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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 Duran, M.; Godoy, E.; Roman-Catafau, E.; Toledo, P.A. doi  openurl
  Title Open-pit slope design using a DtN-FEM: Parameter space exploration Type
  Year 2022 Publication International Journal Of Rock Mechanics And Mining Sciences Abbreviated Journal Int. J. Rock Mech. Min. Sci.  
  Volume 149 Issue Pages 104950  
  Keywords Dirichlet-to-Neumann map; Finite elements; Open-pit; Slope design  
  Abstract Given the sustained mineral-deposits ore-grade decrease, it becomes necessary to reach greater depths when extracting ore by open-pit mining. Steeper slope angles are thus likely to be required, leading to geomechanical instabilities. In order to determine excavation stability, mathematical modelling and numerical simulation are often used to compute the rock-mass stress-state, to which some stability criterion needs to be added. A problem with this approach is that the volume surrounding the excavation has no clear borders and in practice it might be regarded as an unbounded region. Then, it is necessary to use advanced methods capable of dealing efficiently with this difficulty. In this work, a DtN-FEM procedure is applied to calculate displacements and stresses in open-pit slopes under geostatic stress conditions. This procedure was previously devised by the authors to numerically treat this kind of problems where the surrounding domain is semi-infinite. Its efficiency makes possible to simulate, in a short amount of time, multiple open-pit slope configurations. Therefore, the method potentiality for open-pit slope design is investigated. A regular open-pit slope geometry is assumed, parameterised by the overall-slope and bench-face angles. Multiple geometrically admissible slopes are explored and their stability is assessed by using the computed stress-field and the Mohr-Coulomb failure criterion. Regions of stability and instability are thus explored in the parametric space, opening the way for a new and flexible designing tool for open-pit slopes and related problems.  
  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 1365-1609 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000784231200005 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1681  
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