Isogeometric multilevel quadrature for forward and inverse random acoustic scattering

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 framework, realizations random scatterer can efficiently be computed simply updating NURBS mappings which represent scatterer. This way, we end up with deformation field. In particular, show that it suffices to know field’s expectation covariance at scatterer’s model surface’s Karhunen–Loève expansion. Leveraging on employ multilevel quadrature methods approximate quantities interest such as scattered wave’s variance. By computing Cauchy data an artificial, fixed interface enclosing obstacle, also directly infer free space. Adopting Bayesian paradigm, finally compute expected shape variance from noisy measurements wave artificial interface. Numerical results for validate proposed approach.