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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.  
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  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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