A BEM sensitivity formulation for three-dimensional active noise control

In this paper a novel Boundary Element (BE) formulation for sen- sitivity analysis of local active noise control in a three-dimensional field is presented. The formulation is based on the Helmholtz differential equation and it is valid for internal as well as for scattering wave propagation problems. The primary noise is attenuated within an enclosure, called control volume, by adding a control source modelled as an object with a vibrating surface. Both the optimum position of the control volume and the optimum location/orientation of the secondary source are determined by minimisation of a suitable cost function. The sensitivities are determined by implicit differentiation. A hierarchical adaptive cross approximation approach in conjunction with the GMRES solver. is implemented to accelerate the convergence. Four numerical examples are presented to demonstrate accuracy and efficiency of the proposed formulations.