Edit Profile Navon, Ionel Michael Compute Distance To: Compute Author ID: navon.ionel-michael Published as: Navon, I. M.; Navon, I. Michael; Navon, Ionel M.; Navon, Ionel Michael External Links: MGP Documents Indexed: 95 Publications since 1978, including 6 Books all top 5 Co-Authors 10 single-authored 23 Fang, Fangxin 20 Pain, Christopher C. 12 Alekseev, Aleksey K. 9 Luo, Zhendong 9 Xiao, Dianshi 7 Zhu, Jiang 6 Du, Juan 5 Buchan, Andrew G. 5 Gorman, Gerard J. 5 Piggott, Matthew D. 5 Ştefănescu, Răzvan 4 Allison, P. A. 4 Chen, Xiao 4 Goddard, Anthony J. H. 4 Li, Jichun 3 Cacuci, Dan Gabriel 3 Chen, Jing 3 Daescu, Dacian N. 3 Dimitriu, Gabriel 3 Homescu, Chris 3 Le Dimet, Francois-Xavier 2 Akella, Srinivas 2 Cai, Yujin 2 Cao, Yanhua 2 Elsheikh, Ahmed H. 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 Xiang, Jiansheng 1 Al-Haik, M. S. 1 An, Jing 1 Aristodemou, Elsa 1 Berger, M. F. 1 Bistrian, Diana Alina 1 Cai, Yanjiao 1 Calloo, A. A. 1 Castaings, W. 1 Chen, Mengshan 1 Cheng, Men 1 Cheng, Mingdong 1 Cheng, Yue 1 Copeland, Graham J. M. 1 Dargaville, Steven 1 de Villiers, Rosalie 1 Di, Zhenhua 1 Fairweather, Graeme 1 Farrell, Patrick E. 1 Garmestani, Hamid 1 Gejadze, Igor Yu. 1 Geng, Jian 1 Giraldo, Francis X. 1 Goffin, M. G. 1 Guan, Yuanhong 1 Ham, David A. 1 Holter, William H. 1 Hu, Guoding 1 Hu, Guyu 1 Hu, Rong 1 Hussaini, M. Yousuff 1 Li, Hong 1 Lu, Huei-Iin 1 Mottet, Laetitia 1 Muggeridge, Ann H. 1 Müller, Ulrich A. 1 Oppe, Thomas C. 1 Phua, Kang-Hoh 1 Phua, Paul Kang-Hoh 1 Power, P. W. 1 Ramamurthy, M. 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, Yuepeng 1 Wang, Zhi 1 Xie, Zhenghui 1 Yang, Peikang 1 Yang, Pengji 1 Yang, Xiaozhong 1 Zelentsov, M. E. 1 Zhu, Joe 1 Zou, Xiaochen 1 Zou, Xiaorong 1 Zupanski, M. all top 5 Serials 21 International Journal for Numerical Methods in Fluids 13 Computer Methods in Applied Mechanics and Engineering 13 Journal of Computational Physics 10 Computers & Mathematics with Applications 4 International Journal of Computational Fluid Dynamics 3 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 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 Contributions to Atmospheric Physics all top 5 Fields 59 Numerical analysis (65-XX) 59 Fluid mechanics (76-XX) 20 Partial differential equations (35-XX) 17 Geophysics (86-XX) 7 Operations research, mathematical programming (90-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Computer science (68-XX) 4 Mechanics of deformable solids (74-XX) 3 Statistics (62-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Biology and other natural sciences (92-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 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-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 82 Publications have been cited 840 times in 469 Documents Cited by ▼ Year ▼ 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 45 2007 Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type. Zbl 0907.65109Li, J.; Navon, I. M. 39 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 36 2009 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. 35 2007 An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems. Zbl 1161.76032Luo, Zhendong; Chen, Jing; Navon, I. M.; Zhu, Jiang 34 2009 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. 34 2006 Suppression of vortex shedding for flow around a circular cylinder using optimal control. Zbl 1007.76019Homescu, C.; Navon, I. M.; Li, Z. 34 2002 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. 33 2007 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. 30 2014 POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model. Zbl 1286.76106Ştefănescu, R.; Navon, I. M. 27 2013 Efficiency of a POD-based reduced second-order adjoint model in 4D-var data assimilation. Zbl 1370.76122Daescu, D. N.; Navon, I. M. 25 2007 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 Optimal control of cylinder wakes via suction and blowing. Zbl 1151.76443Li, Zhijin; Navon, I. M.; Hussaini, M. Y.; Le Dimet, F.-X. 20 2003 Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Convection-diffusion type. Zbl 0936.65134Li, Jichun; Navon, I. M. 20 1998 Sensitivity and uncertainty analysis. Vol. 2: Applications to large-scale systems. Zbl 1083.60002Cacuci, Dan G.; Ionescu-Bujor, Mihaela; Navon, Ionel Michael 19 2005 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. 19 1993 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. 17 2015 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. 15 2013 POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation. Zbl 1349.76535Ştefănescu, R.; Sandu, A.; Navon, I. M. 14 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. 14 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. 14 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. 13 2013 An optimizing finite difference scheme based on proper orthogonal decomposition for CVD equations. Zbl 1429.35184Du, Juan; Zhu, Jiang; Luo, Zhendong; Navon, I. M. 13 2011 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. 13 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. 13 2009 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 POD-DEIM approach on dimension reduction of a multi-species host-parasitoid system. Zbl 06542730Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. 11 2015 Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements. Zbl 0946.65113Li, Jichun; Navon, I. M. 11 1999 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. 10 2016 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. 9 2017 PENT: A periodic pentadiagonal systems solver. Zbl 0609.65015Navon, I. M. 9 1987 Finite-element simulation of the shallow-water equations model on a limited-area domain. Zbl 0438.76017Navon, I. M. 9 1979 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. 8 1997 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 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. 6 2015 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. 6 2012 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. 6 2011 Comparison of sequential data assimilation methods for the Kuramoto-Sivashinsky equation. Zbl 1425.76242Jardak, M.; Navon, I. M.; Zupanski, M. 6 2010 Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems. Zbl 0984.65125Castaings, W.; Navon, I. M. 6 2001 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 implicit compact fourth-order algorithm for solving the shallow-water equations in conservation-law form. Zbl 0434.65079Navon, I. M.; Riphagen, H. A. 6 1979 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. 5 2017 Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems. Zbl 1348.92122Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. 5 2017 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. 5 2013 The estimation of functional uncertainty using polynomial chaos and adjoint equations. Zbl 1226.65075Alekseev, A. K.; Navon, I. M.; Zelentsov, M. E. 5 2011 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 posteriori pointwise error estimation for compressible fluid flows using adjoint parameters and Lagrange remainder. Zbl 1063.76067Alekseev, A. K.; Navon, I. M. 5 2005 An analysis of a hybrid optimization method for variational data assimilation. Zbl 1161.76449Daescu, Dacian; Navon, I. M. 5 2003 Computational methods for data evaluation and assimilation. Zbl 1283.68014Cacuci, Dan Gabriel; Navon, Ionel Michael; Ionescu-Bujor, Mihaela 4 2014 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 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 Numerical and theoretical considerations for sensitivity calculation of discontinuous flow. Zbl 1157.93361Homescu, Chris; Navon, I. M. 4 2003 Optimal control of flow with discontinuities. Zbl 1061.76076Homescu, Chris; Navon, I. M. 4 2003 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 A linear ADI method for the shallow-water equations. Zbl 0454.76032Fairweather, G.; Navon, I. M. 4 1980 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. 3 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. 3 2012 Truncated-Newton training algorithm for neurocomputational viscoplastic model. Zbl 1119.74622Al-Haik, M. S.; Garmestani, H.; Navon, I. M. 3 2003 A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem. Zbl 0937.65114Li, Jichun; Navon, I. M. 3 1999 Analysis of the Turkel-Zwas scheme for the shallow-water equations. Zbl 0669.76037Neta, B.; Navon, I. M. 3 1989 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 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. 2 2020 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 Effect of random perturbations on adaptive observation techniques. Zbl 1426.76632Hossen, M. J.; Navon, I. M.; Daescu, D. N. 2 2012 A posteriori error estimation by postprocessor independent of method of flow field calculation. Zbl 1103.76037Alekseev, A. K.; Navon, I. M. 2 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 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 Finite-element schemes for extended integrations of atmospheric models. Zbl 0696.76031Steppeler, J.; Navon, I. M.; Lu, H.-I. 2 1990 SHALL 4 - an implicit compact fourth-order Fortran program for solving the shallow-water equations in conservation-law form. Zbl 0473.76030Navon, I. M.; Riphagen, H. A. 2 1981 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. 1 2019 Parameter identification techniques applied to an environmental pollution model. Zbl 1412.65043Wang, Yuepeng; Cheng, Yue; Navon, I. Michael; Guan, Yuanhong 1 2018 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 1 2014 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 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. 1 2011 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 Estimation of goal functional error arising from iterative solution of Euler equations. Zbl 1184.76765Alekseev, A. K.; Navon, I. M. 1 2008 Adjoint correction and bounding of error using Lagrange form of truncation term. Zbl 1083.65087Alekseev, A. K.; Navon, I. M. 1 2005 Calculation of uncertainty propagation using adjoint equations. Zbl 1043.76515Alekseev, A. K.; Navon, I. M. 1 2003 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 Numerical methods for the solution of the shallow-water equations in meteorology. Zbl 0443.76014Navon, I. M. 1 1979 FESW - a finite-element Fortran IV program for solving the shallow-water equations. Zbl 0412.65055Navon, I. M.; Muller, U. 1 1979 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. 2 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. 3 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. 1 2019 Parameter identification techniques applied to an environmental pollution model. Zbl 1412.65043Wang, Yuepeng; Cheng, Yue; Navon, I. Michael; Guan, Yuanhong 1 2018 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. 9 2017 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. 5 2017 Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems. Zbl 1348.92122Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. 5 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. 10 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. 17 2015 POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation. Zbl 1349.76535Ştefănescu, R.; Sandu, A.; Navon, I. M. 14 2015 POD-DEIM approach on dimension reduction of a multi-species host-parasitoid system. Zbl 06542730Dimitriu, Gabriel; Ştefănescu, Răzvan; Navon, Ionel M. 11 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. 6 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. 30 2014 Computational methods for data evaluation and assimilation. Zbl 1283.68014Cacuci, Dan Gabriel; Navon, Ionel Michael; Ionescu-Bujor, Mihaela 4 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 1 2014 POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model. Zbl 1286.76106Ştefănescu, R.; Navon, I. M. 27 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. 15 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. 14 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. 14 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. 13 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. 5 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. 6 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. 3 2012 Effect of random perturbations on adaptive observation techniques. Zbl 1426.76632Hossen, M. J.; Navon, I. M.; Daescu, D. N. 2 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. 13 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. 6 2011 The estimation of functional uncertainty using polynomial chaos and adjoint equations. Zbl 1226.65075Alekseev, A. K.; Navon, I. M.; Zelentsov, M. E. 5 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. 1 2011 Comparison of sequential data assimilation methods for the Kuramoto-Sivashinsky equation. Zbl 1425.76242Jardak, M.; Navon, I. M.; Zupanski, M. 6 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 36 2009 An optimizing reduced PLSMFE formulation for non-stationary conduction-convection problems. Zbl 1161.76032Luo, Zhendong; Chen, Jing; Navon, I. M.; Zhu, Jiang 34 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. 13 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. 13 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 45 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. 35 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. 33 2007 Efficiency of a POD-based reduced second-order adjoint model in 4D-var data assimilation. Zbl 1370.76122Daescu, D. N.; Navon, I. M. 25 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. 34 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. 2 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 19 2005 On a posteriori pointwise error estimation using adjoint temperature and Lagrange remainder. Zbl 1102.80005Alekseev, A. K.; Navon, I. M. 5 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 Adjoint correction and bounding of error using Lagrange form of truncation term. Zbl 1083.65087Alekseev, A. K.; Navon, I. M. 1 2005 Optimal control of cylinder wakes via suction and blowing. Zbl 1151.76443Li, Zhijin; Navon, I. M.; Hussaini, M. Y.; Le Dimet, F.-X. 20 2003 An analysis of a hybrid optimization method for variational data assimilation. Zbl 1161.76449Daescu, Dacian; Navon, I. M. 5 2003 Numerical and theoretical considerations for sensitivity calculation of discontinuous flow. Zbl 1157.93361Homescu, Chris; Navon, I. M. 4 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. 3 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. 34 2002 Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems. Zbl 0984.65125Castaings, W.; Navon, I. M. 6 2001 Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements. Zbl 0946.65113Li, Jichun; Navon, I. M. 11 1999 A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem. Zbl 0937.65114Li, Jichun; Navon, I. M. 3 1999 Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type. Zbl 0907.65109Li, J.; Navon, I. M. 39 1998 Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Convection-diffusion type. Zbl 0936.65134Li, Jichun; Navon, I. M. 20 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. 8 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. 19 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 Analysis of the Turkel-Zwas scheme for the shallow-water equations. Zbl 0669.76037Neta, B.; Navon, I. M. 3 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 SHALL 4 - an implicit compact fourth-order Fortran program for solving the shallow-water equations in conservation-law form. Zbl 0473.76030Navon, I. M.; Riphagen, H. A. 2 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. 9 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. 6 1979 Numerical methods for the solution of the shallow-water equations in meteorology. Zbl 0443.76014Navon, I. M. 1 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 781 Authors 50 Navon, Ionel Michael 47 Luo, Zhendong 22 Pain, Christopher C. 20 Fang, Fangxin 13 Li, Jichun 12 Iliescu, Traian 11 Sandu, Adrian 10 Alekseev, Aleksey K. 10 Teng, Fei 9 Abbaszadeh, Mostafa 9 Dehghan Takht Fooladi, Mehdi 9 Li, Hong 9 Protas, Bartosz 9 Si, Zhiyong 8 Rozza, Gianluigi 8 Wang, Zhu 8 Xiao, Dianshi 8 Zhou, Yanjie 7 Buchan, Andrew G. 7 Chen, Jing 6 He, Yinnian 6 Piggott, Matthew D. 6 Rebholz, Leo G. 6 Stabile, Giovanni 6 Sun, Ping 6 Xie, Zhenghui 5 Du, Juan 5 Gejadze, Igor Yu. 5 Giraldo, Francis X. 5 Gorman, Gerard J. 5 Hou, Yanren 5 Huang, Pengzhan 5 Jia, Jiteng 5 Zhang, Yunzhang 4 Allison, P. A. 4 Bergmann, Michel 4 Carlberg, Kevin T. 4 Chen, Shaochun 4 Cordier, Laurent 4 Daescu, Dacian N. 4 Gao, Junqiang 4 Giannakoglou, Kyriakos C. 4 Goddard, Anthony J. H. 4 Kawahara, Mutsuto 4 Quarteroni, Alfio M. 4 Sheela, Suresh Mandir 4 Singh, Arindama 4 Singler, John R. 4 Xia, Hong 4 Zhang, Jicai 4 Zhu, Jiang 3 Arcucci, Rossella 3 Bistrian, Diana Alina 3 Borggaard, Jeff T. 3 Brancher, Jean-Pierre 3 Cacuci, Dan Gabriel 3 Chaturantabut, Saifon 3 Chen, Xiao 3 Dimitriu, Gabriel 3 Durlofsky, Louis J. 3 Feng, Xinlong 3 Han, Houde 3 Heemink, Arnold Willem 3 Hoteit, Ibrahim 3 Huang, Zhongyi 3 Jiang, Yaolin 3 Karatzas, Efthymios N. 3 Kloosterman, Jan Leen 3 Lathouwers, Danny 3 Lv, Xianqing 3 Manzoni, Andrea 3 Papadimitriou, Dimitrios I. 3 Perkó, Zoltán 3 Rao, Vishwas 3 Ryckelynck, David 3 San, Omer 3 Scovazzi, Guglielmo 3 Ştefănescu, Răzvan 3 Volkov, Oleg 3 Wang, Yuepeng 3 Willcox, Karen E. 3 Xiang, Jiansheng 3 Xie, Xuping 3 Yang, Xiaozhong 3 Zhu, Guoqing 2 Akhtar, Imran 2 Al-Baali, Mehiddin 2 Al-Haik, M. S. 2 Alexe, Mihai 2 Alsayyari, Fahad 2 Altaf, M. Umer 2 Alvarez, Gustavo Benitez 2 Ballarin, Francesco 2 Bukshtynov, Vladislav 2 Cao, Yanhua 2 Cardoso, M. A. 2 Carmichael, Gregory R. 2 Chai, Tianfeng 2 Chen, Haibo 2 Chen, Zhihua ...and 681 more Authors all top 5 Cited in 109 Serials 60 Journal of Computational Physics 52 Computer Methods in Applied Mechanics and Engineering 37 Computers & Mathematics with Applications 23 Computers and Fluids 18 International Journal for Numerical Methods in Fluids 18 Journal of Computational and Applied Mathematics 16 Applied Mathematics and Computation 15 Applied Numerical Mathematics 12 International Journal for Numerical Methods in Engineering 8 Journal of Fluid Mechanics 8 Journal of Mathematical Analysis and Applications 8 Journal of Scientific Computing 8 Applied Mathematical Modelling 7 International Journal of Computational Fluid Dynamics 6 Mathematical Problems in Engineering 5 Mathematics and Computers in Simulation 5 Numerical Algorithms 5 SIAM Journal on Scientific Computing 5 Advances in Computational Mathematics 5 Computational Geosciences 4 Mathematics of Computation 4 SIAM Journal on Numerical Analysis 4 Numerical Methods for Partial Differential Equations 4 Physics of Fluids 4 Engineering Analysis with Boundary Elements 4 European Journal of Mechanics. 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Series B 2 Inverse Problems in Science and Engineering 2 SIAM/ASA Journal on Uncertainty Quantification 2 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Communications on Pure and Applied Mathematics 1 International Journal of Heat and Mass Transfer 1 Journal of Engineering Mathematics 1 Molecular Simulation 1 Bulletin of Mathematical Biology 1 Theoretical and Computational Fluid Dynamics 1 Theoretical Population Biology 1 Systems & Control Letters 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Physica D 1 Optimization 1 Journal of Complexity 1 Constructive Approximation 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 Applied Mathematics. Series B (English Edition) 1 Russian Journal of Mathematical Physics 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Differential Equations and Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Abstract and Applied Analysis 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Discrete Dynamics in Nature and Society 1 International Journal of Theoretical and Applied Finance 1 Mathematical & Computational Applications 1 Natural Resource Modeling 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Applied Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Thai Journal of Mathematics 1 International Journal of Computational Methods 1 Mediterranean Journal of Mathematics 1 Journal of Industrial and Management Optimization 1 Acta Mechanica Sinica 1 Journal of Biological Dynamics 1 Frontiers of Mathematics in China 1 Nonlinear Analysis. Hybrid Systems ...and 9 more Serials all top 5 Cited in 29 Fields 301 Numerical analysis (65-XX) 206 Fluid mechanics (76-XX) 134 Partial differential equations (35-XX) 41 Geophysics (86-XX) 28 Mechanics of deformable solids (74-XX) 26 Calculus of variations and optimal control; optimization (49-XX) 25 Systems theory; control (93-XX) 22 Classical thermodynamics, heat transfer (80-XX) 21 Operations research, mathematical programming (90-XX) 19 Biology and other natural sciences (92-XX) 15 Statistics (62-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Probability theory and stochastic processes (60-XX) 10 Computer science (68-XX) 10 Statistical mechanics, structure of matter (82-XX) 8 Ordinary differential equations (34-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Real functions (26-XX) 2 Integral equations (45-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Optics, electromagnetic theory (78-XX) 1 Information and communication theory, circuits (94-XX) 1 Mathematics education (97-XX) Citations by Year