Karhunen-Loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis
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Christian Soize | Guillaume Perrin | D. Duhamel | C. Funfschilling | Christian Soize | D. Duhamel | C. Funfschilling | G. Perrin
[1] Christian Soize. Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions , 2010 .
[2] Omar M. Knio,et al. Spectral Methods for Uncertainty Quantification , 2010 .
[3] Dongxiao Zhang,et al. An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loève and polynomial expansions , 2004 .
[4] Roger Ghanem,et al. Simulation of multi-dimensional non-gaussian non-stationary random fields , 2002 .
[5] Habib N. Najm,et al. Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems , 2008, J. Comput. Phys..
[6] Stefan Volkwein,et al. Galerkin proper orthogonal decomposition methods for parabolic problems , 2001, Numerische Mathematik.
[7] Roger G. Ghanem,et al. Polynomial chaos representation of spatio-temporal random fields from experimental measurements , 2009, J. Comput. Phys..
[8] Pol D. Spanos,et al. Karhunen-Loéve Expansion of Stochastic Processes with a Modified Exponential Covariance Kernel , 2007 .
[9] Bin Wen,et al. A multiscale approach for model reduction of random microstructures , 2012 .
[10] Pol D. Spanos,et al. Galerkin Sampling Method for Stochastic Mechanics Problems , 1994 .
[11] G. PERRIN,et al. Identification of Polynomial Chaos Representations in High Dimension from a Set of Realizations , 2012, SIAM J. Sci. Comput..
[12] K. Phoon,et al. Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion , 2005 .
[13] Christoph Schwab,et al. Karhunen-Loève approximation of random fields by generalized fast multipole methods , 2006, J. Comput. Phys..
[14] Joseph M. Powers,et al. A Karhunen-Loève least-squares technique for optimization of geometry of a blunt body in supersonic flow , 2004 .
[15] H. Matthies,et al. Finite elements for stochastic media problems , 1999 .
[16] Hermann G. Matthies,et al. Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations , 2005 .
[17] Roger G. Ghanem,et al. Identification of Bayesian posteriors for coefficients of chaos expansions , 2010, J. Comput. Phys..
[18] R. Ghanem,et al. Polynomial chaos decomposition for the simulation of non-gaussian nonstationary stochastic processes , 2002 .
[19] P. Holmes,et al. The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows , 1993 .
[20] Anthony Nouy,et al. Generalized spectral decomposition for stochastic nonlinear problems , 2009, J. Comput. Phys..
[21] Jens Nørkær Sørensen,et al. Evaluation of Proper Orthogonal Decomposition-Based Decomposition Techniques Applied to Parameter-Dependent Nonturbulent Flows , 1999, SIAM J. Sci. Comput..
[22] Sq Q. Wu,et al. Statistical moving load identification including uncertainty , 2012 .
[23] Roger G. Ghanem,et al. Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure , 2005, SIAM J. Sci. Comput..
[24] K. Phoon,et al. Comparison between Karhunen-Loève expansion and translation-based simulation of non-Gaussian processes , 2007 .
[25] Belinda B. King,et al. Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations , 2001 .
[26] David Ryckelynck,et al. A priori reduction method for solving the two-dimensional Burgers' equations , 2011, Appl. Math. Comput..
[27] Kok-Kwang Phoon,et al. Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes , 2001 .
[28] K. Phoon,et al. Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme , 2002 .
[29] P. Hansen. Numerical tools for analysis and solution of Fredholm integral equations of the first kind , 1992 .
[30] J. Weese. A reliable and fast method for the solution of Fredhol integral equations of the first kind based on Tikhonov regularization , 1992 .
[31] Xiang Ma,et al. Kernel principal component analysis for stochastic input model generation , 2010, J. Comput. Phys..
[32] M.M.R. Williams. The eigenfunctions of the Karhunen–Loeve integral equation for a spherical system , 2011 .