A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered Lagrange multipliers and pressure unknowns used to impose the constraints and solve the fluid flow in the fractures, respectively. This formulation does not require any interpolation between different fields, but is not uniformly inf-sup stable and requires a stabilization. For the resulting 3 x 3 block Jacobian matrix, we design scalable preconditioning strategies, based on the physically-informed block partitioning of the unknowns and state-of-the-art multigrid preconditioners. The key idea is to restrict the system to a single-physics problem, approximately solve it by an inner algebraic multigrid approach, and finally prolong it back to the fully-coupled problem. Two different techniques are presented, analyzed and compared by changing the ordering of the restrictions. Numerical results illustrate the algorithmic scalability, the impact of the relative number of fracture-based unknowns, and the performance on a real-world problem.
翻译:提出了在断裂网络中摩擦接触力学和流体流动等共同问题的先决条件框架。多孔介质使用低序连续限制元素,以细胞为中心拉格朗增殖器和压力未知器,分别用来施加限制和解决断裂体的液体流动。这种配方并不要求不同领域之间的任何内插,但并不是统一的内向稳定,需要稳定。对于由此产生的3x3块Jacobian矩阵,我们设计了可扩展的先决条件战略,其依据是未知物和最新多电格预设物的物理知情区块分割。关键思想是将系统限制在单一物理问题上,大约通过内向代数多电网方法解决,最后将系统延回到完全交错的问题。提出了两种不同的技术,通过改变限制的顺序进行分析和比较。数字结果说明了算法的可扩展性、基于未知物的相对数量的影响,以及实际世界问题的性能。