This paper simulates the three-dimensional transient heat diffusion conduction in a solid medium containing multi-layered cylindrical circular heterogeneities using a coupling formulation between the boundary element method (BEM) and analytical solutions. The analytical solutions are incorporated as Green's functions, thereby making the discretization of the interfaces of the multi-layered system unnecessary; this improves the efficiency of the algorithm. The coupling is enforced by imposing the continuity of temperature and heat fluxes at virtual interfaces created around each heterogeneity.

The solution is first computed in the frequency domain, for a wide range of frequencies and axial wavenumbers, using complex frequencies to avoid aliasing phenomenon. Time series can then be obtained by means of a (fast) inverse Fourier transform.

The accuracy, efficiency, and stability of the proposed algorithms are confirmed by comparing the results against reference solutions. The transient analysis of heat diffusion in a solid medium in the presence of multi-layered inclusions is used to illustrate the potential of the proposed coupling formulation.

本文使用边界元法（BEM）与分析溶液之间的耦合公式，模拟了包含多层圆柱圆形异质性的固体介质中的三维瞬态热扩散传导。分析解决方案作为格林的功能被合并，从而使多层系统接口的离散化成为不必要。这提高了算法的效率。通过在围绕每个异质性创建的虚拟界面处施加温度和热通量的连续性，可以实现这种耦合。

首先在频域中针对宽范围的频率和轴向波数计算解决方案，并使用复杂的频率以避免混叠现象。然后可以通过（快速）傅立叶逆变换获得时间序列。

通过将结果与参考解决方案进行比较，可以确认所提出算法的准确性，效率和稳定性。在存在多层夹杂物的情况下，对固体介质中热扩散的瞬态分析用于说明所提出的偶联剂配方的潜力。