Poromechanics problems in geotechnical and geological contexts often involve complex formations with numerous boundaries and material interfaces, which significantly complicate numerical analysis and simulation. The traditional finite element method (FEM) encounters substantial challenges in these scenarios because it requires the mesh to conform precisely to each boundary and interface. This requirement complicates preprocessing and necessitates meticulous manual control to achieve a high-quality mesh. In contrast, unfitted FEMs are well-suited for these problems as they do not require the mesh to align with the model geometry. We propose a stabilized unfitted FEM that incorporates Nitsche's method and ghost penalty stabilization techniques to address complex poroelasticity problems. This approach treats material interfaces as weak discontinuities and ensures that compatibility conditions are satisfied. The proposed method allows the mesh to be independent of both boundaries and material interfaces. Nitsche's method is used to weakly enforce both Dirichlet boundary conditions and interface compatibility conditions, resulting in a symmetric weak form. Additionally, three types of ghost penalty terms are introduced for elements intersected by boundaries or interfaces, effectively eliminating cut-induced ill-conditioning. The proposed methodology has been validated through benchmark and practical problems, demonstrating optimal convergence and exceptional stability. This approach significantly enhances the stability and efficiency of hydro-mechanical analyses for complex geotechnical and geological problems.

中文翻译：

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弱不连续性多孔弹性的稳定非拟合有限元方法


岩土工程和地质环境中的多孔力学问题通常涉及具有许多边界和材料界面的复杂地层，这使数值分析和模拟变得非常复杂。传统的有限元方法 （FEM） 在这些情况下遇到了巨大的挑战，因为它要求网格精确地符合每个边界和界面。这一要求使预处理复杂化，需要细致的手动控制才能获得高质量的网格。相比之下，未拟合的 FEM 非常适合这些问题，因为它们不需要网格与模型几何对齐。我们提出了一种稳定的未拟合有限元，它结合了 Nitsche 的方法和鬼罚稳定技术来解决复杂的多孔弹性问题。这种方法将材料界面视为弱不连续性，并确保满足兼容性条件。所提出的方法允许网格独立于边界和材料界面。Nitsche 的方法用于弱强制执行狄利克雷边界条件和界面兼容性条件，从而产生对称的弱形式。此外，为边界或界面相交的单元引入了三种类型的幽灵罚项，有效地消除了切割引起的病态。所提出的方法已通过基准和实际问题进行了验证，展示了最佳收敛性和卓越的稳定性。这种方法显著提高了复杂岩土工程和地质问题的水力学分析的稳定性和效率。