A hybrid Laplace-Galerkin method is proposed for modeling thermo-hydro-mechanical coupled problems of fluid saturated porous media in unsteady state regime. It consists of transforming the weak form equations into the Laplace space where they are solved by the Galerkin finite element method. Results in time space are then obtained by the Stehfest method of inverse Laplace transformation. This technique does not require any time stepping comparing to the traditional implicit or explicit time discretization method. Its exactitude is confirmed by comparing with existent analytical results as well as the one obtained by the implicit time stepping method.

中文翻译：

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流体饱和多孔介质中热-水-机械耦合的混合拉普拉斯-伽辽金方法：在钻孔问题中的应用

提出了一种混合拉普拉斯-伽辽金方法来模拟非稳态状态下流体饱和多孔介质的热-水-机械耦合问题。它包括将弱形式方程转换到拉普拉斯空间，在那里它们通过伽辽金有限元方法求解。然后通过逆拉普拉斯变换的 Stehfest 方法获得时间空间中的结果。与传统的隐式或显式时间离散化方法相比，该技术不需要任何时间步长。通过与已有的分析结果以及隐式时间步长法得到的结果进行比较，证实了其正确性。