准静态场的主动操纵及其应用
On the active manipulation of quasistatic fields and its applications
摘要：
根据\cite{OMV1}和\cite{OMV2}中提出的关于主动外部隐身的思想，我们在这里提出了一个系统的积分方程方法，以产生合适的准静态场，用于多个感兴趣区域的隐身、错觉和能量聚焦（具有给定的精度）。在准静态区域，中心问题是为拉普拉斯方程设计合适的源函数，使得所得解满足所需的性质。我们证明了问题解的存在性和非唯一性，并研究了物理上唯一的$L^2$ -最小能量解。我们还提供了一些数值证据的可行性所提出的方法。
英文摘要：
Following the ideas proposed in \cite{OMV1} and \cite{OMV2} on active exterior cloaking, we present here a systematic integral equation method to generate suitable quasistatic fields for cloaking, illusions and energy focusing (with given accuracy) in multiple regions of interests. In the quasistatic regime, the central issue is to design appropriate source functions for the Laplace equation so that the resulting solution will satisfy the required properties. We show the existence and non-uniqueness of solutions to the problem and study the physically relevant unique $L^2$-minimal energy solution. We also provide some numerical evidences on the feasibility of the proposed approach.
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