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A nonintrusive stochastic multiscale solver
Author(s) -
Fish Jacob,
Wu Wei
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3201
Subject(s) - solver , homogenization (climate) , latin hypercube sampling , computer science , uncertainty quantification , monte carlo method , sparse grid , collocation (remote sensing) , grid , polynomial chaos , mathematical optimization , multiscale modeling , mathematics , computational science , algorithm , machine learning , biodiversity , ecology , statistics , chemistry , geometry , computational chemistry , biology
In this paper, we describe a practical nonintrusive multiscale solver that permits consideration of uncertainties in heterogeneous materials without exhausting the available computational resources. The computational complexity of analyzing heterogeneous material systems is governed by the physical and probability spaces at multiple scales. To deal with these large spaces, we employ reduced order homogenization approach in combination with the Karhunen–Loeve expansion and stochastic collocation method based on sparse grid. The resulting nonintrusive multiscale solver, which is aimed at providing practical solutions for complex multiscale stochastic problems, has been verified against the Latin Hypercube Monte–Carlo method. Copyright © 2011 John Wiley & Sons, Ltd.