Isogeometric multilevel quadrature for forward and inverse random acoustic scattering

Jürgen Dölz, Helmut Harbrecht, Carlos Jerez-Hanckes, Michael Multerer

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 field's expectation and covariance at the scatterer's boundary to model the surface's Karhunen–Loève expansion. Leveraging on the isogeometric framework, we employ multilevel quadrature methods to approximate quantities of interest such as the scattered wave's expectation and variance. By computing the wave's 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.

Original languageEnglish
Article number114242
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - 1 Jan 2022
Externally publishedYes


  • Bayesian inversion
  • Boundary Integral Methods
  • Helmholtz scattering
  • Isogeometric Analysis
  • Multilevel quadrature
  • Uncertainty quantification


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