A Parallel Implementation of the Algebraic Multigrid Method for Solving Problems in Dynamics of Viscous Incompressible Fluid

Abstract

An algorithm for improving the scalability of the multigrid method used for solving the system of difference equations obtained by the finite volume discretization of the Navier–Stokes equations on unstructured grids with an arbitrary cell topology is proposed. It is based on the cascade assembly of the global level; the cascade procedure gradually decreases the number of processors involved in the computations. Specific features of the proposed approach are described, and the results of solving benchmark problems in the dynamics of viscous incompressible fluid are discussed; the scalability and efficiency of the proposed method are estimated. The advantages of using the global level in the parallel implementation of the multigrid method which sometimes makes it possible to speed up the computations by several fold.