Bucket-based multigrid preconditioner for solving pressure Poisson equation using a particle method

Abstract

The execution time for incompressible particle methods is dominated by solving large sparse linear systems. In this study, a novel simple bucket-based multigrid (BMG) preconditioner is presented to retrieve linear scaling. In the algorithm, the domain is decomposed into cubic boxes, to enable recursive aggregation of the closest neighboring particles. Under a moving particle semi-implicit (MPS) discretization scheme, parametric, verification, and performance studies were conducted for basic problems. From the parametric study, the BMG preconditioner was accompanied with a Krylov subspace accelerated multigrid cycle strategy and incorporated into a generalized conjugate residual method. Regardless of dimension and degree of particle distribution irregularity, the method significantly outperformed a conjugate gradient (CG), an incomplete Cholesky CG, and a conventional plain aggregation-based algebraic multigrid preconditioned solver. For a dam-break problem with 1.3 M and 2.3 M particles in 2D and 3D, the proposed method, as a linear solver for the MPS method, was 27 and 5.4 times faster than the CG method.