FMM modelling of acoustic scattering with geometrical uncertainty
* Presenting author
Predicting the sound field scattered by objects with uncertain geometry plays an important role in source localisation, shape optimisation or modelling reflections from rough surfaces. Boundary integral equation methods are an adequate choice for the simulation of scattering into free field, as they inherently model the radiation condition. In the high frequency regime, fast multipole methods are usually applied to the fast evaluation of boundary integrals.For the case of scatteres with random geometry, the nonlinear dependency of the boundary integrals on the scatterer's geometry poses a tough modelling challenge. However, assuming small variations of the geometry, low order perturbations of the scattered field and their statistics can be computed by solving boundary integral equations on the mean boundary. This paper investigates the application of the fast multipole method (FMM) for the simulation of acoustic scattering from 2D objects with geometrical uncertainty. The uncertain geometry is characterised by its two point autocorrelation function, and is decomposed into a polynomial chaos (PC) expansion. The low order dependency of the scattered field on the PC coefficients is computed by solving similar deterministic boundary value problems. The advantages of applying the FMM for the deterministic problems are highlighted by numerical examples.