Precondicionador multigrid algébrico para métodos iterativos não estacionários na solução de sistemas lineares de grande porte

Abstract

The objective of this work is to evaluate the computational performance of Algebraic Multigrid (AMG) as a preconditioner for methods based on Krylov subspaces. An alternative coarsening strategy known as Double Pairwise Aggregation (DPA) has been implemented which applies a graph matching algorithm twice at each level of the hierarchy in order to produce the coarsening operators. In this context, matrices of different origins were used to compare the different AMG coarsening strategies with each other and with preconditioners derived from the incomplete LU factorization (ILU) and the Gauss-Seidel factorization applied to the Generalized Minimum Residual Method (GMRES). Additional computational experiments were performed with stencil matrices and with matrices originating from problems governed by Euler equations discretized by the Finite Element method, where a row and column reordering algorithm was also taken into account. Finally, the strengths and weaknesses of each method and coarsening algorithms are highlighted in each context, with emphasis on the advantages obtained with the implementation of DPA.