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
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
Dehghan, Mehdi; Hooshyarfarzin, Baharak; Abbaszadeh, Mostafa Radial basis function partition of unity procedure combined with the reduced-order method for solving Zakharov-Rubenchik equations. (English) Zbl 07789075 Eng. Anal. Bound. Elem. 145, 93-116 (2022). MSC: 35C08 35L05 35G20 PDFBibTeX XMLCite \textit{M. Dehghan} et al., Eng. Anal. Bound. Elem. 145, 93--116 (2022; Zbl 07789075) Full Text: DOI
Florez, Horacio; Gildin, Eduardo; Morkos, Patrick Model-order reduction for coupled flow and linear thermal-poroplasticity with applications to unconventional reservoirs. (English) Zbl 1504.93039 Beattie, Christopher (ed.) et al., Realization and model reduction of dynamical systems. A festschrift in honor of the 70th birthday of Thanos Antoulas. Cham: Springer. 387-407 (2022). MSC: 93B11 86A04 86A20 PDFBibTeX XMLCite \textit{H. Florez} et al., in: Realization and model reduction of dynamical systems. A festschrift in honor of the 70th birthday of Thanos Antoulas. Cham: Springer. 387--407 (2022; Zbl 1504.93039) Full Text: DOI
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
Kirsten, Gerhard Multilinear POD-DEIM model reduction for 2D and 3D semilinear systems of differential equations. (English) Zbl 1497.37106 J. Comput. Dyn. 9, No. 2, 159-183 (2022). MSC: 37M99 65N06 PDFBibTeX XMLCite \textit{G. Kirsten}, J. Comput. Dyn. 9, No. 2, 159--183 (2022; Zbl 1497.37106) Full Text: DOI arXiv
Khodabakhshi, Parisa; Willcox, Karen E. Non-intrusive data-driven model reduction for differential-algebraic equations derived from lifting transformations. (English) Zbl 1507.65135 Comput. Methods Appl. Mech. Eng. 389, Article ID 114296, 20 p. (2022). MSC: 65L80 PDFBibTeX XMLCite \textit{P. Khodabakhshi} and \textit{K. E. Willcox}, Comput. Methods Appl. Mech. Eng. 389, Article ID 114296, 20 p. (2022; Zbl 1507.65135) 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
Ploymaklam, Nattapol; Chaturantabut, Saifon Reduced-order modeling of a local discontinuous Galerkin method for Burgers-Poisson equations. (English) Zbl 1476.65248 Thai J. Math. 18, No. 4, 2053-2069 (2020). MSC: 65M60 PDFBibTeX XMLCite \textit{N. Ploymaklam} and \textit{S. Chaturantabut}, Thai J. Math. 18, No. 4, 2053--2069 (2020; Zbl 1476.65248) Full Text: Link
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
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
Florez, Horacio; Gildin, Eduardo Global/local model order reduction in coupled flow and linear thermal-poroelasticity. (English) Zbl 1434.86013 Comput. Geosci. 24, No. 2, 709-735 (2020). MSC: 86-10 65N30 76S05 PDFBibTeX XMLCite \textit{H. Florez} and \textit{E. Gildin}, Comput. Geosci. 24, No. 2, 709--735 (2020; Zbl 1434.86013) 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
Jiang, Rui; Durlofsky, Louis J. Implementation and detailed assessment of a GNAT reduced-order model for subsurface flow simulation. (English) Zbl 07581569 J. Comput. Phys. 379, 192-213 (2019). MSC: 76Mxx 76Sxx 86Axx PDFBibTeX XMLCite \textit{R. Jiang} and \textit{L. J. Durlofsky}, J. Comput. Phys. 379, 192--213 (2019; Zbl 07581569) Full Text: DOI
Tan, Xiaosi; Gildin, Eduardo; Florez, Horacio; Trehan, Sumeet; Yang, Yahan; Hoda, Nazish Trajectory-based DEIM (TDEIM) model reduction applied to reservoir simulation. (English) Zbl 1411.86003 Comput. Geosci. 23, No. 1, 35-53 (2019). MSC: 86A05 76S05 86-08 PDFBibTeX XMLCite \textit{X. Tan} et al., Comput. Geosci. 23, No. 1, 35--53 (2019; Zbl 1411.86003) Full Text: DOI
Flórez, Horacio; Argáez, Miguel A model-order reduction method based on wavelets and POD to solve nonlinear transient and steady-state continuation problems. (English) Zbl 1480.65310 Appl. Math. Modelling 53, 12-31 (2018). MSC: 65M99 65T60 PDFBibTeX XMLCite \textit{H. Flórez} and \textit{M. Argáez}, Appl. Math. Modelling 53, 12--31 (2018; Zbl 1480.65310) Full Text: DOI
Wen, Baole; Chini, Gregory P. Reduced modeling of porous media convection in a minimal flow unit at large Rayleigh number. (English) Zbl 1415.76507 J. Comput. Phys. 371, 551-563 (2018). MSC: 76M25 76S05 76R10 76M30 PDFBibTeX XMLCite \textit{B. Wen} and \textit{G. P. Chini}, J. Comput. Phys. 371, 551--563 (2018; Zbl 1415.76507) 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
Bonomi, Diana; Manzoni, Andrea; Quarteroni, Alfio A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics. (English) Zbl 1439.74394 Comput. Methods Appl. Mech. Eng. 324, 300-326 (2017). MSC: 74S05 65N30 74L15 92C10 PDFBibTeX XMLCite \textit{D. Bonomi} et al., Comput. Methods Appl. Mech. Eng. 324, 300--326 (2017; Zbl 1439.74394) Full Text: DOI Link
Ghavamian, F.; Tiso, P.; Simone, A. POD-DEIM model order reduction for strain-softening viscoplasticity. (English) Zbl 1439.74073 Comput. Methods Appl. Mech. Eng. 317, 458-479 (2017). MSC: 74C10 74S05 PDFBibTeX XMLCite \textit{F. Ghavamian} et al., Comput. Methods Appl. Mech. Eng. 317, 458--479 (2017; Zbl 1439.74073) Full Text: DOI
Hernández, J. A.; Caicedo, M. A.; Ferrer, A. Dimensional hyper-reduction of nonlinear finite element models via empirical cubature. (English) Zbl 1439.74419 Comput. Methods Appl. Mech. Eng. 313, 687-722 (2017). MSC: 74S05 65M60 74B20 74K20 74H45 PDFBibTeX XMLCite \textit{J. A. Hernández} et al., Comput. Methods Appl. Mech. Eng. 313, 687--722 (2017; Zbl 1439.74419) 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
Boyaval, Sébastien; Enchéry, Guillaume; Sanchez, Riad; Tran, Quang Huy A reduced-basis approach to two-phase flow in porous media. (English) Zbl 1365.76300 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 477-486 (2017). MSC: 76S05 76M12 35J50 65M08 65N15 PDFBibTeX XMLCite \textit{S. Boyaval} et al., Springer Proc. Math. Stat. 200, 477--486 (2017; Zbl 1365.76300) 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
Radermacher, Annika; Reese, Stefanie POD-based model reduction with empirical interpolation applied to nonlinear elasticity. (English) Zbl 1352.74048 Int. J. Numer. Methods Eng. 107, No. 6, 477-495 (2016). MSC: 74B20 74S05 65M60 PDFBibTeX XMLCite \textit{A. Radermacher} and \textit{S. Reese}, Int. J. Numer. Methods Eng. 107, No. 6, 477--495 (2016; Zbl 1352.74048) Full Text: DOI
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y. Adaptive multiscale model reduction with generalized multiscale finite element methods. (English) Zbl 1349.76191 J. Comput. Phys. 320, 69-95 (2016). MSC: 76M10 65N30 76S05 PDFBibTeX XMLCite \textit{E. Chung} et al., J. Comput. Phys. 320, 69--95 (2016; Zbl 1349.76191) Full Text: DOI arXiv
Akkutlu, I. Y.; Efendiev, Yalchin; Vasilyeva, Maria Multiscale model reduction for shale gas transport in fractured media. (English) Zbl 1391.76714 Comput. Geosci. 20, No. 5, 953-973 (2016). MSC: 76S05 76N15 76M10 PDFBibTeX XMLCite \textit{I. Y. Akkutlu} et al., Comput. Geosci. 20, No. 5, 953--973 (2016; Zbl 1391.76714) Full Text: DOI arXiv
Redeker, M.; Haasdonk, B. A POD-EIM reduced two-scale model for precipitation in porous media. (English) Zbl 1348.93064 Math. Comput. Model. Dyn. Syst. 22, No. 4, 323-344 (2016). MSC: 93B11 93C20 93B40 PDFBibTeX XMLCite \textit{M. Redeker} and \textit{B. Haasdonk}, Math. Comput. Model. Dyn. Syst. 22, No. 4, 323--344 (2016; Zbl 1348.93064) Full Text: DOI
Brunton, B. W.; Brunton, S. L.; Proctor, J. L.; Kutz, J. N. Sparse sensor placement optimization for classification. (English) Zbl 1350.49037 SIAM J. Appl. Math. 76, No. 5, 2099-2122 (2016). MSC: 49M30 49N30 94A13 94A20 94A08 PDFBibTeX XMLCite \textit{B. W. Brunton} et al., SIAM J. Appl. Math. 76, No. 5, 2099--2122 (2016; Zbl 1350.49037) Full Text: DOI
Suwartadi, Eka; Krogstad, Stein; Foss, Bjarne Adjoint-based surrogate optimization of oil reservoir water flooding. (English) Zbl 1365.90244 Optim. Eng. 16, No. 2, 441-481 (2015). MSC: 90C30 49M37 49J20 PDFBibTeX XMLCite \textit{E. Suwartadi} et al., Optim. Eng. 16, No. 2, 441--481 (2015; Zbl 1365.90244) Full Text: DOI
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
Kaulmann, S.; Flemisch, B.; Haasdonk, B.; Lie, K.-a.; Ohlberger, M. The localized reduced basis multiscale method for two-phase flows in porous media. (English) Zbl 1352.76057 Int. J. Numer. Methods Eng. 102, No. 5, 1018-1040 (2015). MSC: 76M10 65N30 76S05 PDFBibTeX XMLCite \textit{S. Kaulmann} et al., Int. J. Numer. Methods Eng. 102, No. 5, 1018--1040 (2015; Zbl 1352.76057) 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
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
Hernández, J. A.; Oliver, J.; Huespe, A. E.; Caicedo, M. A.; Cante, J. C. High-performance model reduction techniques in computational multiscale homogenization. (English) Zbl 1423.74785 Comput. Methods Appl. Mech. Eng. 276, 149-189 (2014). MSC: 74Q05 65N30 74S05 PDFBibTeX XMLCite \textit{J. A. Hernández} et al., Comput. Methods Appl. Mech. Eng. 276, 149--189 (2014; Zbl 1423.74785) 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
Benner, Peter; Embree, Mark; Lehoucq, Richard B.; Kelley, C. T. A mathematical biography of Danny C. Sorensen. (English) Zbl 1238.01104 Linear Algebra Appl. 436, No. 8, 2717-2724 (2012). MSC: 01A70 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 436, No. 8, 2717--2724 (2012; Zbl 1238.01104) Full Text: DOI