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

Abstract

In this paper, we continue to study the feasibility of active manipulation of Helmholtz fields and by using an improved and more robust numerical strategy we present a detailed sensitivity analysis for the active methods proposed in our previous works [Onofrei D. Active manipulation of fields modelled by the Helmholtz equation. J Integral Equ. Appl. 2014;26(4):553–579; Onofrei D, Platt E. On the synthesis of acoustic sources with controllable near fields. Wave Motion. 2018;77:12–27]. In this regard, we study the behaviour of physically relevant parameters (i.e. source power, control accuracy, stability) with respect to variations in the type of control regions (bounded or unbounded), relative position of the control regions, distances between the control regions and the source, frequency range and fields to be approximated. We produce strong numerical evidence indicating the accuracy of our scheme and at the same time develop a better understanding of several important challenges for its physical implementation.

Keywords:

• Acoustic control
• inverse source problem
• field synthesis
• sensitivity analysis

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was initially supported by the Office of Naval Research under the award N00014-15-1-2462 and then supported by the Army Research Office under the award W911NF- 17-1-0478.