Edit Profile (opens in new tab) Navon, Ionel Michael Co-Author Distance Author ID: navon.ionel-michael Published as: Navon, I. M.; Navon, Ionel M.; Navon, Ionel Michael; Navon, I. Michael more...less External Links: MGP Documents Indexed: 102 Publications since 1978, including 6 Books Co-Authors: 91 Co-Authors with 88 Joint Publications 1,537 Co-Co-Authors all top 5 Co-Authors 10 single-authored 25 Fang, Fangxin 21 Pain, Christopher C. 12 Alekseev, Aleksey K. 9 Luo, Zhendong 8 Xiao, Dunhui 7 Zhu, Jiang 6 Buchan, Andrew G. 6 Du, Juan 5 Gorman, Gerard J. 5 Piggott, Matthew D. 5 Ştefănescu, Răzvan 4 Allison, P. A. 4 Chen, Xiao 4 Dimitriu, Gabriel 4 Goddard, A. J. H. 4 Li, Jichun 3 Bistrian, Diana Alina 3 Cacuci, Dan Gabriel 3 Chen, Jing 3 Daescu, Dacian N. 3 Homescu, Chris 3 Le Dimet, Francois-Xavier 2 Akella, Srinivas 2 Arcucci, Rossella 2 Cao, Yanhua 2 Heaney, Claire E. 2 Hossen, M. J. 2 Ionescu-Bujor, Mihaela 2 Jardak, M. 2 Li, Zhijin 2 Neta, Beny 2 Riphagen, H. A. 2 Wang, Ruiwen 2 Wang, Yuepeng 2 Xiang, Jiansheng 1 Al-Haik, M. S. 1 An, Jing 1 Ardjmandpour, N. 1 Aristodemou, Elsa 1 Ashwin Renganathan, S. 1 Calloo, A. A. 1 Castaings, W. 1 Cheng, Yue 1 Copeland, Graham J. M. 1 Dargaville, Steven 1 de Villiers, Rosalie 1 Di, Zhenhua 1 Ding, Xuemei 1 Fairweather, Graeme 1 Farrell, Patrick E. 1 Fu, Jinlong 1 Fu, Rui 1 Garmestani, Hamid 1 Gejadze, Igor Yu. 1 Geng, Jian 1 Giraldo, Francis X. 1 Goffin, M. G. 1 Guan, Yuanhong 1 Guo, Yike 1 Ham, David A. 1 Holter, William H. 1 Hu, Kun 1 Hussaini, M. Yousuff 1 Li, Chenfeng 1 Li, Hong 1 Lin, Guang 1 Mottet, Laetitia 1 Muggeridge, Ann H. 1 Oppe, Thomas C. 1 Pawar, Suraj 1 Phua, Paul Kang-Hoh 1 Player, M. A. 1 Power, P. W. 1 Ramamurthy, M. 1 Rao, Vishwas 1 Rasheed, Adil 1 San, Omer 1 Sandu, Adrian 1 Schlick, Tamar 1 Steppeler, Juergen 1 Steward, J. L. 1 Sun, Ping 1 Umpleby, A. P. 1 Wang, Aiwen 1 Wang, Zhi 1 Wu, Pin 1 Xie, Zhenghui 1 Yang, Xiaozhong 1 Zelentsov, M. E. 1 Zhu, Chuanhua 1 Zupanski, Milija all top 5 Serials 21 International Journal for Numerical Methods in Fluids 15 Journal of Computational Physics 13 Computer Methods in Applied Mechanics and Engineering 10 Computers & Mathematics with Applications 6 International Journal of Computational Fluid Dynamics 4 Computers and Fluids 2 International Journal for Numerical Methods in Engineering 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 Mathematics and Computers in Simulation 1 SIAM Journal on Numerical Analysis 1 Advances in Engineering Software 1 Systems & Control Letters 1 Communications in Applied Numerical Methods 1 Applied Mathematical Modelling 1 Analele Științifice ale Universității Al. I. Cuza din Iași. Serie Nouă. Matematică 1 SIAM Journal on Optimization 1 Computational Optimization and Applications 1 Optimization Methods & Software 1 Quantitative Finance 1 Journal of Industrial and Management Optimization 1 Annals of the Academy of Romanian Scientists. Mathematics and its Applications 1 International Journal for Numerical Methods in Biomedical Engineering 1 GEM - International Journal on Geomathematics 1 Contributions to Atmospheric Physics all top 5 Fields 64 Numerical analysis (65-XX) 62 Fluid mechanics (76-XX) 19 Partial differential equations (35-XX) 17 Geophysics (86-XX) 8 Operations research, mathematical programming (90-XX) 7 Computer science (68-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 4 Statistics (62-XX) 4 Mechanics of deformable solids (74-XX) 4 Biology and other natural sciences (92-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Optics, electromagnetic theory (78-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 93 Publications have been cited 1,176 times in 646 Documents Cited by ▼ Year ▼ Nonlinear model reduction for the Navier-Stokes equations using residual DEIM method. Zbl 1349.76288Xiao, D.; Fang, F.; Buchan, A. G.; Pain, C. C.; Navon, I. M.; Du, J.; Hu, G. 58 2014 A reduced-order approach to four-dimensional variational data assimilation using proper orthogonal decomposition. Zbl 1370.86002Cao, Yanhua; Zhu, Jiang; Navon, I. M.; Luo, Zhendong 56 2007 POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model. Zbl 1286.76106Ştefănescu, R.; Navon, I. M. 48 2013 Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type. Zbl 0907.65109Li, J.; Navon, I. M. 48 1998 Mixed finite element formulation and error estimates based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations. Zbl 1391.76351Luo, Zhendong; Chen, Jing; Navon, I. M.; Yang, Xiaozhong 45 2009 An optimizing reduced order FDS for the tropical Pacific Ocean reduced gravity model. Zbl 1205.86007Luo, Zhendong; Chen, Jing; Zhu, Jiang; Wang, Ruiwen; Navon, I. M. 44 2007 Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model. Zbl 1173.76348Luo, Zhendong; Zhu, Jiang; Wang, Ruiwen; Navon, I. M. 39 2007 Suppression of vortex shedding for flow around a circular cylinder using optimal control. Zbl 1007.76019Homescu, C.; Navon, I. M.; Li, Z. 36 2002 Reduced-order modeling of the upper tropical Pacific ocean model using proper orthogonal decomposition. Zbl 1161.86002Cao, Yanhua; Zhu, Jiang; Luo, Zhendong; Navon, I. M. 36 2006 An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems. Zbl 1161.76032Luo, Zhendong; Chen, Jing; Navon, I. M.; Zhu, Jiang 36 2009 Non-intrusive reduced order modelling of the Navier-Stokes equations. Zbl 1423.76287Xiao, D.; Fang, F.; Buchan, A. G.; Pain, C. C.; Navon, I. M.; Muggeridge, A. 35 2015 Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair. Zbl 1297.76107Xiao, D.; Fang, F.; Du, J.; Pain, C. C.; Navon, I. M.; Buchan, A. G.; ElSheikh, A. H.; Hu, G. 29 2013 A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications. Zbl 1439.65124Xiao, D.; Fang, F.; Pain, C. C.; Navon, I. M. 29 2017 POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation. Zbl 1349.76535Ştefănescu, R.; Sandu, A.; Navon, I. M. 29 2015 Efficiency of a POD-based reduced second-order adjoint model in 4D-var data assimilation. Zbl 1370.76122Daescu, D. N.; Navon, I. M. 28 2007 Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods. Zbl 1284.65132Fang, F.; Pain, C. C.; Navon, I. M.; Elsheikh, A. H.; Du, J.; Xiao, D. 25 2013 Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Convection-diffusion type. Zbl 0936.65134Li, Jichun; Navon, I. M. 25 1998 Optimal control of cylinder wakes via suction and blowing. Zbl 1151.76443Li, Zhijin; Navon, I. M.; Hussaini, M. Y.; Le Dimet, F.-X. 23 2003 Sensitivity and uncertainty analysis. Vol. 2: Applications to large-scale systems. Zbl 1083.60002Cacuci, Dan G.; Ionescu-Bujor, Mihaela; Navon, Ionel Michael 22 2005 Reduced order modeling based on POD of a parabolized Navier-Stokes equations model II: trust region POD 4D VAR data assimilation. Zbl 1319.76030Du, Juan; Navon, I. M.; Zhu, Jiang; Fang, Fangxin; Alekseev, A. K. 22 2013 Numerical experience with limited-memory quasi-Newton and truncated Newton methods. Zbl 0784.90086Zou, X.; Navon, I. M.; Berger, M.; Phua, K. H.; Schlick, T.; Le Dimet, F. X. 21 1993 A POD reduced-order 4D-Var adaptive mesh ocean modelling approach. Zbl 1163.86002Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Farrell, P. E.; Allison, P. A.; Goddard, A. J. H. 21 2009 POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow. Zbl 1319.76026Du, J.; Fang, F.; Pain, C. C.; Navon, I. M.; Zhu, J.; Ham, D. A. 20 2013 Non-intrusive reduced order modelling of fluid-structure interactions. Zbl 1425.74167Xiao, D.; Yang, P.; Fang, F.; Xiang, J.; Pain, C. C.; Navon, I. M. 20 2016 Reduced-order modelling of an adaptive mesh ocean model. Zbl 1155.86004Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Allison, P. A.; Goddard, A. J. H. 19 2009 Comparison of advanced large-scale minimization algorithms for the solution of inverse ill-posed problems. Zbl 1189.90221Alekseev, A. K.; Navon, I. M.; Steward, J. L. 16 2009 An optimizing finite difference scheme based on proper orthogonal decomposition for CVD equations. Zbl 1429.35184Du, Juan; Zhu, Jiang; Luo, Zhendong; Navon, I. M. 16 2011 A POD reduced order model for resolving angular direction in neutron/photon transport problems. Zbl 1352.82030Buchan, A. G.; Calloo, A. A.; Goffin, M. G.; Dargaville, S.; Fang, F.; Pain, C. C.; Navon, I. M. 16 2015 Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements. Zbl 0946.65113Li, Jichun; Navon, I. M. 15 1999 POD-DEIM approach on dimension reduction of a multi-species host-parasitoid system. Zbl 1515.35131Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. 14 2015 A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products. Zbl 0831.90124Wang, Zhi; Navon, I. M.; Zou, X.; Le Dimet, F. X. 13 1995 A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting. Zbl 1378.74067Xiao, D.; Yang, P.; Fang, F.; Xiang, J.; Pain, C. C.; Navon, I. M.; Chen, M. 12 2017 Finite-element simulation of the shallow-water equations model on a limited-area domain. Zbl 0438.76017Navon, I. M. 11 1979 Comparison of sequential data assimilation methods for the Kuramoto-Sivashinsky equation. Zbl 1425.76242Jardak, M.; Navon, I. M.; Zupanski, M. 11 2010 The estimation of functional uncertainty using polynomial chaos and adjoint equations. Zbl 1226.65075Alekseev, A. K.; Navon, I. M.; Zelentsov, M. E. 11 2011 A POD reduced-order model for eigenvalue problems with application to reactor physics. Zbl 1352.82018Buchan, A. G.; Pain, C. C.; Fang, F.; Navon, I. M. 11 2013 Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems. Zbl 1348.92122Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. 10 2017 PENT: A periodic pentadiagonal systems solver. Zbl 0609.65015Navon, I. M. 9 1987 Analysis of the Turkel-Zwas scheme for the two-dimensional shallow water equations in spherical coordinates. Zbl 0883.76060Neta, B.; Giraldo, F. X.; Navon, I. M. 9 1997 A dual-weighted trust-region adaptive POD 4D-VAR applied to a finite-element shallow-water equations model. Zbl 1428.76145Chen, X.; Navon, I. M.; Fang, F. 9 2011 An implicit compact fourth-order algorithm for solving the shallow-water equations in conservation-law form. Zbl 0434.65079Navon, I. M.; Riphagen, H. A. 8 1979 A dual-weighted trust-region adaptive POD 4-D var applied to a finite-volume shallow water equations model on the sphere. Zbl 1426.76347Chen, X.; Akella, S.; Navon, I. M. 8 2012 Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems. Zbl 0984.65125Castaings, W.; Navon, I. M. 7 2001 Parallel block preconditioning techniques for the numerical simulation of the shallow water flow using finite element methods. Zbl 0840.76031Cai, Y.; Navon, I. M. 7 1995 Domain decomposition and parallel processing of a finite element model of the shallow water equations. Zbl 0784.76052Navon, I. M.; Cai, Y. 6 1993 An analysis of a hybrid optimization method for variational data assimilation. Zbl 1161.76449Daescu, Dacian; Navon, I. M. 6 2003 Application of POD-DEIM approach for dimension reduction of a diffusive predator-prey system with Allee effect. Zbl 1448.92187Dimitriu, Gabriel; Navon, Ionel M.; Ştefănescu, Răzvan 6 2014 A domain decomposition non-intrusive reduced order model for turbulent flows. Zbl 1411.76072Xiao, D.; Heaney, C. E.; Fang, F.; Mottet, L.; Hu, R.; Bistrian, D. A.; Aristodemou, E.; Navon, I. M.; Pain, C. C. 6 2019 An optimizing implicit difference scheme based on proper orthogonal decomposition for the two-dimensional unsaturated soil water flow equation. Zbl 1426.76466Di, Zhenhua; Luo, Zhendong; Xie, Zhenghui; Wang, Aiwen; Navon, I. M. 6 2012 Computational methods for data evaluation and assimilation. Zbl 1283.68014Cacuci, Dan Gabriel; Navon, Ionel Michael; Ionescu-Bujor, Mihaela 6 2014 A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems. Zbl 1490.65171Luo, Zhendong; Li, Hong; Sun, Ping; An, Jing; Navon, Ionel Michael 6 2013 A posteriori pointwise error estimation for compressible fluid flows using adjoint parameters and Lagrange remainder. Zbl 1063.76067Alekseev, A. K.; Navon, I. M. 5 2005 Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation. Zbl 1118.49017Gejadze, I. Yu.; Copeland, G. J. M.; Navon, I. M. 5 2006 On a posteriori pointwise error estimation using adjoint temperature and Lagrange remainder. Zbl 1102.80005Alekseev, A. K.; Navon, I. M. 5 2005 A POD goal-oriented error measure for mesh optimization. Zbl 1425.65096Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A.; Goddard, A. J. H. 4 2010 A linear ADI method for the shallow-water equations. Zbl 0454.76032Fairweather, G.; Navon, I. M. 4 1980 Optimal control of flow with discontinuities. Zbl 1061.76076Homescu, Chris; Navon, I. M. 4 2003 Adjoint a posteriori error measures for anisotropic mesh optimisation. Zbl 1206.65250Power, P. W.; Pain, C. C.; Piggott, M. D.; Fang, F.; Gorman, G. J.; Umpleby, A. P.; Goddard, A. J. H.; Navon, I. M. 4 2006 Truncated-Newton training algorithm for neurocomputational viscoplastic model. Zbl 1119.74622Al-Haik, M. S.; Garmestani, H.; Navon, I. M. 4 2003 Analysis of the Turkel-Zwas scheme for the shallow-water equations. Zbl 0669.76037Neta, B.; Navon, I. M. 4 1989 Numerical and theoretical considerations for sensitivity calculation of discontinuous flow. Zbl 1157.93361Homescu, Chris; Navon, I. M. 4 2003 A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem. Zbl 0937.65114Li, Jichun; Navon, I. M. 4 1999 Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network. Zbl 1442.76040Cheng, M.; Fang, F.; Pain, C. C.; Navon, I. M. 4 2020 A Numerov-Galerkin technique applied to a finite-element shallow-water equations model with enforced conservation of integral invariants and selective lumping. Zbl 0526.76032Navon, I. M. 4 1983 Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization. Zbl 1294.91187Geng, Jian; Navon, I. Michael; Chen, Xiao 3 2014 Implementation of a posteriori methods for enforcing conservation of potential enstrophy and mass in discretized shallow-water equations models. Zbl 0492.76023Navon, I. M. 3 1981 Efficiency of randomised dynamic mode decomposition for reduced order modelling. Zbl 07474458Bistrian, D. A.; Navon, I. M. 3 2018 Effect of random perturbations on adaptive observation techniques. Zbl 1426.76632Hossen, M. J.; Navon, I. M.; Daescu, D. N. 3 2012 The independent set perturbation adjoint method: a new method of differentiating mesh-based fluids models. Zbl 1285.76015Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A. 3 2011 A posteriori error estimation by postprocessor independent of method of flow field calculation. Zbl 1103.76037Alekseev, A. K.; Navon, I. M. 3 2006 A domain decomposition method for the non-intrusive reduced order modelling of fluid flow. Zbl 1441.76074Xiao, D.; Fang, F.; Heaney, C. E.; Navon, I. M.; Pain, C. C. 3 2019 Numerical methods for the solution of the shallow-water equations in meteorology. Zbl 0443.76014Navon, I. M. 2 1979 Parallelizable PCG methods for the Cray Y-MP and TMC CM-2. Zbl 0847.65020Oppe, Thomas C.; Holter, William H.; Navon, I. M. 2 1994 Adjoint correction and bounding of error using Lagrange form of truncation term. Zbl 1083.65087Alekseev, A. K.; Navon, I. M. 2 2005 The independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and a finite element shallow water model. Zbl 1391.76322Fang, F.; Pain, C. C.; Navon, I. M.; Cacuci, D. G.; Chen, X. 2 2013 Finite-element schemes for extended integrations of atmospheric models. Zbl 0696.76031Steppeler, J.; Navon, I. M.; Lu, H.-I. 2 1990 A comparative study of the performance of high-resolution advection schemes in the context of data assimilation. Zbl 1124.76036Akella, S.; Navon, I. M. 2 2006 Reduced order borehole induction modelling. Zbl 07512419Ardjmandpour, N.; Pain, C. C.; Fang, F.; Buchan, A. G.; Singer, J.; Player, M. A.; Xu, Xu; Navon, I. M.; Carter, J. 2 2014 Parameter identification techniques applied to an environmental pollution model. Zbl 1412.65043Wang, Yuepeng; Cheng, Yue; Navon, I. Michael; Guan, Yuanhong 2 2018 Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes. Zbl 07644844Fu, Jinlong; Xiao, Dunhui; Fu, Rui; Li, Chenfeng; Zhu, Chuanhua; Arcucci, Rossella; Navon, Ionel M. 2 2023 Estimation of goal functional error arising from iterative solution of Euler equations. Zbl 1184.76765Alekseev, A. K.; Navon, I. M. 1 2008 Combined penalty-multiplier nonlinearly constrained optimization methods for enforcing conservation of integral invariants in shallow-water equations models. Zbl 0509.76021Navon, I. M.; de Villiers, R. 1 1982 FESW - a finite-element Fortran IV program for solving the shallow-water equations. Zbl 0412.65055Navon, I. M.; Muller, U. 1 1979 Calculation of uncertainty propagation using adjoint equations. Zbl 1043.76515Alekseev, A. K.; Navon, I. M. 1 2003 Numerical control of two-dimensional shock waves in dual solution domain by instant temperature disturbances. Zbl 1430.76356Alekseev, A. K.; Navon, I. M. 1 2013 A nonintrusive hybrid neural-physics modeling of incomplete dynamical systems: Lorenz equations. Zbl 1486.37045Pawar, Suraj; San, Omer; Rasheed, Adil; Navon, Ionel M. 1 2021 Criteria of optimality for sensors’ location based on adjoint transformation of observation data interpolation error. Zbl 1196.80004Alekseev, A. K.; Navon, I. M. 1 2010 A penalized four-dimensional variational data assimilation method for reducing forecast error related to adaptive observations. Zbl 1412.86004Hossen, M. J.; Navon, I. M.; Fang, F. 1 2012 Vectorization of conjugate-gradient methods for large-scale minimization in meteorology. Zbl 0681.90065Navon, I. M.; Phua, P. K. H.; Ramamurthy, M. 1 1990 Spectral stochastic two-scale convergence method for parabolic PDEs. Zbl 1217.74098Jardak, M.; Navon, I. M. 1 2011 Feasibility of DEIM for retrieving the initial field via dimensionality reduction. Zbl 07500740Wang, Yuepeng; Ding, Xuemei; Hu, Kun; Fang, Fangxin; Navon, I. M.; Lin, Guang 1 2021 CAMERA: a method for cost-aware, adaptive, multifidelity, efficient reliability analysis. Zbl 07620378Ashwin Renganathan, S.; Rao, Vishwas; Navon, Ionel M. 1 2023 Application of deterministic and randomized dynamic mode decomposition in epidemiology and fluid dynamics. Zbl 07621964Bistrian, Diana A.; Dimitriu, Gabriel; Navon, Ionel M. 1 2020 Physics-data combined machine learning for parametric reduced-order modelling of nonlinear dynamical systems in small-data regimes. Zbl 07644844Fu, Jinlong; Xiao, Dunhui; Fu, Rui; Li, Chenfeng; Zhu, Chuanhua; Arcucci, Rossella; Navon, Ionel M. 2 2023 CAMERA: a method for cost-aware, adaptive, multifidelity, efficient reliability analysis. Zbl 07620378Ashwin Renganathan, S.; Rao, Vishwas; Navon, Ionel M. 1 2023 A nonintrusive hybrid neural-physics modeling of incomplete dynamical systems: Lorenz equations. Zbl 1486.37045Pawar, Suraj; San, Omer; Rasheed, Adil; Navon, Ionel M. 1 2021 Feasibility of DEIM for retrieving the initial field via dimensionality reduction. Zbl 07500740Wang, Yuepeng; Ding, Xuemei; Hu, Kun; Fang, Fangxin; Navon, I. M.; Lin, Guang 1 2021 Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network. Zbl 1442.76040Cheng, M.; Fang, F.; Pain, C. C.; Navon, I. M. 4 2020 Application of deterministic and randomized dynamic mode decomposition in epidemiology and fluid dynamics. Zbl 07621964Bistrian, Diana A.; Dimitriu, Gabriel; Navon, Ionel M. 1 2020 A domain decomposition non-intrusive reduced order model for turbulent flows. Zbl 1411.76072Xiao, D.; Heaney, C. E.; Fang, F.; Mottet, L.; Hu, R.; Bistrian, D. A.; Aristodemou, E.; Navon, I. M.; Pain, C. C. 6 2019 A domain decomposition method for the non-intrusive reduced order modelling of fluid flow. Zbl 1441.76074Xiao, D.; Fang, F.; Heaney, C. E.; Navon, I. M.; Pain, C. C. 3 2019 Efficiency of randomised dynamic mode decomposition for reduced order modelling. Zbl 07474458Bistrian, D. A.; Navon, I. M. 3 2018 Parameter identification techniques applied to an environmental pollution model. Zbl 1412.65043Wang, Yuepeng; Cheng, Yue; Navon, I. Michael; Guan, Yuanhong 2 2018 A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications. Zbl 1439.65124Xiao, D.; Fang, F.; Pain, C. C.; Navon, I. M. 29 2017 A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting. Zbl 1378.74067Xiao, D.; Yang, P.; Fang, F.; Xiang, J.; Pain, C. C.; Navon, I. M.; Chen, M. 12 2017 Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems. Zbl 1348.92122Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. 10 2017 Non-intrusive reduced order modelling of fluid-structure interactions. Zbl 1425.74167Xiao, D.; Yang, P.; Fang, F.; Xiang, J.; Pain, C. C.; Navon, I. M. 20 2016 Non-intrusive reduced order modelling of the Navier-Stokes equations. Zbl 1423.76287Xiao, D.; Fang, F.; Buchan, A. G.; Pain, C. C.; Navon, I. M.; Muggeridge, A. 35 2015 POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation. Zbl 1349.76535Ştefănescu, R.; Sandu, A.; Navon, I. M. 29 2015 A POD reduced order model for resolving angular direction in neutron/photon transport problems. Zbl 1352.82030Buchan, A. G.; Calloo, A. A.; Goffin, M. G.; Dargaville, S.; Fang, F.; Pain, C. C.; Navon, I. M. 16 2015 POD-DEIM approach on dimension reduction of a multi-species host-parasitoid system. Zbl 1515.35131Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. 14 2015 Nonlinear model reduction for the Navier-Stokes equations using residual DEIM method. Zbl 1349.76288Xiao, D.; Fang, F.; Buchan, A. G.; Pain, C. C.; Navon, I. M.; Du, J.; Hu, G. 58 2014 Application of POD-DEIM approach for dimension reduction of a diffusive predator-prey system with Allee effect. Zbl 1448.92187Dimitriu, Gabriel; Navon, Ionel M.; Ştefănescu, Răzvan 6 2014 Computational methods for data evaluation and assimilation. Zbl 1283.68014Cacuci, Dan Gabriel; Navon, Ionel Michael; Ionescu-Bujor, Mihaela 6 2014 Non-parametric calibration of the local volatility surface for European options using a second-order Tikhonov regularization. Zbl 1294.91187Geng, Jian; Navon, I. Michael; Chen, Xiao 3 2014 Reduced order borehole induction modelling. Zbl 07512419Ardjmandpour, N.; Pain, C. C.; Fang, F.; Buchan, A. G.; Singer, J.; Player, M. A.; Xu, Xu; Navon, I. M.; Carter, J. 2 2014 POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model. Zbl 1286.76106Ştefănescu, R.; Navon, I. M. 48 2013 Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair. Zbl 1297.76107Xiao, D.; Fang, F.; Du, J.; Pain, C. C.; Navon, I. M.; Buchan, A. G.; ElSheikh, A. H.; Hu, G. 29 2013 Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods. Zbl 1284.65132Fang, F.; Pain, C. C.; Navon, I. M.; Elsheikh, A. H.; Du, J.; Xiao, D. 25 2013 Reduced order modeling based on POD of a parabolized Navier-Stokes equations model II: trust region POD 4D VAR data assimilation. Zbl 1319.76030Du, Juan; Navon, I. M.; Zhu, Jiang; Fang, Fangxin; Alekseev, A. K. 22 2013 POD reduced-order unstructured mesh modeling applied to 2D and 3D fluid flow. Zbl 1319.76026Du, J.; Fang, F.; Pain, C. C.; Navon, I. M.; Zhu, J.; Ham, D. A. 20 2013 A POD reduced-order model for eigenvalue problems with application to reactor physics. Zbl 1352.82018Buchan, A. G.; Pain, C. C.; Fang, F.; Navon, I. M. 11 2013 A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems. Zbl 1490.65171Luo, Zhendong; Li, Hong; Sun, Ping; An, Jing; Navon, Ionel Michael 6 2013 The independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and a finite element shallow water model. Zbl 1391.76322Fang, F.; Pain, C. C.; Navon, I. M.; Cacuci, D. G.; Chen, X. 2 2013 Numerical control of two-dimensional shock waves in dual solution domain by instant temperature disturbances. Zbl 1430.76356Alekseev, A. K.; Navon, I. M. 1 2013 A dual-weighted trust-region adaptive POD 4-D var applied to a finite-volume shallow water equations model on the sphere. Zbl 1426.76347Chen, X.; Akella, S.; Navon, I. M. 8 2012 An optimizing implicit difference scheme based on proper orthogonal decomposition for the two-dimensional unsaturated soil water flow equation. Zbl 1426.76466Di, Zhenhua; Luo, Zhendong; Xie, Zhenghui; Wang, Aiwen; Navon, I. M. 6 2012 Effect of random perturbations on adaptive observation techniques. Zbl 1426.76632Hossen, M. J.; Navon, I. M.; Daescu, D. N. 3 2012 A penalized four-dimensional variational data assimilation method for reducing forecast error related to adaptive observations. Zbl 1412.86004Hossen, M. J.; Navon, I. M.; Fang, F. 1 2012 An optimizing finite difference scheme based on proper orthogonal decomposition for CVD equations. Zbl 1429.35184Du, Juan; Zhu, Jiang; Luo, Zhendong; Navon, I. M. 16 2011 The estimation of functional uncertainty using polynomial chaos and adjoint equations. Zbl 1226.65075Alekseev, A. K.; Navon, I. M.; Zelentsov, M. E. 11 2011 A dual-weighted trust-region adaptive POD 4D-VAR applied to a finite-element shallow-water equations model. Zbl 1428.76145Chen, X.; Navon, I. M.; Fang, F. 9 2011 The independent set perturbation adjoint method: a new method of differentiating mesh-based fluids models. Zbl 1285.76015Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A. 3 2011 Spectral stochastic two-scale convergence method for parabolic PDEs. Zbl 1217.74098Jardak, M.; Navon, I. M. 1 2011 Comparison of sequential data assimilation methods for the Kuramoto-Sivashinsky equation. Zbl 1425.76242Jardak, M.; Navon, I. M.; Zupanski, M. 11 2010 A POD goal-oriented error measure for mesh optimization. Zbl 1425.65096Fang, F.; Pain, C. C.; Navon, I. M.; Gorman, G. J.; Piggott, M. D.; Allison, P. A.; Goddard, A. J. H. 4 2010 Criteria of optimality for sensors’ location based on adjoint transformation of observation data interpolation error. Zbl 1196.80004Alekseev, A. K.; Navon, I. M. 1 2010 Mixed finite element formulation and error estimates based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations. Zbl 1391.76351Luo, Zhendong; Chen, Jing; Navon, I. M.; Yang, Xiaozhong 45 2009 An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems. Zbl 1161.76032Luo, Zhendong; Chen, Jing; Navon, I. M.; Zhu, Jiang 36 2009 A POD reduced-order 4D-Var adaptive mesh ocean modelling approach. Zbl 1163.86002Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Farrell, P. E.; Allison, P. A.; Goddard, A. J. H. 21 2009 Reduced-order modelling of an adaptive mesh ocean model. Zbl 1155.86004Fang, F.; Pain, C. C.; Navon, I. M.; Piggott, M. D.; Gorman, G. J.; Allison, P. A.; Goddard, A. J. H. 19 2009 Comparison of advanced large-scale minimization algorithms for the solution of inverse ill-posed problems. Zbl 1189.90221Alekseev, A. K.; Navon, I. M.; Steward, J. L. 16 2009 Estimation of goal functional error arising from iterative solution of Euler equations. Zbl 1184.76765Alekseev, A. K.; Navon, I. M. 1 2008 A reduced-order approach to four-dimensional variational data assimilation using proper orthogonal decomposition. Zbl 1370.86002Cao, Yanhua; Zhu, Jiang; Navon, I. M.; Luo, Zhendong 56 2007 An optimizing reduced order FDS for the tropical Pacific Ocean reduced gravity model. Zbl 1205.86007Luo, Zhendong; Chen, Jing; Zhu, Jiang; Wang, Ruiwen; Navon, I. M. 44 2007 Proper orthogonal decomposition approach and error estimation of mixed finite element methods for the tropical Pacific Ocean reduced gravity model. Zbl 1173.76348Luo, Zhendong; Zhu, Jiang; Wang, Ruiwen; Navon, I. M. 39 2007 Efficiency of a POD-based reduced second-order adjoint model in 4D-var data assimilation. Zbl 1370.76122Daescu, D. N.; Navon, I. M. 28 2007 Reduced-order modeling of the upper tropical Pacific ocean model using proper orthogonal decomposition. Zbl 1161.86002Cao, Yanhua; Zhu, Jiang; Luo, Zhendong; Navon, I. M. 36 2006 Open boundary control problem for Navier-Stokes equations including a free surface: data assimilation. Zbl 1118.49017Gejadze, I. Yu.; Copeland, G. J. M.; Navon, I. M. 5 2006 Adjoint a posteriori error measures for anisotropic mesh optimisation. Zbl 1206.65250Power, P. W.; Pain, C. C.; Piggott, M. D.; Fang, F.; Gorman, G. J.; Umpleby, A. P.; Goddard, A. J. H.; Navon, I. M. 4 2006 A posteriori error estimation by postprocessor independent of method of flow field calculation. Zbl 1103.76037Alekseev, A. K.; Navon, I. M. 3 2006 A comparative study of the performance of high-resolution advection schemes in the context of data assimilation. Zbl 1124.76036Akella, S.; Navon, I. M. 2 2006 Sensitivity and uncertainty analysis. Vol. 2: Applications to large-scale systems. Zbl 1083.60002Cacuci, Dan G.; Ionescu-Bujor, Mihaela; Navon, Ionel Michael 22 2005 A posteriori pointwise error estimation for compressible fluid flows using adjoint parameters and Lagrange remainder. Zbl 1063.76067Alekseev, A. K.; Navon, I. M. 5 2005 On a posteriori pointwise error estimation using adjoint temperature and Lagrange remainder. Zbl 1102.80005Alekseev, A. K.; Navon, I. M. 5 2005 Adjoint correction and bounding of error using Lagrange form of truncation term. Zbl 1083.65087Alekseev, A. K.; Navon, I. M. 2 2005 Optimal control of cylinder wakes via suction and blowing. Zbl 1151.76443Li, Zhijin; Navon, I. M.; Hussaini, M. Y.; Le Dimet, F.-X. 23 2003 An analysis of a hybrid optimization method for variational data assimilation. Zbl 1161.76449Daescu, Dacian; Navon, I. M. 6 2003 Optimal control of flow with discontinuities. Zbl 1061.76076Homescu, Chris; Navon, I. M. 4 2003 Truncated-Newton training algorithm for neurocomputational viscoplastic model. Zbl 1119.74622Al-Haik, M. S.; Garmestani, H.; Navon, I. M. 4 2003 Numerical and theoretical considerations for sensitivity calculation of discontinuous flow. Zbl 1157.93361Homescu, Chris; Navon, I. M. 4 2003 Calculation of uncertainty propagation using adjoint equations. Zbl 1043.76515Alekseev, A. K.; Navon, I. M. 1 2003 Suppression of vortex shedding for flow around a circular cylinder using optimal control. Zbl 1007.76019Homescu, C.; Navon, I. M.; Li, Z. 36 2002 Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems. Zbl 0984.65125Castaings, W.; Navon, I. M. 7 2001 Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements. Zbl 0946.65113Li, Jichun; Navon, I. M. 15 1999 A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem. Zbl 0937.65114Li, Jichun; Navon, I. M. 4 1999 Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type. Zbl 0907.65109Li, J.; Navon, I. M. 48 1998 Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Convection-diffusion type. Zbl 0936.65134Li, Jichun; Navon, I. M. 25 1998 Analysis of the Turkel-Zwas scheme for the two-dimensional shallow water equations in spherical coordinates. Zbl 0883.76060Neta, B.; Giraldo, F. X.; Navon, I. M. 9 1997 A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products. Zbl 0831.90124Wang, Zhi; Navon, I. M.; Zou, X.; Le Dimet, F. X. 13 1995 Parallel block preconditioning techniques for the numerical simulation of the shallow water flow using finite element methods. Zbl 0840.76031Cai, Y.; Navon, I. M. 7 1995 Parallelizable PCG methods for the Cray Y-MP and TMC CM-2. Zbl 0847.65020Oppe, Thomas C.; Holter, William H.; Navon, I. M. 2 1994 Numerical experience with limited-memory quasi-Newton and truncated Newton methods. Zbl 0784.90086Zou, X.; Navon, I. M.; Berger, M.; Phua, K. H.; Schlick, T.; Le Dimet, F. X. 21 1993 Domain decomposition and parallel processing of a finite element model of the shallow water equations. Zbl 0784.76052Navon, I. M.; Cai, Y. 6 1993 Finite-element schemes for extended integrations of atmospheric models. Zbl 0696.76031Steppeler, J.; Navon, I. M.; Lu, H.-I. 2 1990 Vectorization of conjugate-gradient methods for large-scale minimization in meteorology. Zbl 0681.90065Navon, I. M.; Phua, P. K. H.; Ramamurthy, M. 1 1990 Analysis of the Turkel-Zwas scheme for the shallow-water equations. Zbl 0669.76037Neta, B.; Navon, I. M. 4 1989 PENT: A periodic pentadiagonal systems solver. Zbl 0609.65015Navon, I. M. 9 1987 A Numerov-Galerkin technique applied to a finite-element shallow-water equations model with enforced conservation of integral invariants and selective lumping. Zbl 0526.76032Navon, I. M. 4 1983 Combined penalty-multiplier nonlinearly constrained optimization methods for enforcing conservation of integral invariants in shallow-water equations models. Zbl 0509.76021Navon, I. M.; de Villiers, R. 1 1982 Implementation of a posteriori methods for enforcing conservation of potential enstrophy and mass in discretized shallow-water equations models. Zbl 0492.76023Navon, I. M. 3 1981 A linear ADI method for the shallow-water equations. Zbl 0454.76032Fairweather, G.; Navon, I. M. 4 1980 Finite-element simulation of the shallow-water equations model on a limited-area domain. Zbl 0438.76017Navon, I. M. 11 1979 An implicit compact fourth-order algorithm for solving the shallow-water equations in conservation-law form. Zbl 0434.65079Navon, I. M.; Riphagen, H. A. 8 1979 Numerical methods for the solution of the shallow-water equations in meteorology. Zbl 0443.76014Navon, I. M. 2 1979 FESW - a finite-element Fortran IV program for solving the shallow-water equations. Zbl 0412.65055Navon, I. M.; Muller, U. 1 1979 all cited Publications top 5 cited Publications all top 5 Cited by 1,104 Authors 54 Navon, Ionel Michael 53 Luo, Zhendong 26 Pain, Christopher C. 23 Fang, Fangxin 17 Iliescu, Traian 16 Dehghan Takht Fooladi, Mehdi 15 Abbaszadeh, Mostafa 14 Rozza, Gianluigi 12 Li, Jichun 12 Teng, Fei 11 Alekseev, Aleksey K. 11 Sandu, Adrian 10 Stabile, Giovanni 9 Li, Hong 9 Protas, Bartosz 9 Si, Zhiyong 9 Wang, Zhu 8 Buchan, Andrew G. 8 San, Omer 8 Xiao, Dunhui 8 Zhou, Yanjie 7 Chen, Jing 7 Choi, Youngsoo 6 Chaturantabut, Saifon 6 Cordier, Laurent 6 He, Yinnian 6 Piggott, Matthew D. 6 Rebholz, Leo G. 6 Sun, Ping 6 Willcox, Karen E. 6 Xie, Zhenghui 5 Ahmed, Shady E. 5 Arcucci, Rossella 5 Ballarin, Francesco 5 Bergmann, Michel 5 Carlberg, Kevin T. 5 Du, Juan 5 Gejadze, Igor Yu. 5 Giannakoglou, Kyriakos C. 5 Giraldo, Francis X. 5 Gorman, Gerard J. 5 Hesthaven, Jan S. 5 Hou, Yanren 5 Huang, Pengzhan 5 Jia, Jiteng 5 Maday, Yvon 5 Rui, Hongxing 5 Singler, John R. 5 Zhang, Yunzhang 4 Allison, P. A. 4 Bistrian, Diana Alina 4 Borggaard, Jeff T. 4 Chen, Shaochun 4 Daescu, Dacian N. 4 Feng, Xinlong 4 Gao, Junqiang 4 Goddard, A. J. H. 4 Heemink, Arnold Willem 4 Karatzas, Efthymios N. 4 Kawahara, Mutsuto 4 Li, Huanrong 4 Quarteroni, Alfio M. 4 Rasheed, Adil 4 Rubino, Samuele 4 Song, Junpeng 4 Soulaimani, Azzeddine 4 Tu, Xuemin 4 Wang, Yuepeng 4 Xia, Hong 4 Xie, Xuping 4 Zhang, Jicai 4 Zhu, Jiang 3 Allery, Cyrille 3 Altaf, M. Umer 3 Brancher, Jean-Pierre 3 Cacuci, Dan Gabriel 3 Chen, Haibo 3 Chen, Xiao 3 D’Amore, Luisa 3 Di, Zhenhua 3 Dimitriu, Gabriel 3 Duressa, Gemechis File 3 Durlofsky, Louis J. 3 Farthing, Matthew W. 3 Guo, Yike 3 Han, Houde 3 Heaney, Claire E. 3 Hoteit, Ibrahim 3 Huang, Zhongyi 3 Huynh, Kevin 3 Jiang, Yaolin 3 Kloosterman, Jan Leen 3 Koc, Birgul 3 Lathouwers, Danny 3 Le Dimet, Francois-Xavier 3 Liu, Xiaowei 3 Lv, Xianqing 3 Manzoni, Andrea 3 Papadimitriou, Dimitrios I. 3 Perkó, Zoltán ...and 1,004 more Authors all top 5 Cited in 131 Serials 82 Journal of Computational Physics 76 Computer Methods in Applied Mechanics and Engineering 52 Computers & Mathematics with Applications 35 Computers and Fluids 22 Journal of Computational and Applied Mathematics 18 International Journal for Numerical Methods in Fluids 17 Applied Mathematics and Computation 15 Applied Numerical Mathematics 15 International Journal of Computational Fluid Dynamics 14 Journal of Scientific Computing 12 International Journal for Numerical Methods in Engineering 10 Journal of Fluid Mechanics 9 Journal of Mathematical Analysis and Applications 9 Applied Mathematical Modelling 9 SIAM Journal on Scientific Computing 8 Mathematics and Computers in Simulation 7 Advances in Computational Mathematics 7 Engineering Analysis with Boundary Elements 7 Computational Geosciences 6 Mathematical Problems in Engineering 5 SIAM Journal on Numerical Analysis 5 Physica D 5 Numerical Algorithms 5 European Journal of Mechanics. 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Series B 1 Acta Applicandae Mathematicae 1 Optimization 1 Journal of Complexity 1 Constructive Approximation 1 Computational Mechanics 1 SIAM Journal on Matrix Analysis and Applications 1 Science in China. Series A 1 Japan Journal of Industrial and Applied Mathematics 1 International Journal of High Speed Computing 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Statistical Computation and Simulation 1 SIAM Review 1 Advances in Engineering Software 1 Tatra Mountains Mathematical Publications 1 Applied Mathematics. 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Mathematical, Physical and Engineering Sciences 1 Discrete Dynamics in Nature and Society ...and 31 more Serials all top 5 Cited in 31 Fields 419 Numerical analysis (65-XX) 287 Fluid mechanics (76-XX) 168 Partial differential equations (35-XX) 54 Geophysics (86-XX) 40 Mechanics of deformable solids (74-XX) 35 Systems theory; control (93-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 29 Statistics (62-XX) 29 Biology and other natural sciences (92-XX) 27 Classical thermodynamics, heat transfer (80-XX) 26 Operations research, mathematical programming (90-XX) 21 Computer science (68-XX) 17 Probability theory and stochastic processes (60-XX) 12 Dynamical systems and ergodic theory (37-XX) 12 Statistical mechanics, structure of matter (82-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 9 Ordinary differential equations (34-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Optics, electromagnetic theory (78-XX) 5 Approximations and expansions (41-XX) 5 Quantum theory (81-XX) 4 Real functions (26-XX) 3 Integral equations (45-XX) 3 Mechanics of particles and systems (70-XX) 3 Information and communication theory, circuits (94-XX) 2 Differential geometry (53-XX) 2 Mathematics education (97-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year