Active control of Helmholtz fields in 3D using an array of sources

In this paper, we present a strategy for the active manipulation of Helmholtz fields using an array (swarm) of coupling sources with prescribed fixed positions. More specifically, we consider the problem of using an array of active surface sources to approximate prescribed fields in several given exterior regions of space including possibly the far field region. In this regard, we extend the results presented in our previous works for the case of a single source to allow for multiple active sources considering the first-order mutual coupling between them. We prove the existence of boundary inputs on the sources (pressure or normal velocity), so that the desired control effect is obtained. We also devise a stable numerical scheme to compute these boundary inputs by using local basis functions defined on the source boundaries in a method of moments approach together with a Morozov discrepancy principle-based Tikhonov regularization. Several numerical simulations were presented to demonstrate the accuracy of the proposed scheme. (C) 2020 Elsevier B.V. All rights reserved.