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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 Fierro, I.; Jerez-Hanckes, C. doi  openurl
  Title Fast Calderon preconditioning for Helmholtz boundary integral equations Type
  Year 2020 Publication Journal Of Computational Physics Abbreviated Journal J. Comput. Phys.  
  Volume 409 Issue Pages 22 pp  
  Keywords Operator preconditioning; Calderon preconditioning; Helmholtz equations; Hierarchical matrices; Fast solvers; Boundary elements method  
  Abstract Calderon multiplicative preconditioners are an effective way to improve the condition number of first kind boundary integral equations yielding provable mesh independent bounds. However, when discretizing by local low-order basis functions as in standard Galerkin boundary element methods, their computational performance worsens as meshes are refined. This stems from the barycentric mesh refinement used to construct dual basis functions that guarantee the discrete stability of L-2-pairings. Based on coarser quadrature rules over dual cells and H-matrix compression, we propose a family of fast preconditioners that significantly reduce assembly and computation times when compared to standard versions of Calderon preconditioning for the three-dimensional Helmholtz weakly and hyper-singular boundary integral operators. Several numerical experiments validate our claims and point towards further enhancements. (C) 2020 Elsevier Inc. All rights reserved.  
  Address [Fierro, Ignacia] UCL, Dept Math, Gower St, London, England, Email: carlos.jerez@uai.cl  
  Corporate Author Thesis  
  Publisher Academic Press Inc Elsevier Science Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0021-9991 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000522726000020 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1153  
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