Helmholtz标量场的主动操纵：具有定向远场控制的近场合成
Active manipulation of Helmholtz scalar fields: Near field synthesis with directional far field control
摘要：
在这篇文章中，我们提出了一种策略，在有界的近场区域的有源源的标量亥姆霍兹场的主动操纵，同时保持所需的辐射模式在规定的远场方向。这个控制问题被认为是在两个环境中：自由空间和分别，均匀海洋的恒定深度。在这两种介质中，我们证明了表面输入的存在和特点，建模为诺依曼数据（正常速度）或狄利克雷数据（表面压力），使辐射场满足控制约束。我们还提供了一个数值策略来构建这个预测的表面输入，通过使用一个基于Morozov差异原则的Tikhonov正则化的矩方法。几个数值模拟，以证明所提出的计划在相关的实际应用场景。
英文摘要：
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.
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