız, Süleyman Reduced order modelling of nonlinear cross-diffusion systems. (English) Zbl 1508.37116 Appl. Math. Comput. 401, Article ID 126058, 16 p. (2021). MSC: 37N25 35K57 35K61 65L05 65M06 92D25 PDFBibTeX XMLCite \textit{B. Karasözen} et al., Appl. Math. Comput. 401, Article ID 126058, 16 p. (2021; Zbl 1508.37116) Full Text: DOI arXiv
Hale, Jack S.; Schenone, Elisa; Baroli, Davide; Beex, Lars A. A.; Bordas, Stéphane P. A. A hyper-reduction method using adaptivity to cut the assembly costs of reduced order models. (English) Zbl 1506.65179 Comput. Methods Appl. Mech. Eng. 380, Article ID 113723, 27 p. (2021). MSC: 65M99 65M22 PDFBibTeX XMLCite \textit{J. S. Hale} et al., Comput. Methods Appl. Mech. Eng. 380, Article ID 113723, 27 p. (2021; Zbl 1506.65179) Full Text: DOI
Uy, Wayne Isaac Tan; Peherstorfer, Benjamin Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations. (English) Zbl 1480.65269 ESAIM, Math. Model. Numer. Anal. 55, No. 3, 735-761 (2021). Reviewer: Marius Ghergu (Dublin) MSC: 65M60 62G15 65C05 65M15 65K10 PDFBibTeX XMLCite \textit{W. I. T. Uy} and \textit{B. Peherstorfer}, ESAIM, Math. Model. Numer. Anal. 55, No. 3, 735--761 (2021; Zbl 1480.65269) Full Text: DOI arXiv
Koc, Birgul; Rubino, Samuele; Schneier, Michael; Singler, John; Iliescu, Traian On optimal pointwise in time error bounds and difference quotients for the proper orthogonal decomposition. (English) Zbl 1493.65154 SIAM J. Numer. Anal. 59, No. 4, 2163-2196 (2021). Reviewer: Bülent Karasözen (Ankara) MSC: 65M60 65M99 65F20 65M15 35K05 35Q79 PDFBibTeX XMLCite \textit{B. Koc} et al., SIAM J. Numer. Anal. 59, No. 4, 2163--2196 (2021; Zbl 1493.65154) Full Text: DOI arXiv
Hesthaven, Jan S.; Pagliantini, Cecilia Structure-preserving reduced basis methods for Poisson systems. (English) Zbl 1465.37095 Math. Comput. 90, No. 330, 1701-1740 (2021). MSC: 37M15 37M05 65P10 PDFBibTeX XMLCite \textit{J. S. Hesthaven} and \textit{C. Pagliantini}, Math. Comput. 90, No. 330, 1701--1740 (2021; Zbl 1465.37095) Full Text: DOI Link
Li, Kun; Huang, Ting-Zhu; Li, Liang; Lanteri, Stéphane Non-intrusive reduced-order modeling of parameterized electromagnetic scattering problems using cubic spline interpolation. (English) Zbl 1472.65122 J. Sci. Comput. 87, No. 2, Paper No. 52, 29 p. (2021). MSC: 65M60 65M06 65N30 65D07 65M99 65F20 78A45 78M34 78M10 78M20 35Q60 PDFBibTeX XMLCite \textit{K. Li} et al., J. Sci. Comput. 87, No. 2, Paper No. 52, 29 p. (2021; Zbl 1472.65122) Full Text: DOI Link
Bai, Feng; Wang, Yi Reduced-order modeling based on hybrid snapshot simulation. (English) Zbl 07342028 Int. J. Comput. Methods 18, No. 1, Article ID 2050029, 33 p. (2021). MSC: 65-XX 68-XX PDFBibTeX XMLCite \textit{F. Bai} and \textit{Y. Wang}, Int. J. Comput. Methods 18, No. 1, Article ID 2050029, 33 p. (2021; Zbl 07342028) Full Text: DOI
Bannenberg, M. W. F. M.; Ciccazzo, A.; Günther, M. Coupling of model order reduction and multirate techniques for coupled dynamical systems. (English) Zbl 1462.34066 Appl. Math. Lett. 112, Article ID 106780, 8 p. (2021). MSC: 34C20 34A09 65L80 65L04 PDFBibTeX XMLCite \textit{M. W. F. M. Bannenberg} et al., Appl. Math. Lett. 112, Article ID 106780, 8 p. (2021; Zbl 1462.34066) Full Text: DOI
Cho, Haeseong; Shin, Sangjoon; Kim, Haedong; Cho, Maenghyo Enhanced model-order reduction approach via online adaptation for parametrized nonlinear structural problems. (English) Zbl 1490.74121 Comput. Mech. 65, No. 2, 331-353 (2020). MSC: 74S99 74S05 74K99 PDFBibTeX XMLCite \textit{H. Cho} et al., Comput. Mech. 65, No. 2, 331--353 (2020; Zbl 1490.74121) Full Text: DOI
Chaturantabut, Saifon Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework. (English) Zbl 1461.93057 Int. J. Appl. Math. Comput. Sci. 30, No. 4, 615-628 (2020). MSC: 93B11 93C15 93C20 93C10 PDFBibTeX XMLCite \textit{S. Chaturantabut}, Int. J. Appl. Math. Comput. Sci. 30, No. 4, 615--628 (2020; Zbl 1461.93057) Full Text: DOI
Sipp, Denis; Fosas de Pando, Miguel; Schmid, Peter J. Nonlinear model reduction: a comparison between POD-Galerkin and POD-DEIM methods. (English) Zbl 1502.76029 Comput. Fluids 208, Article ID 104628, 21 p. (2020). MSC: 76D25 PDFBibTeX XMLCite \textit{D. Sipp} et al., Comput. Fluids 208, Article ID 104628, 21 p. (2020; Zbl 1502.76029) Full Text: DOI arXiv
Sukuntee, Norapon; Chaturantabut, Saifon Parametric nonlinear model reduction using \(K\)-means clustering for miscible flow simulation. (English) Zbl 1499.76077 J. Appl. Math. 2020, Article ID 3904606, 12 p. (2020). MSC: 76M20 76M22 76S05 PDFBibTeX XMLCite \textit{N. Sukuntee} and \textit{S. Chaturantabut}, J. Appl. Math. 2020, Article ID 3904606, 12 p. (2020; Zbl 1499.76077) Full Text: DOI
Chen, Dongqin; Song, Huailing The POD-DEIM reduced-order method for stochastic Allen-Cahn equations with multiplicative noise. (English) Zbl 07283130 Comput. Math. Appl. 80, No. 12, 2691-2706 (2020). MSC: 65C30 60H15 65M60 60H35 65N30 PDFBibTeX XMLCite \textit{D. Chen} and \textit{H. Song}, Comput. Math. Appl. 80, No. 12, 2691--2706 (2020; Zbl 07283130) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi Simulation flows with multiple phases and components via the radial basis functions-finite difference (RBF-FD) procedure: Shan-Chen model. (English) Zbl 1464.65081 Eng. Anal. Bound. Elem. 119, 151-161 (2020). MSC: 65M06 65D12 65M70 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Eng. Anal. Bound. Elem. 119, 151--161 (2020; Zbl 1464.65081) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi A POD-based reduced-order Crank-Nicolson/fourth-order alternating direction implicit (ADI) finite difference scheme for solving the two-dimensional distributed-order Riesz space-fractional diffusion equation. (English) Zbl 1452.65145 Appl. Numer. Math. 158, 271-291 (2020). MSC: 65M06 65N06 65M99 65M15 65M12 65D30 35R11 26A33 35K57 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Numer. Math. 158, 271--291 (2020; Zbl 1452.65145) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi Reduced order modeling of time-dependent incompressible Navier-Stokes equation with variable density based on a local radial basis functions-finite difference (LRBF-FD) technique and the POD/DEIM method. (English) Zbl 1442.65287 Comput. Methods Appl. Mech. Eng. 364, Article ID 112914, 28 p. (2020). MSC: 65M70 65D12 76D05 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Comput. Methods Appl. Mech. Eng. 364, Article ID 112914, 28 p. (2020; Zbl 1442.65287) Full Text: DOI
Kastian, Steffen; Reese, Stefanie An adaptive way of choosing significant snapshots for proper orthogonal decomposition. (English) Zbl 1425.74471 Fehr, Jörg (ed.) et al., IUTAM symposium on model order reduction of coupled systems. MORCOS 2018. Proceedings of the IUTAM symposium, Stuttgart, Germany, May 22–25, 2018. Cham: Springer. IUTAM Bookser. 36, 67-79 (2020). MSC: 74S05 65M60 65K10 74P10 PDFBibTeX XMLCite \textit{S. Kastian} and \textit{S. Reese}, IUTAM Bookser. 36, 67--79 (2020; Zbl 1425.74471) Full Text: DOI
Li, Kun; Huang, Ting-Zhu; Li, Liang; Lanteri, Stéphane POD-based model order reduction with an adaptive snapshot selection for a discontinuous Galerkin approximation of the time-domain Maxwell’s equations. (English) Zbl 1452.78035 J. Comput. Phys. 396, 106-128 (2019). MSC: 78M34 78M10 65M60 78A40 PDFBibTeX XMLCite \textit{K. Li} et al., J. Comput. Phys. 396, 106--128 (2019; Zbl 1452.78035) Full Text: DOI Link
Sukuntee, Norapon; Chaturantabut, Saifon Model order reduction for sine-Gordon equation using POD and DEIM. (English) Zbl 1463.65212 Thai J. Math., Spec. Iss.: Annual Meeting in Mathematics 2018, 222-256 (2019). MSC: 65L99 34A45 PDFBibTeX XMLCite \textit{N. Sukuntee} and \textit{S. Chaturantabut}, Thai J. Math., 222--256 (2019; Zbl 1463.65212) Full Text: Link
Xiao, D. Error estimation of the parametric non-intrusive reduced order model using machine learning. (English) Zbl 1441.62081 Comput. Methods Appl. Mech. Eng. 355, 513-534 (2019). MSC: 62F15 62G05 62-08 PDFBibTeX XMLCite \textit{D. Xiao}, Comput. Methods Appl. Mech. Eng. 355, 513--534 (2019; Zbl 1441.62081) Full Text: DOI Link
Miyatake, Yuto Structure-preserving model reduction for dynamical systems with a first integral. (English) Zbl 1427.65408 Japan J. Ind. Appl. Math. 36, No. 3, 1021-1037 (2019). MSC: 65P10 65L05 65M06 37M15 PDFBibTeX XMLCite \textit{Y. Miyatake}, Japan J. Ind. Appl. Math. 36, No. 3, 1021--1037 (2019; Zbl 1427.65408) Full Text: DOI arXiv
Akman Yıldız, Tuğba; Uzunca, Murat; Karasözen, Bülent Structure preserving reduced order modeling for gradient systems. (English) Zbl 1429.65223 Appl. Math. Comput. 347, 194-209 (2019). MSC: 65M60 65P10 PDFBibTeX XMLCite \textit{T. Akman Yıldız} et al., Appl. Math. Comput. 347, 194--209 (2019; Zbl 1429.65223) Full Text: DOI arXiv
Dehghan, Mehdi; Abbaszadeh, Mostafa A combination of proper orthogonal decomposition-discrete empirical interpolation method (POD-DEIM) and meshless local RBF-DQ approach for prevention of groundwater contamination. (English) Zbl 1409.76095 Comput. Math. Appl. 75, No. 4, 1390-1412 (2018). MSC: 76M22 76M10 65M70 86A05 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Comput. Math. Appl. 75, No. 4, 1390--1412 (2018; Zbl 1409.76095) Full Text: DOI
Dehghan, Mehdi; Abbaszadeh, Mostafa An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation. (English) Zbl 1403.65109 Eng. Anal. Bound. Elem. 92, 244-256 (2018). MSC: 65M99 35Q31 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Eng. Anal. Bound. Elem. 92, 244--256 (2018; Zbl 1403.65109) Full Text: DOI
Fritzen, Felix; Haasdonk, Bernard; Ryckelynck, David; Schöps, Sebastian An algorithmic comparison of the hyper-reduction and the discrete empirical interpolation method for a nonlinear thermal problem. (English) Zbl 1390.80017 Math. Comput. Appl. 23, No. 1, Paper No. 8, 25 p. (2018). MSC: 80M10 65N30 PDFBibTeX XMLCite \textit{F. Fritzen} et al., Math. Comput. Appl. 23, No. 1, Paper No. 8, 25 p. (2018; Zbl 1390.80017) Full Text: DOI arXiv
Fu, Hongfei; Wang, Hong; Wang, Zhu POD/DEIM reduced-order modeling of time-fractional partial differential equations with applications in parameter identification. (English) Zbl 1404.65140 J. Sci. Comput. 74, No. 1, 220-243 (2018). MSC: 65M32 35R11 65M06 65M22 65K05 90C30 PDFBibTeX XMLCite \textit{H. Fu} et al., J. Sci. Comput. 74, No. 1, 220--243 (2018; Zbl 1404.65140) Full Text: DOI arXiv
Dehghan, Mehdi; Abbaszadeh, Mostafa A reduced proper orthogonal decomposition (POD) element free Galerkin (POD-EFG) method to simulate two-dimensional solute transport problems and error estimate. (English) Zbl 1380.65255 Appl. Numer. Math. 126, 92-112 (2018). MSC: 65M60 65M12 65M15 35L04 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Appl. Numer. Math. 126, 92--112 (2018; Zbl 1380.65255) Full Text: DOI
Kostova-Vassilevska, Tanya; Oxberry, Geoffrey M. Model reduction of dynamical systems by proper orthogonal decomposition: error bounds and comparison of methods using snapshots from the solution and the time derivatives. (English) Zbl 1376.65099 J. Comput. Appl. Math. 330, 553-573 (2018). MSC: 65K10 93C20 93B11 PDFBibTeX XMLCite \textit{T. Kostova-Vassilevska} and \textit{G. M. Oxberry}, J. Comput. Appl. Math. 330, 553--573 (2018; Zbl 1376.65099) Full Text: DOI Link
Gong, Yuezheng; Wang, Qi; Wang, Zhu Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems. (English) Zbl 1439.37083 Comput. Methods Appl. Mech. Eng. 315, 780-798 (2017). MSC: 37M25 65L60 65P10 93A15 93B11 PDFBibTeX XMLCite \textit{Y. Gong} et al., Comput. Methods Appl. Mech. Eng. 315, 780--798 (2017; Zbl 1439.37083) Full Text: DOI arXiv
Uzunca, Murat; Karasözen, Bülent Energy stable model order reduction for the Allen-Cahn equation. (English) Zbl 1468.76042 Benner, Peter (ed.) et al., Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Cham: Springer. MS&A, Model. Simul. Appl. 17, 403-419 (2017). MSC: 76M10 76T99 76M30 65M12 65M15 PDFBibTeX XMLCite \textit{M. Uzunca} and \textit{B. Karasözen}, MS\&A, Model. Simul. Appl. 17, 403--419 (2017; Zbl 1468.76042) Full Text: DOI arXiv
Dehghan, Mehdi; Abbaszadeh, Mostafa The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations. (English) Zbl 1380.65301 J. Comput. Phys. 351, 478-510 (2017). MSC: 65M70 65D05 76M25 35Q35 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, J. Comput. Phys. 351, 478--510 (2017; Zbl 1380.65301) Full Text: DOI
Chaturantabut, Saifon Temporal localized nonlinear model reduction with a priori error estimate. (English) Zbl 1368.65189 Appl. Numer. Math. 119, 225-238 (2017). MSC: 65M60 35G25 65M15 65M12 PDFBibTeX XMLCite \textit{S. Chaturantabut}, Appl. Numer. Math. 119, 225--238 (2017; Zbl 1368.65189) Full Text: DOI
Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems. (English) Zbl 1348.92122 J. Comput. Appl. Math. 310, 32-43 (2017). MSC: 92D25 92B15 62P10 PDFBibTeX XMLCite \textit{G. Dimitriu} et al., J. Comput. Appl. Math. 310, 32--43 (2017; Zbl 1348.92122) Full Text: DOI
Fosas de Pando, Miguel; Schmid, Peter J.; Sipp, Denis Nonlinear model-order reduction for compressible flow solvers using the discrete empirical interpolation method. (English) Zbl 1371.76103 J. Comput. Phys. 324, 194-209 (2016). MSC: 76M25 65M20 76Nxx PDFBibTeX XMLCite \textit{M. Fosas de Pando} et al., J. Comput. Phys. 324, 194--209 (2016; Zbl 1371.76103) Full Text: DOI Link
Pulch, Roland; ter Maten, E. Jan W.; Augustin, Florian Sensitivity analysis and model order reduction for random linear dynamical systems. (English) Zbl 07313360 Math. Comput. Simul. 111, 80-95 (2015). MSC: 41Axx PDFBibTeX XMLCite \textit{R. Pulch} et al., Math. Comput. Simul. 111, 80--95 (2015; Zbl 07313360) Full Text: DOI Link
He, Jiajun; Durlofsky, L. J. Constraint reduction procedures for reduced-order subsurface flow models based on POD-TPWL. (English) Zbl 1352.76112 Int. J. Numer. Methods Eng. 103, No. 1, 1-30 (2015). MSC: 76S05 PDFBibTeX XMLCite \textit{J. He} and \textit{L. J. Durlofsky}, Int. J. Numer. Methods Eng. 103, No. 1, 1--30 (2015; Zbl 1352.76112) Full Text: DOI
Ştefănescu, R.; Sandu, A.; Navon, I. M. POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation. (English) Zbl 1349.76535 J. Comput. Phys. 295, 569-595 (2015). MSC: 76M20 65M06 65M32 76B15 90C90 PDFBibTeX XMLCite \textit{R. Ştefănescu} et al., J. Comput. Phys. 295, 569--595 (2015; Zbl 1349.76535) Full Text: DOI arXiv
Wang, Zhu Nonlinear model reduction based on the finite element method with interpolated coefficients: Semilinear parabolic equations. (English) Zbl 1334.65159 Numer. Methods Partial Differ. Equations 31, No. 6, 1713-1741 (2015). MSC: 65M60 35K58 65M15 PDFBibTeX XMLCite \textit{Z. Wang}, Numer. Methods Partial Differ. Equations 31, No. 6, 1713--1741 (2015; Zbl 1334.65159) Full Text: DOI arXiv
Fritzen, Felix; Leuschner, Matthias Nonlinear reduced order homogenization of materials including cohesive interfaces. (English) Zbl 1329.74240 Comput. Mech. 56, No. 1, 131-151 (2015). MSC: 74Q05 PDFBibTeX XMLCite \textit{F. Fritzen} and \textit{M. Leuschner}, Comput. Mech. 56, No. 1, 131--151 (2015; Zbl 1329.74240) Full Text: DOI
Zhao, Pengfei; Liu, Cai; Feng, Xuan POD-DEIM based model order reduction for the spherical shallow water equations with Turkel-Zwas finite difference discretization. (English) Zbl 1437.76037 J. Appl. Math. 2014, Article ID 292489, 10 p. (2014). MSC: 76M20 76B15 PDFBibTeX XMLCite \textit{P. Zhao} et al., J. Appl. Math. 2014, Article ID 292489, 10 p. (2014; Zbl 1437.76037) Full Text: DOI
Xiao, D.; Fang, F.; Buchan, A. G.; Pain, C. C.; Navon, I. M.; Du, J.; Hu, G. Nonlinear model reduction for the Navier-Stokes equations using residual DEIM method. (English) Zbl 1349.76288 J. Comput. Phys. 263, 1-18 (2014). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., J. Comput. Phys. 263, 1--18 (2014; Zbl 1349.76288) Full Text: DOI
Caiazzo, Alfonso; Iliescu, Traian; John, Volker; Schyschlowa, Swetlana A numerical investigation of velocity-pressure reduced order models for incompressible flows. (English) Zbl 1349.76050 J. Comput. Phys. 259, 598-616 (2014). MSC: 76D05 76M10 PDFBibTeX XMLCite \textit{A. Caiazzo} et al., J. Comput. Phys. 259, 598--616 (2014; Zbl 1349.76050) Full Text: DOI
Ghiglieri, Jane; Ulbrich, Stefan Optimal flow control based on POD and MPC and an application to the cancellation of Tollmien-Schlichting waves. (English) Zbl 1301.49078 Optim. Methods Softw. 29, No. 5, 1042-1074 (2014). MSC: 49M27 49K20 35Q30 65K05 76D55 76D05 PDFBibTeX XMLCite \textit{J. Ghiglieri} and \textit{S. Ulbrich}, Optim. Methods Softw. 29, No. 5, 1042--1074 (2014; Zbl 1301.49078) Full Text: DOI
Capiez-Lernout, E.; Soize, C.; Mignolet, M.-P. Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation. (English) Zbl 1296.74042 Comput. Methods Appl. Mech. Eng. 271, 210-230 (2014). MSC: 74H60 74-05 74G60 74H50 74K25 PDFBibTeX XMLCite \textit{E. Capiez-Lernout} et al., Comput. Methods Appl. Mech. Eng. 271, 210--230 (2014; Zbl 1296.74042) Full Text: DOI Link
Xiao, D.; Fang, F.; Du, J.; Pain, C. C.; Navon, I. M.; Buchan, A. G.; ElSheikh, A. H.; Hu, G. Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair. (English) Zbl 1297.76107 Comput. Methods Appl. Mech. Eng. 255, 147-157 (2013). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 255, 147--157 (2013; Zbl 1297.76107) Full Text: DOI
Carlberg, Kevin; Farhat, Charbel; Cortial, Julien; Amsallem, David The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows. (English) Zbl 1299.76180 J. Comput. Phys. 242, 623-647 (2013); corrigendum ibid. 250, 713 (2013). MSC: 76M25 76M10 PDFBibTeX XMLCite \textit{K. Carlberg} et al., J. Comput. Phys. 242, 623--647 (2013; Zbl 1299.76180) Full Text: DOI arXiv
Iliescu, Traian; Wang, Zhu Variational multiscale proper orthogonal decomposition: convection-dominated convection-diffusion-reaction equations. (English) Zbl 1336.76017 Math. Comput. 82, No. 283, 1357-1378 (2013). MSC: 76F65 65M60 76D05 PDFBibTeX XMLCite \textit{T. Iliescu} and \textit{Z. Wang}, Math. Comput. 82, No. 283, 1357--1378 (2013; Zbl 1336.76017) Full Text: DOI arXiv
Wang, Zhu; Akhtar, Imran; Borggaard, Jeff; Iliescu, Traian Proper orthogonal decomposition closure models for turbulent flows: a numerical comparison. (English) Zbl 1253.76050 Comput. Methods Appl. Mech. Eng. 237-240, 10-26 (2012). MSC: 76F65 PDFBibTeX XMLCite \textit{Z. Wang} et al., Comput. Methods Appl. Mech. Eng. 237--240, 10--26 (2012; Zbl 1253.76050) Full Text: DOI arXiv