The BPS preconditioner on Beowulf cluster

This work presents the implementation on a Linux Cluster of a parallel preconditionerfor the solution of the linear system resulting from the finite element discretizationof a 2D second order elliptic boundary value problem. The numerical method,proposed by Bramble, Pasciak and Schatz, is developed...

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Autores Principales: Salas Huertas, Oscar, Marazzina, Daniele, Rovida, Sergio, Sacchi, Giovanni, Scacchi, Simone
Formato: Artículo
Idioma: Español
Publicado: 2015
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/1424
http://hdl.handle.net/10669/12952
Sumario: This work presents the implementation on a Linux Cluster of a parallel preconditionerfor the solution of the linear system resulting from the finite element discretizationof a 2D second order elliptic boundary value problem. The numerical method,proposed by Bramble, Pasciak and Schatz, is developed using Domain Decompositiontechniques, which are based on the splitting of the computational domain into subregionsof smaller size, enforcing suitable compatibility conditions. The Fortran codeis implemented using PETSc: a suite of data structures and routines devoted to thescientific parallel computing and based on the MPI standard for all message-passingcommunications. The main interest of the paper is to present an efficient and portablecode for the solution of large-scale linear systems and to investigate how the architecturalaspects of the cluster influence the performance of the considered algorithm. Weprovide an analysis of the execution times as well as of the scalability, using as testcase the classical Poisson equation with Dirichlet boundary conditions.Keywords: Domain Decomposition, Parallelization, Partial Differential Equation, Preconditioner,Beowulf Cluster.