Koc, Birgul; Mou, Changhong; Liu, Honghu; Wang, Zhu; Rozza, Gianluigi; Iliescu, Traian Verifiability of the data-driven variational multiscale reduced order model. (English) Zbl 1503.65234 J. Sci. Comput. 93, No. 2, Paper No. 54, 26 p. (2022). MSC: 65M60 65M06 65N30 65K10 49M41 65M15 76F65 35Q53 PDFBibTeX XMLCite \textit{B. Koc} et al., J. Sci. Comput. 93, No. 2, Paper No. 54, 26 p. (2022; Zbl 1503.65234) Full Text: DOI arXiv
Sharma, Harsh; Wang, Zhu; Kramer, Boris Hamiltonian operator inference: physics-preserving learning of reduced-order models for canonical Hamiltonian systems. (English) Zbl 1487.65193 Physica D 431, Article ID 133122, 15 p. (2022). MSC: 65P10 PDFBibTeX XMLCite \textit{H. Sharma} et al., Physica D 431, Article ID 133122, 15 p. (2022; Zbl 1487.65193) Full Text: DOI arXiv
Liu, Jun; Wang, Zhu A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems in unsteady convection-diffusion PDEs. (English) Zbl 1510.65199 Appl. Math. Comput. 416, Article ID 126750, 18 p. (2022). MSC: 65M06 35K57 65F08 65Y05 65Y20 PDFBibTeX XMLCite \textit{J. Liu} and \textit{Z. Wang}, Appl. Math. Comput. 416, Article ID 126750, 18 p. (2022; Zbl 1510.65199) 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
Xie, Xuping; Wells, David; Wang, Zhu; Iliescu, Traian Numerical analysis of the Leray reduced order model. (English) Zbl 1431.65182 J. Comput. Appl. Math. 328, 12-29 (2018). MSC: 65M60 65M99 76D05 76M10 76M99 PDFBibTeX XMLCite \textit{X. Xie} et al., J. Comput. Appl. Math. 328, 12--29 (2018; Zbl 1431.65182) Full Text: DOI arXiv
Xie, Xuping; Wells, David; Wang, Zhu; Iliescu, Traian Approximate deconvolution reduced order modeling. (English) Zbl 1439.76038 Comput. Methods Appl. Mech. Eng. 313, 512-534 (2017). MSC: 76F65 76D05 PDFBibTeX XMLCite \textit{X. Xie} et al., Comput. Methods Appl. Mech. Eng. 313, 512--534 (2017; Zbl 1439.76038) Full Text: DOI arXiv
Borggaard, Jeff; Wang, Zhu; Zietsman, Lizette A goal-oriented reduced-order modeling approach for nonlinear systems. (English) Zbl 1443.65195 Comput. Math. Appl. 71, No. 11, 2155-2169 (2016). MSC: 65M60 35K20 35K59 35Q53 PDFBibTeX XMLCite \textit{J. Borggaard} et al., Comput. Math. Appl. 71, No. 11, 2155--2169 (2016; Zbl 1443.65195) Full Text: DOI
Wang, Zhu; McBee, Brian; Iliescu, Traian Approximate partitioned method of snapshots for POD. (English) Zbl 1382.65108 J. Comput. Appl. Math. 307, 374-384 (2016). MSC: 65F15 65Y05 PDFBibTeX XMLCite \textit{Z. Wang} et al., J. Comput. Appl. Math. 307, 374--384 (2016; Zbl 1382.65108) Full Text: DOI
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
Iliescu, Traian; Wang, Zhu Variational multiscale proper orthogonal decomposition: Navier-Stokes equations. (English) Zbl 1452.76048 Numer. Methods Partial Differ. Equations 30, No. 2, 641-663 (2014). MSC: 76D05 76M10 76M30 PDFBibTeX XMLCite \textit{T. Iliescu} and \textit{Z. Wang}, Numer. Methods Partial Differ. Equations 30, No. 2, 641--663 (2014; Zbl 1452.76048) 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
Borggaard, Jeff; Iliescu, Traian; Wang, Zhu Artificial viscosity proper orthogonal decomposition. (English) Zbl 1211.76077 Math. Comput. Modelling 53, No. 1-2, 269-279 (2011). MSC: 76M25 65M15 76F65 PDFBibTeX XMLCite \textit{J. Borggaard} et al., Math. Comput. Modelling 53, No. 1--2, 269--279 (2011; Zbl 1211.76077) Full Text: DOI
Wang, Z.; Akhtar, I.; Borggaard, J.; Iliescu, T. Two-level discretizations of nonlinear closure models for proper orthogonal decomposition. (English) Zbl 1427.76226 J. Comput. Phys. 230, No. 1, 126-146 (2011). MSC: 76M99 76F99 PDFBibTeX XMLCite \textit{Z. Wang} et al., J. Comput. Phys. 230, No. 1, 126--146 (2011; Zbl 1427.76226) Full Text: DOI