Sensitivity analysis for the active manipulation of Helmholtz fields in 3D

Active manipulation of Helmholtz scalar fields: near-field synthesis with directional far-field control

“…Other approaches include wave-domain methods (as used in [17,18]) and modal-domain approaches (for instance [37,51]). The approach employed in this paper (as well as previous works such as [11,12,21,39,40]) is the use of the Green's function to represent the solution to the Helmholtz equation in terms of a propagator operator and then employ a Tikhonov regulariation scheme with the Morozov discrepancy principle to solve the resulting operatorial equation. For underwater acoustic control problems, three strategies are commonly used in expressing the propagated field (see [22,25] for a discussion of each approach), namely normal modes, the Hankel transform and the ray representation (or the multiple reflection representation for stratified oceans).…”

“…In our previous works [11,39,40], we used global basis representation of the desired inputs in the spirit of [10]. In this paper, we present new theoretical results and propose novel numerical schemes on the active control of acoustic fields in free space and in a homogeneous ocean of finite depth.…”

“…The main novelty of this paper is the simultaneous active control of near fields in prescribed exterior bounded regions and various far-field directions with different prescribed far-field patterns in two separate environments: free space and homogeneous finite-depth ocean environment. In [11,39,40], only near region field control and the case of an almost nonradiating source were considered. In the latter, a null field was prescribed in the entire far-field region which is a far stronger condition than the one considered in the current study where we allow different far-field radiation patterns to be prescribed in different fixed far-field directions.…”

Feasibility analysis for active near/far field acoustic pattern synthesis in free space and shallow water environments

“…The matrix A is not invertible in most cases, thus the linear system ( 24) is solved using a regularization routine to minimize the sum of squared residuals. Following the strategy in [16,20,21], the unknown coefficients in w d are obtained by using Tikhonov regularization, and can be compactly written as…”

“…These include, but are not limited to, active noise control [2][3][4], personal sound zones or multizone sound reproduction [5][6][7], active acoustic cloaking [2,[8][9][10], remote sensing [11,12] and metamaterial design [13][14][15]. Active sound control techniques are becoming increasingly ubiquitous to enhance sound-based systems [16][17][18][19][20][21]. Forward and inverse problems for sound in underwater environments have been widely studied in the literature (see monographs [22][23][24] and references therein).…”