Helmholtz Scattering by Random Domains: First-Order Sparse Boundary Elements Approximation
Escapil-Inchauspe
P
author
Jerez-Hanckes
C
author
2020
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.
Helmholtz equation
shape calculus
uncertainty quantification
boundary element method
combination technique
exported from refbase (show.php?record=1205), last updated on Thu, 14 Jan 2021 18:47:42 -0300
text
10.1137/19M1279277
Escapil-Inchauspe+Jerez-Hanckes2020
SIAM Journal of Scientific Computing
SIAM J. Sci. Comput.
2020
continuing
periodical
academic journal
42
5
A2561-A2592
1064-8275