Parallel Algebraic Multigrid Methods on Distributed Memory Computers

Abstract

Algebraic multigrid methods are well suited as preconditioners for iterative solvers. We consider linear systems of equations which are sparse and symmetric positive definite and which stem from a finite element discretization of a second order self-adjoint elliptic partial differential equation or a system of them. Since preconditioners based on algebraic multigrid are very efficient, additional speedup can only be achieved by parallelization. In this paper, we propose a general parallel algebraic multigrid algorithm for finite element discretizations based on domain decomposition ideas which is well suited for distributed memory computers. This paper pays special attention to the coarsening strategy which has to be adapted in the parallel case. Moreover, a general framework of data distribution gives rise to a construction scheme for the prolongation operators. Results of numerical studies on parallel computers with distributed memory are presented which show the high efficiency of the approach.