On the Finite Volume Multigrid Method: Comparison of Intergrid Transfer Operators

Abstract In this paper, we consider finite volume multigrid methods on triangular meshes with control volume based intergrid transfer operators. We review the error analysis of the finite volume methods and the convergence analysis on the multigrid method. For several different triangulations, we investigate the error reduction factors of the multigrid method as a solver, and also as a preconditioner in the Preconditioned CGM and GMRES solvers. We also study the scaling properties of the finite volume multigrid method on a High Performance Computer. We identify that the intergrid transfer operator based on the trial function space has the best properties.