Numerical methods for the discretization of random fields by means of the Karhunen-Loève expansion

DOI10.1016/j.cma.2013.12.010zbMath1296.65191OpenAlexW2097718805MaRDI QIDQ460805

Daniel Straub, Wolfgang Betz, Iason Papaioannou

Publication date: 9 October 2014

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2013.12.010

zbMATH Keywords

collocation methodGalerkin methodNyström methodKarhunen-Loève expansionfinite cell methodrandom field discretization

Mathematics Subject Classification ID

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Uses Software

• Algorithm 876

Cites Work

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• An eigen-based high-order expansion basis for structured spectral elements
• The stochastic finite element method: past, present and future
• Stochastic meshfree method for elasto-plastic damage analysis
• Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
• A sharp error estimate for the fast Gauss transform
• The finite cell method for three-dimensional problems of solid mechanics
• Application of hierarchical matrices for computing the Karhunen-Loève expansion
• Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
• Assessment of spectral representation and Karhunen-Loève expansion methods for the simulation of Gaussian stochastic fields
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• Finite elements for elliptic problems with stochastic coefficients
• Small and large deformation analysis with the \(p\)- and B-spline versions of the finite cell method
• Ingredients for a general purpose stochastic finite elements implementation
• Karhunen-Loève approximation of random fields by generalized fast multipole methods
• The Quadratic Eigenvalue Problem
• Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes
• Karhunen-Loève decomposition of random fields based on a hierarchical matrix approach
• Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method
• Algorithm 876
• On the numerical expansion of a second order stochastic process
• The Numerical Solution of Integral Equations of the Second Kind
• Random Fields
• Spectral/hp Element Methods for Computational Fluid Dynamics

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