Zappon, Elena; Manzoni, Andrea; Gervasio, Paola; Quarteroni, Alfio A reduced order model for domain decompositions with non-conforming interfaces. (English) Zbl 07818687 J. Sci. Comput. 99, No. 1, Paper No. 22, 41 p. (2024). MSC: 65N55 65N30 65D05 65N12 35J15 35K57 35K05 65M06 PDFBibTeX XMLCite \textit{E. Zappon} et al., J. Sci. Comput. 99, No. 1, Paper No. 22, 41 p. (2024; Zbl 07818687) Full Text: DOI arXiv
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
Bertrand, Fleurianne; Boffi, Daniele; Halim, Abdul Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression. (English) Zbl 07766241 J. Comput. Phys. 495, Article ID 112503, 28 p. (2023). MSC: 65Nxx 65Mxx 35Pxx PDFBibTeX XMLCite \textit{F. Bertrand} et al., J. Comput. Phys. 495, Article ID 112503, 28 p. (2023; Zbl 07766241) Full Text: DOI arXiv
Chen, Yuanhong; Sun, Xiang; Lin, Yifan; Gao, Zhen An adaptive non-intrusive multi-fidelity reduced basis method for parameterized partial differential equations. (English) Zbl 1514.65125 East Asian J. Appl. Math. 13, No. 2, 398-419 (2023). MSC: 65M60 35A24 78A48 PDFBibTeX XMLCite \textit{Y. Chen} et al., East Asian J. Appl. Math. 13, No. 2, 398--419 (2023; Zbl 1514.65125) Full Text: DOI
Bertrand, Fleurianne; Boffi, Daniele; Halim, Abdul A reduced order model for the finite element approximation of eigenvalue problems. (English) Zbl 07644830 Comput. Methods Appl. Mech. Eng. 404, Article ID 115696, 26 p. (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{F. Bertrand} et al., Comput. Methods Appl. Mech. Eng. 404, Article ID 115696, 26 p. (2023; Zbl 07644830) Full Text: DOI arXiv
Li, Kun; Huang, Ting-Zhu; Li, Liang; Zhao, Ying; Lanteri, Stéphane A non-intrusive model order reduction approach for parameterized time-domain Maxwell’s equations. (English) Zbl 1498.78046 Discrete Contin. Dyn. Syst., Ser. B 28, No. 1, 449-473 (2023). MSC: 78M34 78M10 65M60 65M99 65F20 78A25 60G15 62F15 35Q60 PDFBibTeX XMLCite \textit{K. Li} et al., Discrete Contin. Dyn. Syst., Ser. B 28, No. 1, 449--473 (2023; Zbl 1498.78046) 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
Hughes, Alexander C.; Buchan, Andrew G. An adaptive reduced order model for the angular discretization of the Boltzmann transport equation using independent basis sets over a partitioning of the space-angle domain. (English) Zbl 07768052 Int. J. Numer. Methods Eng. 123, No. 16, 3781-3799 (2022). MSC: 65Nxx 82Cxx 35Jxx PDFBibTeX XMLCite \textit{A. C. Hughes} and \textit{A. G. Buchan}, Int. J. Numer. Methods Eng. 123, No. 16, 3781--3799 (2022; Zbl 07768052) Full Text: DOI OA License
Ebrahimijahan, Ali; Dehghan, Mehdi; Abbaszadeh, Mostafa Simulation of Maxwell equation based on an ADI approach and integrated radial basis function-generalized moving least squares (IRBF-GMLS) method with reduced order algorithm based on proper orthogonal decomposition. (English) Zbl 1521.78016 Eng. Anal. Bound. Elem. 143, 397-417 (2022). MSC: 78M10 65M70 35D35 65D12 78A25 86A10 PDFBibTeX XMLCite \textit{A. Ebrahimijahan} et al., Eng. Anal. Bound. Elem. 143, 397--417 (2022; Zbl 1521.78016) 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
Karasözen, Bülent; Mülayim, Gülden; Uzunca, Murat Nonintrusive model order reduction for cross-diffusion systems. (English) Zbl 1501.65089 Commun. Nonlinear Sci. Numer. Simul. 115, Article ID 106734, 17 p. (2022). Reviewer: Zhen Chao (Milwaukee) MSC: 65N06 65D12 65F20 15A69 35A01 35K51 35K58 65L10 65L12 65L20 65L70 92D25 92C40 35Q92 PDFBibTeX XMLCite \textit{B. Karasözen} et al., Commun. Nonlinear Sci. Numer. Simul. 115, Article ID 106734, 17 p. (2022; Zbl 1501.65089) 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
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
Huang, Juntao; Cheng, Yingda; Christlieb, Andrew J.; Roberts, Luke F. Machine learning moment closure models for the radiative transfer equation. I: Directly learning a gradient based closure. (English) Zbl 1522.65143 J. Comput. Phys. 453, Article ID 110941, 21 p. (2022). MSC: 65M06 65L06 65N06 85A25 80A21 68Q32 68T07 68T09 82C70 35R09 35Q20 PDFBibTeX XMLCite \textit{J. Huang} et al., J. Comput. Phys. 453, Article ID 110941, 21 p. (2022; Zbl 1522.65143) Full Text: DOI arXiv
Peng, Zhichao; Chen, Yanlai; Cheng, Yingda; Li, Fengyan A reduced basis method for radiative transfer equation. (English) Zbl 1493.65162 J. Sci. Comput. 91, No. 1, Paper No. 5, 27 p. (2022). MSC: 65M60 65N30 65K10 65N12 35R09 45K05 35Q49 82D75 PDFBibTeX XMLCite \textit{Z. Peng} et al., J. Sci. Comput. 91, No. 1, Paper No. 5, 27 p. (2022; Zbl 1493.65162) Full Text: DOI arXiv
Star, S. Kelbij; Stabile, Giovanni; Belloni, Francesco; Rozza, Gianluigi; Degroote, Joris A novel iterative penalty method to enforce boundary conditions in finite volume POD-Galerkin reduced order models for fluid dynamics problems. (English) Zbl 1473.65144 Commun. Comput. Phys. 30, No. 1, 34-66 (2021). MSC: 65M08 35Q35 65M22 76D05 76M12 PDFBibTeX XMLCite \textit{S. K. Star} et al., Commun. Comput. Phys. 30, No. 1, 34--66 (2021; Zbl 1473.65144) Full Text: DOI arXiv
Sun, Xiang; Choi, Jung-Il Non-intrusive reduced-order modeling for uncertainty quantification of space-time-dependent parameterized problems. (English) Zbl 1524.76230 Comput. Math. Appl. 87, 50-64 (2021). MSC: 76M10 65M60 76D05 65N99 35B30 76M22 PDFBibTeX XMLCite \textit{X. Sun} and \textit{J.-I. Choi}, Comput. Math. Appl. 87, 50--64 (2021; Zbl 1524.76230) 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
Georgaka, Sokratia; Stabile, Giovanni; Rozza, Gianluigi; Bluck, Michael J. Parametric POD-Galerkin model order reduction for unsteady-state heat transfer problems. (English) Zbl 1473.78016 Commun. Comput. Phys. 27, No. 1, 1-32 (2020). MSC: 78M34 97N40 35Q35 PDFBibTeX XMLCite \textit{S. Georgaka} et al., Commun. Comput. Phys. 27, No. 1, 1--32 (2020; Zbl 1473.78016) Full Text: DOI arXiv
Zhang, Min; Huang, Weizhang; Qiu, Jianxian High-order conservative positivity-preserving DG-interpolation for deforming meshes and application to moving mesh DG simulation of radiative transfer. (English) Zbl 1454.65122 SIAM J. Sci. Comput. 42, No. 5, A3109-A3135 (2020). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 65M60 65M50 65D05 35R09 45J05 85A25 PDFBibTeX XMLCite \textit{M. Zhang} et al., SIAM J. Sci. Comput. 42, No. 5, A3109--A3135 (2020; Zbl 1454.65122) Full Text: DOI arXiv
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
Yang, Feng-Lian; Yan, Liang A non-intrusive reduced basis EKI for time fractional diffusion inverse problems. (English) Zbl 1431.65161 Acta Math. Appl. Sin., Engl. Ser. 36, No. 1, 183-202 (2020). MSC: 65M32 62F15 35R11 PDFBibTeX XMLCite \textit{F.-L. Yang} and \textit{L. Yan}, Acta Math. Appl. Sin., Engl. Ser. 36, No. 1, 183--202 (2020; Zbl 1431.65161) Full Text: DOI arXiv
Karatzas, Efthymios N.; Stabile, Giovanni; Atallah, Nabil; Scovazzi, Guglielmo; Rozza, Gianluigi A reduced order approach for the embedded shifted boundary FEM and a heat exchange system on parametrized geometries. (English) Zbl 1442.65376 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, 111-125 (2020). MSC: 65N30 65N38 65N50 80M10 80M15 80A19 35K05 PDFBibTeX XMLCite \textit{E. N. Karatzas} et al., IUTAM Bookser. 36, 111--125 (2020; Zbl 1442.65376) Full Text: DOI arXiv
Yu, Jian; Yan, Chao; Jiang, Zhenhua; Yuan, Wu; Chen, Shusheng Adaptive non-intrusive reduced order modeling for compressible flows. (English) Zbl 1453.76118 J. Comput. Phys. 397, Article ID 108855, 27 p. (2019). MSC: 76M12 65M08 68T05 35B30 76N15 PDFBibTeX XMLCite \textit{J. Yu} et al., J. Comput. Phys. 397, Article ID 108855, 27 p. (2019; Zbl 1453.76118) Full Text: DOI
Chakir, R.; Maday, Y.; Parnaudeau, P. A non-intrusive reduced basis approach for parametrized heat transfer problems. (English) Zbl 1416.65587 J. Comput. Phys. 376, 617-633 (2019). MSC: 65Z05 65K10 65N30 35Q79 PDFBibTeX XMLCite \textit{R. Chakir} et al., J. Comput. Phys. 376, 617--633 (2019; Zbl 1416.65587) Full Text: DOI HAL
Peitz, Sebastian; Ober-Blöbaum, Sina; Dellnitz, Michael Multiobjective optimal control methods for the Navier-Stokes equations using reduced order modeling. (English) Zbl 1415.76221 Acta Appl. Math. 161, 171-199 (2019). MSC: 76D55 35Q30 49K20 49M05 90C29 93C20 PDFBibTeX XMLCite \textit{S. Peitz} et al., Acta Appl. Math. 161, 171--199 (2019; Zbl 1415.76221) Full Text: DOI arXiv
Carlberg, Kevin; Choi, Youngsoo; Sargsyan, Syuzanna Conservative model reduction for finite-volume models. (English) Zbl 1415.65208 J. Comput. Phys. 371, 280-314 (2018). MSC: 65M08 35L65 65K10 PDFBibTeX XMLCite \textit{K. Carlberg} et al., J. Comput. Phys. 371, 280--314 (2018; Zbl 1415.65208) Full Text: DOI arXiv
Gräßle, Carmen; Hinze, Michael POD reduced-order modeling for evolution equations utilizing arbitrary finite element discretizations. (English) Zbl 1404.65264 Adv. Comput. Math. 44, No. 6, 1941-1978 (2018). MSC: 65N30 35K90 65K05 35K05 35K55 PDFBibTeX XMLCite \textit{C. Gräßle} and \textit{M. Hinze}, Adv. Comput. Math. 44, No. 6, 1941--1978 (2018; Zbl 1404.65264) Full Text: DOI arXiv
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
Argaud, J.-P.; Bouriquet, B.; de Caso, F.; Gong, H.; Maday, Y.; Mula, O. Sensor placement in nuclear reactors based on the generalized empirical interpolation method. (English) Zbl 1392.82075 J. Comput. Phys. 363, 354-370 (2018). MSC: 82D75 65D05 35B30 PDFBibTeX XMLCite \textit{J. P. Argaud} et al., J. Comput. Phys. 363, 354--370 (2018; Zbl 1392.82075) Full Text: DOI Link
Li, Qiuqi; Wang, Yuhe; Vasilyeva, Maria Multiscale model reduction for fluid infiltration simulation through dual-continuum porous media with localized uncertainties. (English) Zbl 1524.65568 J. Comput. Appl. Math. 336, 127-146 (2018). MSC: 65M60 65N30 76S05 76M10 65N15 35R60 65M99 65K05 90C59 65M06 PDFBibTeX XMLCite \textit{Q. Li} et al., J. Comput. Appl. Math. 336, 127--146 (2018; Zbl 1524.65568) Full Text: DOI
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
Stabile, Giovanni; Hijazi, Saddam; Mola, Andrea; Lorenzi, Stefano; Rozza, Gianluigi POD-Galerkin reduced order methods for CFD using finite volume discretisation: vortex shedding around a circular cylinder. (English) Zbl 1383.35175 Commun. Appl. Ind. Math. 8, No. 1, 210-236 (2017). MSC: 35Q35 97N40 76D17 76D05 65M08 PDFBibTeX XMLCite \textit{G. Stabile} et al., Commun. Appl. Ind. Math. 8, No. 1, 210--236 (2017; Zbl 1383.35175) 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
Zhu, Shengfeng; Dedè, Luca; Quarteroni, Alfio Isogeometric analysis and proper orthogonal decomposition for parabolic problems. (English) Zbl 1380.65295 Numer. Math. 135, No. 2, 333-370 (2017). MSC: 65M60 35K20 65D07 65M12 65M15 PDFBibTeX XMLCite \textit{S. Zhu} et al., Numer. Math. 135, No. 2, 333--370 (2017; Zbl 1380.65295) Full Text: DOI Link
Xiao, D.; Fang, F.; Buchan, A. G.; Pain, C. C.; Navon, I. M.; Muggeridge, A. Non-intrusive reduced order modelling of the Navier-Stokes equations. (English) Zbl 1423.76287 Comput. Methods Appl. Mech. Eng. 293, 522-541 (2015). MSC: 76M10 65M60 76D05 35Q30 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 293, 522--541 (2015; Zbl 1423.76287) 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
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
Chen, X.; Navon, I. M.; Fang, F. A dual-weighted trust-region adaptive POD 4D-VAR applied to a finite-element shallow-water equations model. (English) Zbl 1428.76145 Int. J. Numer. Methods Fluids 65, No. 5, 520-541 (2011). MSC: 76M21 76M10 35Q35 PDFBibTeX XMLCite \textit{X. Chen} et al., Int. J. Numer. Methods Fluids 65, No. 5, 520--541 (2011; Zbl 1428.76145) Full Text: DOI