HELMHOLTZ SCATTERING BY RANDOM DOMAINS: FIRST-ORDER SPARSE BOUNDARY ELEMENT APPROXIMATION

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dc.contributor.authorEscapil-Inchauspe, Paul
dc.contributor.authorJerez-Hanckes, Carlos
dc.date.accessioned2025-01-23T19:46:33Z
dc.date.available2025-01-23T19:46:33Z
dc.date.issued2020
dc.description.abstractWe 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.
dc.description.funderFondecyt Regular
dc.fuente.origenWOS
dc.identifier.doi10.1137/19M1279277
dc.identifier.eissn1095-7197
dc.identifier.issn1064-8275
dc.identifier.urihttps://doi.org/10.1137/19M1279277
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/100303
dc.identifier.wosidWOS:000600650100022
dc.issue.numero5
dc.language.isoen
dc.pagina.finalA2592
dc.pagina.inicioA2561
dc.revistaSiam journal on scientific computing
dc.rightsacceso restringido
dc.subjectHelmholtz equation
dc.subjectshape calculus
dc.subjectuncertainty quantification
dc.subjectboundary element method
dc.subjectcombination technique
dc.titleHELMHOLTZ SCATTERING BY RANDOM DOMAINS: FIRST-ORDER SPARSE BOUNDARY ELEMENT APPROXIMATION
dc.typeartículo
dc.volumen42
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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