在邊界元法的研究中，暫態熱問題已被廣泛應用於等向性材料進行討論，甚至有人使用於非線性熱傳導分析。但目前較少有人研究全異向性材料的暫態熱傳導，本文使用於亥姆霍茲方程式定義下的暫態基礎解分析，可以有效準確的求解暫態熱傳導分析，並加入用夏育群博士所提出的映像法，可以由異向性熱傳導係數來定義新的映像區域，並將在新的座標系下求解的溫度解，映像回原本的座標，來達到異向性熱傳導分析的目的，在將兩個方法合併來求解暫態異向性熱傳導，並比較有限元素方法。

Despite the extensive study of the transient thermal conduction analysis for isotropic media by the boundary element method, its relevant researches in anisotropic transient heat conduction still remain extremely scarce indeed. In the thesis, the author applies the time-stepping scheme [2] for the transient effect and also the domain mapping scheme proposed by Shiah and Tan [4] to treat the anisotropy. For the transient analysis, the fundamental solution of the Helmholz equation is applied. For the domain mapping scheme, coordinates of the boundary are transformed to a new coordinate system by the anisotropic heat conductivities, where the transformed domain is considered to have equivalent isotropic heat conduction. Thus, the anisotropic thermal field in the original domain can be directly obtained via solving the corresponding "isotropic" one in the distorted domain. For the present boundary element analysis, the both schemes are jointly applied to solve for the problem of transient heat conduction in anisotropic media. In the end, a few benchmark examples are studied by the proposed schemes and the results are compared with finite element analysis.

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