Karhunen-Loève approximation of random fields by generalized fast multipole methods

By Christoph Schwab, Radu Alexandru Todor. Journal of Computational Physics, 2006

417 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Ocean Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a27ff37a2d3a9f721bcb445008f8b5d17f7215e4

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In Atomic and Molecular Physics, and Optics

In Ocean Engineering

In Statistics and Probability

Citations in the corpus

Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs (2010, methodology): “These estimates depend on the smoothness properties of the covariance function Ca(x, y), see [20, 18].”
Mathematik in den Naturwissenschaften Leipzig Tensor-Structured Galerkin Approximation of parametric and stochastic Elliptic PDEs (2010, background): “Tensor-structured techniques in higher dimensions [7, 13, 15, 23, 26] have already demonstrated their solid potential in electronic structure calculations [3, 12, 23, 24, 25], in PDEs with random input [34, 37, 35, 4], and in machine learning [1].”
Stochastic collocation and mixed finite elements for flow in porous media (2008, methodology): “Efficient methods for numerically computing the KL expansion are reported in [35].”
Approximation of bi-variate functions: singular value decomposition versus sparse grids (2014, methodology): “According to [28], the singular values of an analytical kernel decay exponentially (if n1 = n2 = 1).”
Inverse problems: A Bayesian perspective (2010, methodology): “A rigorous numerical analysis underpinning the work of Spanos and Ghanem (1989, 2003) is an active area of research: see in particular Schwab and Todor (2006) and Todor and Schwab (2007), where the problem is viewed as an example of Schwab’s more general program of tensor product approximation for…”
Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients (2011, background): “(More details on the general case can be found in [Schwab, Todor, 2006].”
Karhunen-Loève expansion for multi-correlated stochastic processes (2013, background): “This is due to the fact that the exponential kernel is less smooth than the Gaussian one [46].”
Solving elliptic problems with non-Gaussian spatially-dependent random coefficients (2009, background): “The eigenvalue problem (4), in general, does not have analytical solutions, which means that numerical approximation is usually necessary [17] [18] [19].”
Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA) (2014, background): “, the number of eigen pairs one should keep, depends on the smoothness of covariance kernel [Frauenfelder et al., 2005; Schwab and Todor, 2006].”
First order second moment analysis for stochastic interface problems based on low-rank approximation (2013, background): “Related decay rates have been proven in [18, 38].”
Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011, neutral): “[33]).”
A non-adapted sparse approximation of PDEs with stochastic inputs (2010, background): “(5) and (6) will be algebraic if Caa(x1,x2) has CðD DÞ regularity for some s > 0 [57].”