Implementation of Karhunen-Loeve expansion for simulation using a wavelet-Galerkin scheme

By Kok-Kwang Phoon, Shuping Huang, S. Quek. 2002

255 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/b3f1a2dc1e008627458aff412520f9da558630e6

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In Atomic and Molecular Physics, and Optics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Assessment of spectral representation and Karhunen–Loève expansion methods for the simulation of Gaussian stochastic fields (2007, methodology): “For an exhaustive description of the method, the reader is referred to [30].”
The stochastic finite element method: Past, present and future (2009, methodology): “Enhanced methods for the solution of the Fredholm integral equation have been proposed in [140,58,164].”
Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014, methodology): “It is applied in [7, 8, 9] for the discretization of the IEVP on one-dimensional domains.”
Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method (2014, methodology): “, 1986) and the KL expansion (Phoon et al., 2002) can be used to discretize the random field.”
Simulation of non-Gaussian processes using fractile correlation (2004, methodology): “(1) for the Gaussian case efficiently using a wavelet-Galerkin scheme [13].”
Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion (2005, methodology): “(2) can be solved quite efficiently using a waveletGalerkin numerical scheme [11].”
Response surface methods for slope reliability analysis: Review and comparison (2016, methodology): “…ξ when spatial variability of soil properties is considered, Np realizations of independent or cross-correlated random fields are generated using the Karhunen–Loève expansion technique (e.g., Ghiocel and Ghanem, 2002; Phoon et al., 2002; Ghanem and Spanos, 2003; Vořechovský, 2008; Cho, 2010).”