An evaluation of parallel multigrid as solver and preconditioner for singular perturbed problems

In this paper we try to achieve h-independent convergence with preconditioned GMRES ((3]) and BiCGSTAB ((4]) for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods diier only in the transfer operators. One uses standard matrix-dependent prolongation operators from 1]. The second uses "upwind" prolonga-tion operators, developed in 6]. They employ Galerkin coarsening and an alternating zebra line Gauss-Seidel smoother. The third method is based the block LU decomposition of a matrix and on the Schur complement approximation. This multigrid variant is presented in 2]. All three multi-grid algorithms are algebraic methods. The methods have been parallelized with a grid partitioning technique, and are compared on an MIMD machine. For Poisson and convection-diiusion problems all components of the methods are investigated and evaluated.