_:nf5b0b260a8154e889d3540056c60234dxb0
<http://schema.org/description>
"We study the numerical solution of forward and inverse acoustic scattering\nproblems by randomly shaped obstacles in three-dimensional space using a fast\nisogeometric boundary element method. Within the isogeometric framework,\nrealizations of the random scatterer can efficiently be computed by simply\nupdating the NURBS mappings which represent the scatterer. This way, we end up\nwith a random deformation field. In particular, we show that the knowledge of\nthe deformation field's expectation and covariance at the surface of the\nscatterer are already sufficient to compute the surface Karhunen-Loève\nexpansion. Leveraging on the isogeometric framework, we utilize multilevel\nquadrature methods for the efficient approximation of quantities of interest,\nsuch as the scattered wave's expectation and variance. Computing the wave's\nCauchy data at an artificial, fixed interface enclosing the random obstacle, we\ncan also directly infer quantities of interest in free space. Adopting the\nBayesian paradigm, we finally compute the expected shape and the variance of\nthe scatterer from noisy measurements of the scattered wave at the artificial\ninterface. Numerical results for the forward and inverse problem are given to\ndemonstrate the feasibility of the proposed approach."
<https://deepai.org/publication/isogeometric-multilevel-quadrature-for-forward-and-inverse-random-acoustic-scattering>