多數熱隱形相關研究僅限於單一物理場的探討，雖然有少數對於多物理場隱形功能的研究，但在熱電隱形方面受限於純拉普拉斯形式的傅立葉定律以及歐姆定律，鮮少探討熱電效應的影響。本研究基於雙層理論中的雙層結構，應用多變數優化方法至熱電耦合的隱形問題之中，透過數值方法，計算出外層遮罩材料參數以設計熱電遮罩，可以適用於不同的背景材料條件，以及高電位的電場分布，同時也能應用至不同的幾何形狀，達成熱電耦合的隱形。本文透過對不同材料、不同邊界條件狀況以及三種幾何形狀進行熱電遮罩隱形效能的探討，結果指出在不同材料情況下會有不同的隱形效果；在幾何結構方面，旋轉角度也會影響隱形效能。總結來說，透過本文方法，可以適用熱電耦合的情況，在工程應用上也可透過優化的結果設計遮罩裝置，改善隱形效能。

Most literature related to the cloak is limited to a single physical field. Although there are some studies on the invisible function of multi-physics, the thermoelectric cloak is limited by the Laplace form of Fourier's law and Ohm's law. Seldom discuss thermoelectric effect in a cloak. This study is based on bilayer theory, uses bilayer structure, and applies multivariable optimization methods to the cloak of thermal and electric field coupling.
By the numerical method, calculate parameters of the outer layer to design thermal and electric cloak, which can be applied to different background conditions and high potential background, and can also be applied to different cloak geometry.
In this paper, discuss the cloaking performance in different materials, different boundary conditions and three geometries. The results show that the cloaking performance will change with different materials. For geometrically anisotropic cloaks, different rotating angle has significant impact on cloaking performance.
In conclusion, the method in this paper can be applied to the case of thermoelectric coupling. In engineering applications, use the optimized results to design cloaking devices, and to improve the cloaking performance.

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