Stochastic collocation for correlated inputs

María Navarro, Jeroen Witteveen, Joke Blom

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

Stochastic Collocation (SC) has been studied and used in different disciplines for Uncertainty Quantification (UQ). The method consists of computing a set of appropriate points, called collocation points, and then using Lagrange interpolation to construct the probability density function (pdf) of the quantity of interest (QoI). The collocation points are usually chosen as Gauss quadrature points, i.e., the roots of orthogonal polynomials with respect to the pdf of the uncertain inputs. If the mathematical model has more than one stochastic parameter, the multidimensional set of points is usually build using the tensor product of the roots of the onedimensional orthogonal polynomials. As a result of that, for multidimensional problems the same set of collocation points is used for both correlated and uncorrelated inputs. In this work, we propose to compute an alternative set of points for correlated inputs. The set will be derived using the orthogonal polynomials for correlated inputs that we developed in a previous work. As these polynomials are not unique, we will obtain multiple sets of collocations points for each input pdf. The aim of this paper is to study the differences between those sets of points and to find and optimal one.
Original languageEnglish (US)
Title of host publicationProceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECOMP 2015)
PublisherInstitute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece
Pages218-236
Number of pages19
ISBN (Print)9789609999496
DOIs
StatePublished - 2015

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