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
Abbaszadeh, Mostafa; Kalhor, Yasmin; Dehghan, Mehdi; Donatelli, Marco A reduced-order model based on cubic B-spline basis function and SSP Runge-Kutta procedure to investigate option pricing under jump-diffusion models. (English) Zbl 1521.91384 Eng. Anal. Bound. Elem. 150, 154-166 (2023). MSC: 91G60 65M75 65D07 91G20 PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., Eng. Anal. Bound. Elem. 150, 154--166 (2023; Zbl 1521.91384) Full Text: DOI
Damiano, Lombardi State estimation in nonlinear parametric time dependent systems using tensor train. (English) Zbl 07769317 Int. J. Numer. Methods Eng. 123, No. 20, 4935-4956 (2022). MSC: 65-XX 41-XX PDFBibTeX XMLCite \textit{L. Damiano}, Int. J. Numer. Methods Eng. 123, No. 20, 4935--4956 (2022; Zbl 07769317) 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
Albarakati, Aishah; Budišić, Marko; Crocker, Rose; Glass-Klaiber, Juniper; Iams, Sarah; Maclean, John; Marshall, Noah; Roberts, Colin; Van Vleck, Erik S. Model and data reduction for data assimilation: particle filters employing projected forecasts and data with application to a shallow water model. (English) Zbl 1524.62464 Comput. Math. Appl. 116, 194-211 (2022). MSC: 62M20 93E11 37N10 65C05 37M99 PDFBibTeX XMLCite \textit{A. Albarakati} et al., Comput. Math. Appl. 116, 194--211 (2022; Zbl 1524.62464) Full Text: DOI arXiv
García-Archilla, Bosco; Novo, Julia; Rubino, Samuele Error analysis of proper orthogonal decomposition data assimilation schemes with grad-div stabilization for the Navier-Stokes equations. (English) Zbl 1486.65167 J. Comput. Appl. Math. 411, Article ID 114246, 30 p. (2022). MSC: 65M60 35Q30 65M12 65M15 65M20 76D55 PDFBibTeX XMLCite \textit{B. García-Archilla} et al., J. Comput. Appl. Math. 411, Article ID 114246, 30 p. (2022; Zbl 1486.65167) Full Text: DOI arXiv
Zeng, Yihui; Luo, Zhendong The reduced-dimension technique for the unknown solution coefficient vectors in the Crank-Nicolson finite element method for the Sobolev equation. (English) Zbl 1490.65216 J. Math. Anal. Appl. 513, No. 1, Article ID 126207, 13 p. (2022). MSC: 65M60 65M99 65M12 65M15 PDFBibTeX XMLCite \textit{Y. Zeng} and \textit{Z. Luo}, J. Math. Anal. Appl. 513, No. 1, Article ID 126207, 13 p. (2022; Zbl 1490.65216) 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
Wang, Yuepeng; Ding, Xuemei; Hu, Kun; Fang, Fangxin; Navon, I. M.; Lin, Guang Feasibility of DEIM for retrieving the initial field via dimensionality reduction. (English) Zbl 07500740 J. Comput. Phys. 429, Article ID 110005, 15 p. (2021). MSC: 65Mxx 76Mxx 76Dxx PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Comput. Phys. 429, Article ID 110005, 15 p. (2021; Zbl 07500740) Full Text: DOI
Zhou, Yanjie; Zhang, Yanan; Liang, Ye; Luo, Zhendong A reduced-order extrapolated model based on splitting implicit finite difference scheme and proper orthogonal decomposition for the fourth-order nonlinear Rosenau equation. (English) Zbl 1458.35381 Appl. Numer. Math. 162, 192-200 (2021). MSC: 35Q53 35G20 65M06 65M12 65M99 65B05 PDFBibTeX XMLCite \textit{Y. Zhou} et al., Appl. Numer. Math. 162, 192--200 (2021; Zbl 1458.35381) Full Text: DOI
Teng, Fei; Luo, Zhendong A reduced-order extrapolated approach to solution coefficient vectors in the Crank-Nicolson finite element method for the uniform transmission line equation. (English) Zbl 1452.65250 J. Math. Anal. Appl. 493, No. 1, Article ID 124511, 13 p. (2021). MSC: 65M60 65M06 65M99 65M12 65M15 35Q60 PDFBibTeX XMLCite \textit{F. Teng} and \textit{Z. Luo}, J. Math. Anal. Appl. 493, No. 1, Article ID 124511, 13 p. (2021; Zbl 1452.65250) 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
Luo, Zhendong; Jiang, Wenrui A reduced-order extrapolated technique about the unknown coefficient vectors of solutions in the finite element method for hyperbolic type equation. (English) Zbl 1450.65126 Appl. Numer. Math. 158, 123-133 (2020). Reviewer: Marius Ghergu (Dublin) MSC: 65M60 65M12 65M15 65M99 PDFBibTeX XMLCite \textit{Z. Luo} and \textit{W. Jiang}, Appl. Numer. Math. 158, 123--133 (2020; Zbl 1450.65126) 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
Kärcher, Mark; Boyaval, Sébastien; Grepl, Martin A.; Veroy, Karen Reduced basis approximation and a posteriori error bounds for 4D-Var data assimilation. (English) Zbl 1507.49026 Optim. Eng. 19, No. 3, 663-695 (2018). MSC: 49M20 65K10 PDFBibTeX XMLCite \textit{M. Kärcher} et al., Optim. Eng. 19, No. 3, 663--695 (2018; Zbl 1507.49026) Full Text: DOI arXiv
Wang, Yuepeng; Cheng, Yue; Navon, I. Michael; Guan, Yuanhong Parameter identification techniques applied to an environmental pollution model. (English) Zbl 1412.65043 J. Ind. Manag. Optim. 14, No. 2, 817-831 (2018). MSC: 65K10 PDFBibTeX XMLCite \textit{Y. Wang} et al., J. Ind. Manag. Optim. 14, No. 2, 817--831 (2018; Zbl 1412.65043) Full Text: DOI
Wang, Zhaohong; Jiang, Yaolin; Li, Zhen A trust-region method for optimal \(H_2\) model reduction of discrete-time dynamical systems. (English) Zbl 1405.93055 J. Difference Equ. Appl. 24, No. 10, 1604-1620 (2018). MSC: 93B11 93B60 93C55 93C05 93C10 93C35 93-04 PDFBibTeX XMLCite \textit{Z. Wang} et al., J. Difference Equ. Appl. 24, No. 10, 1604--1620 (2018; Zbl 1405.93055) Full Text: DOI
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
Dehghan, Mehdi; Abbaszadeh, Mostafa Proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) meshless method for solving incompressible Navier-Stokes equation. (English) Zbl 1439.76060 Comput. Methods Appl. Mech. Eng. 311, 856-888 (2016). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Comput. Methods Appl. Mech. Eng. 311, 856--888 (2016; Zbl 1439.76060) Full Text: DOI
Buchan, A. G.; Calloo, A. A.; Goffin, M. G.; Dargaville, S.; Fang, F.; Pain, C. C.; Navon, I. M. A POD reduced order model for resolving angular direction in neutron/photon transport problems. (English) Zbl 1352.82030 J. Comput. Phys. 296, 138-157 (2015). MSC: 82D75 82C80 35Q20 45K05 65N30 PDFBibTeX XMLCite \textit{A. G. Buchan} et al., J. Comput. Phys. 296, 138--157 (2015; Zbl 1352.82030) 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, Yue-Peng; Tao, Su-Lin; Chen, Qun Retrieving the variable coefficient for a nonlinear convection-diffusion problem with spectral conjugate gradient method. (English) Zbl 1326.65080 Inverse Probl. Sci. Eng. 23, No. 8, 1342-1365 (2015). MSC: 65K10 PDFBibTeX XMLCite \textit{Y.-P. Wang} et al., Inverse Probl. Sci. Eng. 23, No. 8, 1342--1365 (2015; Zbl 1326.65080) Full Text: DOI
Buchan, A. G.; Pain, C. C.; Fang, F.; Navon, I. M. A POD reduced-order model for eigenvalue problems with application to reactor physics. (English) Zbl 1352.82018 Int. J. Numer. Methods Eng. 95, No. 12, 1011-1032 (2013). MSC: 82C80 65N25 82D75 PDFBibTeX XMLCite \textit{A. G. Buchan} et al., Int. J. Numer. Methods Eng. 95, No. 12, 1011--1032 (2013; Zbl 1352.82018) Full Text: DOI