An Experimental Study of the Algebraic Multigrid Strategies
Lucia Catabriga1; Maria Claudia Boeres1; Marcelo Carrion1
1 Federal University of Espírito Santo
doi:10.20906/CPS/CILAMCE2017-0204
Resumo
This work presents a study of Algebraic Multigrid strategies, evaluating the performance gain that can be obtained by using them over traditional relaxation methods. The main idea behind Multigrid is to relax on successively smaller problems in a hierarchy of grids to accelerate the solution of the fine-grid problem; in the Algebraic Multigrid (AMG), no explicit knowledge of the problem geometry is needed, and the solver operates directly on the coefficient matrix of the linear system. In the present work, the SOR algorithm is employed as smoother for the AMG method, and coarse-grid level construction is implemented through three different schemes, each one combining particular coarsening and interpolation procedures. Two sets of matrices are considered in the numerical tests: one consists of stencil matrices originated from the discretization of a three-dimensional problem, while the second group has general matrices relating to miscellaneous applications. The computational experiments conducted allow for a detailed comparative analysis, showing the extent to which the Multigrid strategies can reduce the time to convergence of a classical iterative technique, with impactful results achieved in significant cases.
Palavras-chave: Multigrid methods; Algebraic multigrid; Iterative methods