Frequency-Explicit Shape Uncertainty Quantification for Acoustic Scattering

Ralf Hiptmair (ETH Zurich)

Jun 17. 2022, 14:45 — 15:30

 We consider frequency-domain acoustic scattering at a homogeneous star-shaped penetrable
  object, whose shape is uncertain and modeled via a radial spectral parameterization with
  random coefficients. We exploit recent results on the stability of Helmholtz
  transmission problems with piecewise constant coefficients from [A.~Moiola and
    E.~A. Spence,  Acoustic transmission problems: wavenumber-explicit bounds and
    resonance-free regions, Mathematical Models and Methods in Applied Sciences, 29
  (2019), pp.~317--354] to obtain frequency-explicit statements on the holomorphic
  dependence of the scattered field and the far-field pattern on the stochastic
  parameters. This paves the way for applying general results on the efficient
  construction of high-dimensional surrogate models. In addition, frequency-explicit
  spatial regularity estimates permit us to quantify the impact of Galerkin
  discretization using low-order Lagrangian finite-element spaces.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zurich)
Sara van de Geer (ETH Zurich)
Karen Willcox (U of Texas, Austin)