Fast and Scalable Solvers for the Fluid Pressure Equations with Separating Solid Boundary Conditions

This is the peer reviewed version of the following article: Lai, J., Chen, Y., Gu, Y., Batty, C. and Wan, J.W. (2020), Fast and Scalable Solvers for the Fluid Pressure Equations with Separating Solid Boundary Conditions. Computer Graphics Forum, 39: 23-33., which has been published in final form at https://doi.org/10.1111/cgf.13909. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.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