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Author (up) Aylwin, R.; Jerez-Hanckes, C.; Schwab, C.; Zech, J. doi  openurl
  Title Domain Uncertainty Quantification in Computational Electromagnetics Type Journal Article
  Year 2020 Publication SIAM/ASA Journal on Uncertainty Quantification Abbreviated Journal SIAM/ASA J. Uncert. Quant.  
  Volume 8 Issue 1 Pages 301-341  
  Abstract We study the numerical approximation of time-harmonic, electromagnetic fields inside a lossy cavity of uncertain geometry. Key assumptions are a possibly high-dimensional parametrization of the uncertain geometry along with a suitable transformation to a fixed, nominal domain. This uncertainty parametrization results in families of countably parametric, Maxwell-like cavity problems that are posed in a single domain, with inhomogeneous coefficients that possess finite, possibly low spatial regularity, but exhibit holomorphic parametric dependence in the differential operator. Our computational scheme is composed of a sparse grid interpolation in the high-dimensional parameter domain and an ${H}{curl}$ -conforming edge element discretization of the parametric problem in the nominal domain. As a stepping-stone in the analysis, we derive a novel Strang-type lemma for Maxwell-like problems in the nominal domain, which is of independent interest. Moreover, we accommodate arbitrary small Sobolev regularity of the electric field and also cover uncertain isotropic constitutive or material laws. The shape holomorphy and edge-element consistency error analysis for the nominal problem are shown to imply convergence rates for multilevel Monte Carlo and for quasi-Monte Carlo integration, as well as sparse grid approximations, in uncertainty quantification for computational electromagnetics. They also imply expression rate estimates for deep ReLU networks of shape-to-solution maps in this setting. Finally, our computational experiments confirm the presented theoretical results.  
  Corporate Author Thesis  
  Publisher Society for Industrial and Applied Mathematics Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2166-2525 ISBN Medium  
  Area Expedition Conference  
  Notes Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 1100  
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