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Stochastic Collocation on Unstructured Multivariate Meshes

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  03 July 2015

Akil Narayan  and
Tao Zhou
Akil Narayan
Affiliation:
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112, USA
Tao Zhou*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, the Chinese Academy of Sciences, Beijing, China
*
*Corresponding author. Email addresses: akil@sci.utah.edu (A. Narayan), tzhou@lsec.cc.ac.cn (T. Zhou)
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Abstract

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications. Selection of a collocation mesh is frequently a challenge, but methods that construct geometrically unstructured collocation meshes have shown great potential due to attractive theoretical properties and direct, simple generation and implementation. We investigate properties of these meshes, presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.

Keywords

Stochastic collocationunstructured methesleast-squarescompressive samplingleast interpolation

MSC classification

Secondary: 65C20: Models, numerical methods
Type
Review Article
Information
Communications in Computational Physics , Volume 18 , Issue 1 , July 2015 , pp. 1 - 36
Copyright
Copyright © Global-Science Press 2015 

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