暂无分享,去创建一个
[1] Bernard Haasdonk,et al. Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems , 2015, Comput. Optim. Appl..
[2] Gilead Tadmor,et al. System reduction strategy for Galerkin models of fluid flows , 2009 .
[3] Sivasankaran Rajamanickam,et al. EFFICIENT ALGORITHMS FOR SPARSE SINGULAR VALUE DECOMPOSITION , 2009 .
[4] Karen Willcox,et al. Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems , 2010, SIAM J. Sci. Comput..
[5] Charbel Farhat,et al. Nonlinear model order reduction based on local reduced‐order bases , 2012 .
[6] D. Mingori,et al. Approximate Subspace Iteration for constructing internally balanced reduced order models of unsteady aerodynamic systems , 1996 .
[7] H. Hotelling. Analysis of a complex of statistical variables into principal components. , 1933 .
[8] Timo Tonn. Reduced-basis method (RBM) for non-affine elliptic parametrized PDEs - (motivated by optimization in hydromechanics) , 2012 .
[10] Mihai Anitescu,et al. Proper orthogonal decompositions in multifidelity uncertainty quantification of complex simulation models , 2014, Int. J. Comput. Math..
[11] Athanasios C. Antoulas,et al. Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.
[12] A. Patera,et al. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations , 2007 .
[13] Razvan Stefanescu,et al. Application of POD-DEIM Approach for Dimension Reduction of a Diffusive Predator-Prey System with Allee Effect , 2013, LSSC.
[14] Siep Weiland,et al. Missing Point Estimation in Models Described by Proper Orthogonal Decomposition , 2004, IEEE Transactions on Automatic Control.
[15] Lei Xie,et al. HJB-POD-Based Feedback Design for the Optimal Control of Evolution Problems , 2004, SIAM J. Appl. Dyn. Syst..
[16] Jan Vierendeels,et al. Implicit coupling of partitioned fluid-structure interaction problems with reduced order models , 2007 .
[17] Clarence W. Rowley,et al. Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition , 2005, Int. J. Bifurc. Chaos.
[18] José M. Vega,et al. Reduced order models based on local POD plus Galerkin projection , 2010, J. Comput. Phys..
[19] Stefan Volkwein,et al. Galerkin proper orthogonal decomposition methods for parabolic problems , 2001, Numerische Mathematik.
[20] R. Murray,et al. Model reduction for compressible flows using POD and Galerkin projection , 2004 .
[21] R. Freund. Model reduction methods based on Krylov subspaces , 2003, Acta Numerica.
[22] Paul Van Dooren,et al. The Lanczos algorithm and Pad(cid:19)e approximations , 1995 .
[23] L. Sirovich. Turbulence and the dynamics of coherent structures. II. Symmetries and transformations , 1987 .
[24] Arlindo L. Oliveira,et al. Biclustering algorithms for biological data analysis: a survey , 2004, IEEE/ACM Transactions on Computational Biology and Bioinformatics.
[25] C. Kelley. Iterative Methods for Linear and Nonlinear Equations , 1987 .
[26] A. Laub,et al. Approximate solution of large sparse Lyapunov equations , 1994, IEEE Trans. Autom. Control..
[27] W. Gragg,et al. On the partial realization problem , 1983 .
[28] J. Peraire,et al. Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .
[29] W. Gragg,et al. The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis , 1972 .
[30] Bertil Gustafsson,et al. An alternating direction implicit method for solving the shallow water equations , 1971 .
[31] Zhu Wang,et al. Are the Snapshot Difference Quotients Needed in the Proper Orthogonal Decomposition? , 2013, SIAM J. Sci. Comput..
[32] E. Grimme,et al. Pade approximation of large-scale dynamic systems with Lanczos methods , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.
[33] Peter Benner,et al. Two-Sided Projection Methods for Nonlinear Model Order Reduction , 2015, SIAM J. Sci. Comput..
[34] Yuxiang Beckett Zhou,et al. Model reduction for nonlinear dynamical systems with parametric uncertainties , 2012 .
[35] Paul T. Boggs,et al. Efficient structure-preserving model reduction for nonlinear mechanical systems with application to structural dynamics. , 2012 .
[36] A. Grammeltvedt. A SURVEY OF FINITE-DIFFERENCE SCHEMES FOR THE PRIMITIVE EQUATIONS FOR A BAROTROPIC FLUID , 1969 .
[37] Kevin Carlberg,et al. Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting , 2012, 1209.5455.
[38] Yousef Saad,et al. Iterative methods for sparse linear systems , 2003 .
[39] Adrian Sandu,et al. A time-parallel approach to strong-constraint four-dimensional variational data assimilation , 2015, J. Comput. Phys..
[40] K. Karhunen. Zur Spektraltheorie stochastischer prozesse , 1946 .
[41] Danny C. Sorensen,et al. Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..
[42] Kevin Carlberg,et al. The ROMES method for statistical modeling of reduced-order-model error , 2014, SIAM/ASA J. Uncertain. Quantification.
[43] P. Schmid,et al. Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.
[44] A. Patera,et al. A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations , 2005 .
[45] Bernd R. Noack,et al. Model reduction using Dynamic Mode Decomposition , 2014 .
[46] Saifon Chaturantabut. Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods , 2009 .
[47] Eric James Grimme,et al. Krylov Projection Methods for Model Reduction , 1997 .
[48] R. Dedden. Model Order Reduction using the Discrete Empirical Interpolation Method , 2012 .
[49] A. Hodel,et al. Least squares approximate solution of the Lyapunov equation , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.
[50] C. Farhat,et al. Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations , 2011 .
[51] Youcef Saad,et al. A Basic Tool Kit for Sparse Matrix Computations , 1990 .
[52] Ionel Michael Navon,et al. GUSTAF: a quasi-Newton nonlinear ADI FORTRAN IV program for solving the shallow-water equations with augmented Lagrangians , 1984 .
[53] Philipp Birken,et al. Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.
[54] Timothy A. Davis,et al. Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm , 2004, TOMS.
[55] Zlatko Drmac,et al. A New Selection Operator for the Discrete Empirical Interpolation Method - Improved A Priori Error Bound and Extensions , 2015, SIAM J. Sci. Comput..
[56] Juan Du,et al. Non-linear model reduction for the Navier-Stokes equations using residual DEIM method , 2014, J. Comput. Phys..
[57] Zhi Wang,et al. A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products , 1995, Comput. Optim. Appl..
[58] L. Sirovich. Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .
[59] Stefan Volkwein,et al. Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics , 2002, SIAM J. Numer. Anal..
[60] I. Jaimoukha,et al. Krylov subspace methods for solving large Lyapunov equations , 1994 .
[61] Adrian Sandu,et al. A Posteriori Error Estimates for DDDAS Inference Problems , 2014, ICCS.
[62] Benjamin Peherstorfer,et al. Localized Discrete Empirical Interpolation Method , 2014, SIAM J. Sci. Comput..
[63] D. Keyes,et al. Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .
[64] Adrian Sandu,et al. Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations , 2014, International Journal for Numerical Methods in Fluids.
[65] Lawrence Sirovich,et al. Karhunen–Loève procedure for gappy data , 1995 .
[66] Danny C. Sorensen,et al. The Sylvester equation and approximate balanced reduction , 2002 .
[67] Michael Hinze,et al. Discrete Empirical Interpolation in POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks , 2012 .
[68] Roland W. Freund,et al. Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.
[69] N. Nguyen,et al. An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .
[70] D. A. Bistrian,et al. Comparison of optimized Dynamic Mode Decomposition vs POD for the shallow water equations model reduction with large-timestep observations , 2014 .
[71] I. Mezić,et al. Spectral analysis of nonlinear flows , 2009, Journal of Fluid Mechanics.
[72] K. Willcox,et al. Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition , 2004 .
[73] Bernd R. Noack,et al. Cluster-based reduced-order modelling of a mixing layer , 2013, Journal of Fluid Mechanics.
[74] Gianluigi Rozza,et al. Reduced Basis Method for Parametrized Elliptic Optimal Control Problems , 2013, SIAM J. Sci. Comput..
[75] Adhemar Bultheel,et al. Rational approximation in linear systems and control , 2000 .
[76] Timothy A. Davis,et al. A column approximate minimum degree ordering algorithm , 2000, TOMS.
[77] K. Kunisch,et al. Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition , 1999 .
[78] J. MacQueen. Some methods for classification and analysis of multivariate observations , 1967 .
[79] Gene H. Golub,et al. Singular value decomposition and least squares solutions , 1970, Milestones in Matrix Computation.
[80] B. Moore. Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .
[81] L. Sirovich. Turbulence and the dynamics of coherent structures. III. Dynamics and scaling , 1987 .
[82] Razvan Stefanescu,et al. POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model , 2012, J. Comput. Phys..
[83] Adrian Sandu,et al. POD/DEIM reduced-order strategies for efficient four dimensional variational data assimilation , 2014, J. Comput. Phys..
[84] Peter Benner,et al. Partial realization of descriptor systems , 2006, Syst. Control. Lett..
[85] Youcef Saad,et al. A Basic Tool Kit for Sparse Matrix Computations , 1990 .
[86] Arnold W. Heemink,et al. Model-Reduced Variational Data Assimilation , 2006 .
[87] D. Wirtz. Model reduction for nonlinear systems : kernel methods and error estimation (Modellreduktion für nichtlineare Systeme : Kernmethoden und Fehlerschätzung) , 2014 .
[88] William W. Hager,et al. Minimizing the Profile of a Symmetric Matrix , 2001, SIAM J. Sci. Comput..
[89] Graeme Fairweather,et al. A Linear ADI Method for the Shallow-Water Equations , 1980 .
[90] D. Rixen,et al. Discrete Empirical Interpolation Method for Finite Element Structural Dynamics , 2013 .
[91] S. P. Lloyd,et al. Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.
[92] Clifford T. Mullis,et al. Synthesis of minimum roundoff noise fixed point digital filters , 1976 .
[93] Danny C. Sorensen,et al. A Posteriori Error Estimation for DEIM Reduced Nonlinear Dynamical Systems , 2014, SIAM J. Sci. Comput..
[94] Robert H. Halstead,et al. Matrix Computations , 2011, Encyclopedia of Parallel Computing.
[95] Traian Iliescu,et al. Proper orthogonal decomposition closure models for fluid flows: Burgers equation , 2013, 1308.3276.
[96] Richard Barrett,et al. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.
[97] Harbir Antil,et al. Application of the Discrete Empirical Interpolation Method to Reduced Order Modeling of Nonlinear and Parametric Systems , 2014 .
[98] Danny C. Sorensen,et al. A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction , 2012, SIAM J. Numer. Anal..
[99] J. Hesthaven,et al. Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations , 2007 .
[100] J. Peraire,et al. A ‘best points’ interpolation method for efficient approximation of parametrized functions , 2008 .
[101] B. R. Noack,et al. A hierarchy of low-dimensional models for the transient and post-transient cylinder wake , 2003, Journal of Fluid Mechanics.
[102] L. Sirovich. TURBULENCE AND THE DYNAMICS OF COHERENT STRUCTURES PART I : COHERENT STRUCTURES , 2016 .