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International Journal for Uncertainty Quantification

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ISOGEOMETRIC METHODS FOR KARHUNEN-LOEVE REPRESENTATION OF RANDOM FIELDS ON ARBITRARY MULTIPATCH DOMAINS

Volume 11, Issue 3, 2021, pp. 27-57
DOI: 10.1615/Int.J.UncertaintyQuantification.2020035185
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Ramin Jahanbin
College of Engineering, The University of Iowa, Iowa City, Iowa 52242, USA
S. Rahman
College of Engineering, The University of Iowa, Iowa City, Iowa 52242, USA

ABSTRACT

This paper introduces isogeometric Galerkin and collocation methods for solving the Fredholm integral eigenvalue problem on arbitrary multipatch domains, delivering the Karhunen-Loève expansion for random field discretization. In both methods, the unknown eigenfunctions are projected onto concomitant finite-dimensional approximation spaces, where nonuniform rational B-splines and analysis-suitable T-splines reside. In the context of isogeometric analysis, the geometry is modeled precisely, and identical basis functions with significant approximating power are employed for modeling the geometry and constructing the approximation spaces. Numerical analyses of two- and three-dimensional engineering problems indicate that the Galerkin- and collocation-derived eigensolutions are both convergent and accurate. However, the collocation method, by eliminating one d-dimensional domain integration informing the system matrices, produces eigensolutions markedly more economically than the Galerkin method. Highly effective in large-scale applications, the isogeometric collocation method imparts a tremendous boost to computational expediency. As a result, subsequent uncertainty quantification analysis of complex engineering structures requiring multipatch geometry representation can now be performed using the proposed methods for random field discretization.

KEY WORDS: uncertainty quantification, Karhunen-Loeve expansion, isogeometric analysis, NURBS, T-splines, Bezier extraction
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CITED BY

  1. Dixler Steven, Jahanbin Ramin, Rahman Sharif, Uncertainty quantification by optimal spline dimensional decomposition, International Journal for Numerical Methods in Engineering, 122, 20, 2021. Crossref

  2. Burova I. G., Fredholm Integral Equation and Splines of the Fifth Order of Approximation, WSEAS TRANSACTIONS ON MATHEMATICS, 21, 2022. Crossref

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