Isogeometric multilevel quadrature for forward and inverse random acoustic scattering
Dölz
J
author
Harbrecht
H
author
Jerez-Hanckes
C
author
Multerer M.
author
2022
We study the numerical solution of forward and inverse time-harmonic acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations of the random scatterer can efficiently be computed by simply updating the NURBS mappings which represent the scatterer. This way, we end up with a random deformation field. In particular, we show that it suffices to know the deformation fields expectation and covariance at the scatterers boundary to model the surfaces Karhunen–Loève expansion. Leveraging on the isogeometric framework, we employ multilevel quadrature methods to approximate quantities of interest such as the scattered waves expectation and variance. By computing the waves Cauchy data at an artificial, fixed interface enclosing the random obstacle, we can also directly infer quantities of interest in free space. Adopting the Bayesian paradigm, we finally compute the expected shape and variance of the scatterer from noisy measurements of the scattered wave at the artificial interface. Numerical results for the forward and inverse problems validate the proposed approach.
Uncertainty quantification: Helmholtz scattering
Isogeometric Analysis
Boundary Integral Methods
Bayesian inversion
Multilevel quadrature
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text
10.1016/j.cma.2021.114242
Doelz_etal2022
Computer Methods in Applied Mechanics and Engineering
Comput. Methods in Appl. Mech. Eng.
2022
continuing
periodical
academic journal
388
114242
0045-7825