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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018025234
pages 33-57

ASSESSING THE PERFORMANCE OF LEJA AND CLENSHAW-CURTIS COLLOCATION FOR COMPUTATIONAL ELECTROMAGNETICS WITH RANDOM INPUT DATA

Dimitrios Loukrezis
Institute for Accelerator Science and Electromagnetic Fields (TEMF), Technische Universität Darmstadt, Schlossgartenstraße 8, 64289 Darmstadt, Germany; Centre for Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany
Ulrich Römer
Institute of Dynamics and Vibrations, Technische Universität Braunschweig, Schleinitzstraße 20, 38106 Braunschweig, Germany
Herbert De Gersem
Institute for Accelerator Science and Electromagnetic Fields (TEMF), Technische Universität Darmstadt, Schlossgartenstraße 8, 64289 Darmstadt, Germany; Centre for Computational Engineering, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany

ABSTRACT

We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem, in the presence of a large number of uncertain input parameters. In order to reduce the growth in complexity with the number of dimensions, we employ a dimension-adaptive stochastic collocation method based on nested univariate nodes. We examine the accuracy and performance of collocation schemes based on Clenshaw-Curtis and Leja rules, for the cases of uniform and bounded, nonuniform random inputs, respectively. Based on numerical experiments with an academic electromagnetic field model, we compare the two rules in both the univariate and multivariate cases and for both quadrature and interpolation purposes. Results for a real-world electromagnetic field application featuring high-dimensional input uncertainty are also presented.