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

TL;DR

This paper introduces a method for actively controlling Helmholtz scalar fields to achieve specific near field and far field patterns in free space and ocean environments, using a numerical approach with regularization.

Contribution

It presents a novel control strategy for Helmholtz fields in bounded regions with a numerical method for surface input synthesis, applicable in free space and ocean settings.

Findings

Successful numerical simulations demonstrating control in practical scenarios

Characterization of surface inputs for desired field manipulation

Effective regularization approach for inverse control problem

Abstract

In this article, we propose a strategy for the active manipulation of scalar Helmholtz fields in bounded near field regions of an active source while maintaining desired radiation patterns in prescribed far field directions. This control problem is considered in two environments: free space and respectively, homogeneous ocean of constant depth. In both media, we proved the existence of and characterized the surface input, modeled as Neumann data (normal velocity) or Dirichlet data (surface pressure) such that the radiated field satisfies the control constraints. We also provide a numerical strategy to construct this predicted surface input by using a method of moments-approach with a Morozov discrepancy principle-based Tikhonov regularization. Several numerical simulations are presented to demonstrate the proposed scheme in scenarios relevant to practical applications.