An active noise control sensitivity formulation for three dimensional BEM

This paper presents a novel Boundary Element (BE) formulation for sensitivity analysis of local active noise control in a three-dimensional field governed by the Helmholtz differential equation. The formulation is valid for internal as well as for scattering wave propagation problems. The local noise reduction is obtained by attenuating the primary noise within a predefined volume, 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 minimization of a suitable cost function. The sensitivities are determined by an implicit differentiation process. An Adaptive Cross Approximation (ACA) approach in conjunction with the Hierarchical matrix format and the GMRES solver is implemented to accelerate the convergence. Numerical examples demonstrates the accuracy and efficiency of the proposed formulation.