Arcucci, Rossella; Xiao, Dunhui; Fang, Fangxin; Navon, Ionel Michael; Wu, Pin; Pain, Christopher C.; Guo, Yi-Ke A reduced order with data assimilation model: theory and practice. (English) Zbl 1521.76314 Comput. Fluids 257, Article ID 105862, 12 p. (2023). MSC: 76M10 65M60 62R07 76F50 PDFBibTeX XMLCite \textit{R. Arcucci} et al., Comput. Fluids 257, Article ID 105862, 12 p. (2023; Zbl 1521.76314) 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
Cheng, M.; Fang, F.; Pain, C. C.; Navon, I. M. Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network. (English) Zbl 1442.76040 Comput. Methods Appl. Mech. Eng. 365, Article ID 113000, 17 p. (2020). MSC: 76D05 76-10 76M10 65M60 PDFBibTeX XMLCite \textit{M. Cheng} et al., Comput. Methods Appl. Mech. Eng. 365, Article ID 113000, 17 p. (2020; Zbl 1442.76040) Full Text: DOI arXiv
Xiao, D.; Fang, F.; Heaney, C. E.; Navon, I. M.; Pain, C. C. A domain decomposition method for the non-intrusive reduced order modelling of fluid flow. (English) Zbl 1441.76074 Comput. Methods Appl. Mech. Eng. 354, 307-330 (2019). MSC: 76M10 65M60 65M55 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 354, 307--330 (2019; Zbl 1441.76074) Full Text: DOI Link
Yang, P.; Xiang, J.; Fang, F.; Pavlidis, D.; Pain, C. C. Modelling of fluid-structure interaction for moderate Reynolds number flows using an immersed-body method. (English) Zbl 1411.76073 Comput. Fluids 179, 613-631 (2019). MSC: 76M10 76F60 65M60 74F10 76D05 PDFBibTeX XMLCite \textit{P. Yang} et al., Comput. Fluids 179, 613--631 (2019; Zbl 1411.76073) Full Text: DOI
Xiao, D.; Heaney, C. E.; Fang, F.; Mottet, L.; Hu, R.; Bistrian, D. A.; Aristodemou, E.; Navon, I. M.; Pain, C. C. A domain decomposition non-intrusive reduced order model for turbulent flows. (English) Zbl 1411.76072 Comput. Fluids 182, 15-27 (2019). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Fluids 182, 15--27 (2019; Zbl 1411.76072) Full Text: DOI Link
Xiao, D.; Fang, F.; Pain, C. C.; Navon, I. M. A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications. (English) Zbl 1439.65124 Comput. Methods Appl. Mech. Eng. 317, 868-889 (2017). MSC: 65M60 PDFBibTeX XMLCite \textit{D. Xiao} et al., Comput. Methods Appl. Mech. Eng. 317, 868--889 (2017; Zbl 1439.65124) Full Text: DOI Link
Yang, P.; Xiang, J.; Fang, F.; Pavlidis, D.; Latham, J.-P.; Pain, C. C. Modelling of fluid-structure interaction with multiphase viscous flows using an immersed-body method. (English) Zbl 1349.76291 J. Comput. Phys. 321, 571-592 (2016). MSC: 76M10 74S05 65M60 74F10 76D05 76T30 PDFBibTeX XMLCite \textit{P. Yang} et al., J. Comput. Phys. 321, 571--592 (2016; Zbl 1349.76291) Full Text: DOI
Adam, A.; Pavlidis, D.; Percival, J. R.; Salinas, P.; Xie, Z.; Fang, F.; Pain, C. C.; Muggeridge, A. H.; Jackson, M. D. Higher-order conservative interpolation between control-volume meshes: application to advection and multiphase flow problems with dynamic mesh adaptivity. (English) Zbl 1349.76164 J. Comput. Phys. 321, 512-531 (2016). MSC: 76M10 65M60 76T30 PDFBibTeX XMLCite \textit{A. Adam} et al., J. Comput. Phys. 321, 512--531 (2016; Zbl 1349.76164) Full Text: DOI
Xiao, D.; Fang, F.; Pain, C.; Hu, G. Non-intrusive reduced-order modelling of the Navier-Stokes equations based on RBF interpolation. (English) Zbl 1455.76099 Int. J. Numer. Methods Fluids 79, No. 11, 580-595 (2015). MSC: 76M10 76D05 65M60 PDFBibTeX XMLCite \textit{D. Xiao} et al., Int. J. Numer. Methods Fluids 79, No. 11, 580--595 (2015; Zbl 1455.76099) Full Text: DOI
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
Ardjmandpour, N.; Pain, C. C.; Fang, F.; Buchan, A. G.; Singer, J.; Player, M. A.; Xu, Xu; Navon, I. M.; Carter, J. Reduced order borehole induction modelling. (English) Zbl 07512419 Int. J. Comput. Fluid Dyn. 28, No. 3-4, 140-157 (2014). MSC: 78-XX 65-XX PDFBibTeX XMLCite \textit{N. Ardjmandpour} et al., Int. J. Comput. Fluid Dyn. 28, No. 3--4, 140--157 (2014; Zbl 07512419) 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
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
Du, Juan; Navon, I. M.; Zhu, Jiang; Fang, Fangxin; Alekseev, A. K. Reduced order modeling based on POD of a parabolized Navier-Stokes equations model II: trust region POD 4D VAR data assimilation. (English) Zbl 1319.76030 Comput. Math. Appl. 65, No. 3, 380-394 (2013). MSC: 76M20 65M32 65M06 76D05 PDFBibTeX XMLCite \textit{J. Du} et al., Comput. Math. Appl. 65, No. 3, 380--394 (2013; Zbl 1319.76030) Full Text: DOI
Du, J.; Fang, F.; Pain, C. C.; Navon, I. M.; Zhu, J.; Ham, D. A. POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow. (English) Zbl 1319.76026 Comput. Math. Appl. 65, No. 3, 362-379 (2013). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{J. Du} et al., Comput. Math. Appl. 65, No. 3, 362--379 (2013; Zbl 1319.76026) Full Text: DOI
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
Fang, F.; Pain, C. C.; Navon, I. M.; Elsheikh, A. H.; Du, J.; Xiao, D. Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods. (English) Zbl 1284.65132 J. Comput. Phys. 234, 540-559 (2013). MSC: 65M60 35L02 PDFBibTeX XMLCite \textit{F. Fang} et al., J. Comput. Phys. 234, 540--559 (2013; Zbl 1284.65132) Full Text: DOI
Hossen, M. J.; Navon, I. M.; Fang, F. A penalized four-dimensional variational data assimilation method for reducing forecast error related to adaptive observations. (English) Zbl 1412.86004 Int. J. Numer. Methods Fluids 70, No. 10, 1207-1220 (2012). MSC: 86A10 65N08 76M12 PDFBibTeX XMLCite \textit{M. J. Hossen} et al., Int. J. Numer. Methods Fluids 70, No. 10, 1207--1220 (2012; Zbl 1412.86004) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A. The independent set perturbation adjoint method: a new method of differentiating mesh-based fluids models. (English) Zbl 1285.76015 Int. J. Numer. Methods Fluids 66, No. 8, 976-999 (2011). MSC: 76M10 65M99 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 66, No. 8, 976--999 (2011; Zbl 1285.76015) Full Text: DOI
Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A.; Goddard, A. J. H. A POD goal-oriented error measure for mesh optimization. (English) Zbl 1425.65096 Int. J. Numer. Methods Fluids 63, No. 2, 185-206 (2010). MSC: 65M15 65M50 86A05 PDFBibTeX XMLCite \textit{F. Fang} et al., Int. J. Numer. Methods Fluids 63, No. 2, 185--206 (2010; Zbl 1425.65096) Full Text: DOI
Power, P. W.; Pain, C. C.; Piggott, M. D.; Fang, F.; Gorman, G. J.; Umpleby, A. P.; Goddard, A. J. H.; Navon, I. M. Adjoint a posteriori error measures for anisotropic mesh optimisation. (English) Zbl 1206.65250 Comput. Math. Appl. 52, No. 8-9, 1213-1242 (2006). MSC: 65N50 65N15 PDFBibTeX XMLCite \textit{P. W. Power} et al., Comput. Math. Appl. 52, No. 8--9, 1213--1242 (2006; Zbl 1206.65250) Full Text: DOI