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

TL;DR

This paper performs a detailed sensitivity analysis of active Helmholtz field manipulation in 3D, evaluating how various parameters affect control accuracy, stability, and feasibility using an improved numerical method.

Contribution

It introduces a more robust numerical strategy and provides comprehensive sensitivity analysis for active Helmholtz field control, enhancing understanding of physical implementation challenges.

Findings

Numerical evidence confirms the scheme's accuracy.

Control region type and position significantly affect results.

Parameter variations impact stability and control precision.

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 method proposed in our previous works. In this regard, we study the behavior 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 in the same time develop a better understanding of several important challenges for its physical implementation.