In this paper, we propose and evaluate fast, scalable approaches for solving the linear complementarity problems (LCP) arising from the fluid pressure equations with separating solid boundary conditions. Specifically, we present a policy iteration method, a penalty method, and a modified multigrid method, and demonstrate that each is able to properly handle the desired boundary conditions. Moreover, we compare our proposed methods against existing approaches and show that our solvers are more efficient and exhibit better scaling behavior; that is, the number of iterations required for convergence is essentially independent of grid resolution, and thus they are faster at larger grid resolutions. For example, on a 2563 grid our multigrid method was 30 times faster than the prior multigrid method in the literature.

中文翻译：

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具有分离固体边界条件的流体压力方程的快速可扩展求解器

在本文中，我们提出并评估了快速、可扩展的方法，用于解决由具有分离固体边界条件的流体压力方程引起的线性互补问题 (LCP)。具体来说，我们提出了一种策略迭代方法、一种惩罚方法和一种改进的多重网格方法，并证明了每种方法都能够正确处理所需的边界条件。此外，我们将我们提出的方法与现有方法进行了比较，并表明我们的求解器更有效，并表现出更好的缩放行为；也就是说，收敛所需的迭代次数基本上与网格分辨率无关，因此它们在较大的网格分辨率下更快。例如，在 2563 网格上，我们的多重网格方法比文献中先前的多重网格方法快 30 倍。