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Assessing the Performance of Leja and Clenshaw-Curtis Collocation for Computational Electromagnetics with Random Input Data
arXiv - CS - Numerical Analysis Pub Date : 2017-12-19 , DOI: arxiv-1712.07223
Dimitrios Loukrezis, Ulrich R\"omer, and Herbert De Gersem

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, non-uniform random inputs, respectively. Based on numerical experiments with an academic electromagnetic field model, we compare the two rules in both the univariate and multivariate case and for both quadrature and interpolation purposes. Results for a real-world electromagnetic field application featuring high-dimensional input uncertainty are also presented.

中文翻译:

使用随机输入数据评估 Leja 和 Clenshaw-Curtis 搭配的计算电磁学性能

我们考虑在存在大量不确定输入参数的情况下量化有关电磁场输出不确定性的问题。为了减少复杂度随维度数量的增长,我们采用基于嵌套单变量节点的维度自适应随机搭配方法。我们分别针对均匀和有界、非均匀随机输入的情况检查基于 Clenshaw-Curtis 和 Leja 规则的搭配方案的准确性和性能。基于学术电磁场模型的数值实验,我们比较了单变量和多变量情况下以及正交和插值目的的两个规则。还介绍了具有高维输入不确定性的真实电磁场应用的结果。
更新日期:2020-01-17
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