ISPH with a Geometric Multigrid Preconditioning Solver using Background Cells in GPU environment

Incompressible fluid analysis using the ISPH or MPS methods requires the solution of the pressure Poisson equation, which takes up most of the overall computation time. In addition, the iteration number for solving pressure Poisson equations may increase as the simulation model scale increases. This is a common problem in particle methods and the other implicit time integration solvers. In different methods, FEM, etc., good quality preconditioning, such as multigrid preconditioning, can significantly improve the convergence of iterative solution methods. There are two types of multigrid preconditioners, algebraic multigrid and geometric multigrid methods, but there are few examples of their application in particle methods. In this study, we attempted to develop a framework for a geometric multigrid preconditioner for solving the pressure Poisson equation in the ISPH. First, we focused on the geometric multigrid preconditioner using background cells, which are used for neighboring particle search, and implemented it on a GPU environment. Through a simple dam-break problem, we compared the computation time between the Conjugate gradient (CG) solver with a traditional preconditioner and the CG solver with a geometric multigrid preconditioner. We confirmed that the background cell-based geometric multigrid preconditioner is practical for the ISPH method.