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

Name: Henrique Gomes de Jesus
Type: MSc dissertation
Publication date: 05/03/2021

Namesort descending Role
Lucia Catabriga Advisor *
Maria Claudia Silva Boeres Co-advisor *

Examining board:

Namesort descending Role
Adriano Maurício de Almeida Côrtes External Examiner *
Isaac Pinheiro dos Santos Internal Examiner *
Lucia Catabriga Advisor *
Maria Claudia Silva Boeres Co advisor *

Summary: 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.
Keywords: Multigrid Methods. Algebraic Multigrid. Double Pairwise Aggregation.
Preconditioners. Iterative Methods.

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