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Author Aylwin, R.; Jerez-Hanckes, C.; Schwab, C.; Zech, J. doi  openurl
  Title Domain Uncertainty Quantification in Computational Electromagnetics Type
  Year 2020 Publication Siam-Asa Journal On Uncertainty Quantification Abbreviated Journal SIAM-ASA J. Uncertain. Quantif.  
  Volume 8 Issue 1 Pages 301-341  
  Keywords computational electromagnetics; uncertainty quantification; finite elements; shape holomorphy; sparse grid quadrature; Bayesian inverse problems  
  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 Hcurl -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.  
  Address [Aylwin, Ruben] Pontificia Univ Catolica Chile, Sch Engn, Santiago 7820436, Chile, Email: rdaylwin@uc.cl;  
  Corporate Author Thesis  
  Publisher Siam Publications Place of Publication Editor  
  Language English 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 WOS:000551383300011 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1207  
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Author Escapil-Inchauspe, P.; Jerez-Hanckes, C. doi  openurl
  Title Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Elements Approximation Type
  Year 2020 Publication SIAM Journal of Scientific Computing Abbreviated Journal SIAM J. Sci. Comput.  
  Volume 42 Issue 5 Pages A2561-A2592  
  Keywords Helmholtz equation; shape calculus; uncertainty quantification; boundary element method; combination technique  
  Abstract We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance, and transmission boundary conditions. In particular, we aim to quantify diffracted fields originated by small stochastic perturbations of a given relatively smooth nominal shape. Using first-order shape Taylor expansions, we derive tensor deterministic first-kind boundary integral equations for the statistical moments of the scattering problems considered. These are then approximated by sparse tensor Galerkin discretizations via the combination technique [M. Griebel, M. Schneider, and C. Zenger, A combination technique for the solution of sparse grid problems, in Iterative Methods in Linear Algebra, P. de Groen and P. Beauwens, eds., Elsevier, Amsterdam, 1992, pp. 263-281; H. Harbrecht, M. Peters, and M. Siebenmorgen, J. Comput. Phys., 252 (2013), pp. 128-141]. We supply extensive numerical experiments confirming the predicted error convergence rates with polylogarithmic growth in the number of degrees of freedom and accuracy in approximation of the moments. Moreover, we discuss implementation details such as preconditioning to finally point out further research avenues.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1064-8275 ISBN Medium  
  Area Expedition Conference  
  Notes Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1205  
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Author Fuenzalida, C.; Jerez-Hanckes, C.; McClarren, R.G. doi  openurl
  Title Uncertainty Quantification For Multigroup Diffusion Equations Using Sparse Tensor Approximations Type
  Year 2019 Publication Siam Journal On Scientific Computing Abbreviated Journal SIAM J. Sci. Comput.  
  Volume 41 Issue 3 Pages B545-B575  
  Keywords multigroup diffusion equation; uncertainty quantification; sparse tensor approximation; finite element method  
  Abstract We develop a novel method to compute first and second order statistical moments of the neutron kinetic density inside a nuclear system by solving the energy-dependent neutron diffusion equation. Randomness comes from the lack of precise knowledge of external sources as well as of the interaction parameters, known as cross sections. Thus, the density is itself a random variable. As Monte Carlo simulations entail intense computational work, we are interested in deterministic approaches to quantify uncertainties. By assuming as given the first and second statistical moments of the excitation terms, a sparse tensor finite element approximation of the first two statistical moments of the dependent variables for each energy group can be efficiently computed in one run. Numerical experiments provided validate our derived convergence rates and point to further research avenues.  
  Address [Fuenzalida, Consuelo] Pontificia Univ Catolica Chile, Sch Engn, Santiago, Chile, Email: mcfuenzalida@uc.cl;  
  Corporate Author Thesis  
  Publisher Siam Publications Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1064-8275 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000473033300033 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1023  
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