Parallel nonlinear preconditioners on multicore architectures

Authors:
Vicente Galiano;Héctor Migallón;Violeta Migallón;José Penadés
Affiliations:
Departamento de Física y Arquitectura de Computadores, Universidad Miguel Hernández, Elche, Spain 03202;Departamento de Física y Arquitectura de Computadores, Universidad Miguel Hernández, Elche, Spain 03202;Departamento de Ciencia de la Computación e Inteligencia Artificial, Universidad de Alicante, Alicante, Spain 03071;Departamento de Ciencia de la Computación e Inteligencia Artificial, Universidad de Alicante, Alicante, Spain 03071
Venue:
The Journal of Supercomputing
Year:
2011

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Parallel newton iterative methods based on incomplete LU factorizations for solving nonlinear systems

VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science

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Abstract

Parallel nonlinear preconditioners, for solving mildly nonlinear systems, are proposed. These algorithms are based on both the Fletcher---Reeves version of the nonlinear conjugate gradient method and a polynomial preconditioner type based on block two-stage methods. The behavior of these algorithms is analyzed when incomplete LU factorizations are used in order to obtain the inner splittings of the block two-stage method. As our illustrative example we have considered a nonlinear elliptic partial differential equation, known as the Bratu problem. The reported experiments show the performance of the algorithms designed in this work on two multicore architectures.