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.

中文翻译：

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亥姆霍兹标量场的主动操纵：具有定向远场控制的近场合成

在本文中，我们提出了一种在有源源的有界近场区域中主动操纵标量亥姆霍兹场的策略，同时在规定的远场方向上保持所需的辐射模式。这个控制问题在两种环境中被考虑：自由空间和恒定深度的均匀海洋。在这两种媒体中，我们证明了表面输入的存在并对其进行了表征，建模为 Neumann 数据（法向速度）或 Dirichlet 数据（表面压力），使得辐射场满足控制约束。我们还提供了一种数值策略，通过使用基于 Morozov 差异原理的 Tikhonov 正则化的矩方法方法来构建这个预测的表面输入。