A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction
暂无分享,去创建一个
[1] D. Sorensen,et al. Application of POD and DEIM on dimension reduction of non-linear miscible viscous fingering in porous media , 2011 .
[2] C. Loan. The Sensitivity of the Matrix Exponential , 1977 .
[3] Senol Utku,et al. Errors in reduction methods , 1985 .
[4] Germund Dahlquist,et al. 33 years of numerical instability, Part I , 1985 .
[5] Muruhan Rathinam,et al. A New Look at Proper Orthogonal Decomposition , 2003, SIAM J. Numer. Anal..
[6] Ngoc Cuong Nguyen,et al. A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations , 2007, J. Comput. Phys..
[7] T. H. Gronwall. Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations , 1919 .
[8] Stefan Volkwein,et al. Galerkin proper orthogonal decomposition methods for parabolic problems , 2001, Numerische Mathematik.
[9] David Galbally,et al. Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems , 2009 .
[10] Gustaf Stiderlind. Bounds on nonlinear operators in finite-dimensional banach spaces , 1986 .
[11] Falk Ebert,et al. A note on POD model reduction methods for DAEs , 2010 .
[12] Jacob K. White,et al. A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).
[13] J. Hesthaven,et al. Reduced Basis Approximation and A Posteriori Error Estimation for Parametrized Partial Differential Equations , 2007 .
[14] Gianluigi Rozza,et al. Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity , 2005 .
[15] Danny C. Sorensen,et al. Morphologically accurate reduced order modeling of spiking neurons , 2010, Journal of Computational Neuroscience.
[16] Stefan Volkwein,et al. Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics , 2002, SIAM J. Numer. Anal..
[17] Marcus Meyer,et al. Efficient model reduction in non-linear dynamics using the Karhunen-Loève expansion and dual-weighted-residual methods , 2003 .
[18] Gianluigi Rozza,et al. A Reduced Basis Method for Evolution Schemes with Parameter-Dependent Explicit Operators , 2008 .
[19] Danny C. Sorensen,et al. Nonlinear Model Reduction via Discrete Empirical Interpolation , 2010, SIAM J. Sci. Comput..
[20] T. Ström. On Logarithmic Norms , 1975 .
[21] D. Rovas,et al. Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods , 2002 .
[22] Linda R. Petzold,et al. Approved for public release; further dissemination unlimited Error Estimation for Reduced Order Models of Dynamical Systems ∗ , 2003 .
[23] G. Söderlind,et al. The logarithmic norm. History and modern theory , 2006 .
[24] M. Grepl. Reduced-basis approximation a posteriori error estimation for parabolic partial differential equations , 2005 .
[25] Michael Hinze,et al. Discrete Empirical Interpolation in POD Model Order Reduction of Drift-Diffusion Equations in Electrical Networks , 2012 .
[26] M. N. Vrahatis,et al. Ordinary Differential Equations In Theory and Practice , 1997, IEEE Computational Science and Engineering.
[27] N. Nguyen,et al. An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations , 2004 .
[28] S. Volkwein,et al. MODEL REDUCTION USING PROPER ORTHOGONAL DECOMPOSITION , 2008 .
[29] Anthony T. Patera,et al. A Posteriori Error Bounds for the Empirical Interpolation Method , 2010 .
[30] G. Dahlquist. Stability and error bounds in the numerical integration of ordinary differential equations , 1961 .
[31] R. Bellman. The stability of solutions of linear differential equations , 1943 .