This paper is concerned with the solution of block tridiagonal linear algebraic systems by the preconditioned conjugate gradient (PCG) method. If we consider two splittings of the coefficient matrix, it is possible to derive a parallel additive polynomial preconditioner and to give conditions for such preconditioner to be symmetric positive definite. For the diffusion problem this preconditioner can be interpreted as a simple form of domain decomposition preconditioning. In order to solve each subdomain problem we analyse two solvers named Cyclic Reduction solver and Approximate Schur solver. Numerical results carried out on Cray Y-MP for a set of test-problems permit to evaluate the effectiveness of the parallel polynomial preconditioner.
A parallel preconditioner for block tridiagonal matrices / Galligani, Emanuele; V., Ruggiero. - STAMPA. - 9, Series: Advances in Parallel Computing, Eds. G.R. JOUBERT, U. SCHENDEL:(1994), pp. 113-120. (Intervento presentato al convegno International Conference ParCo93 tenutosi a Grenoble nel 7-10 settembre, 1993).
A parallel preconditioner for block tridiagonal matrices
GALLIGANI, Emanuele;
1994
Abstract
This paper is concerned with the solution of block tridiagonal linear algebraic systems by the preconditioned conjugate gradient (PCG) method. If we consider two splittings of the coefficient matrix, it is possible to derive a parallel additive polynomial preconditioner and to give conditions for such preconditioner to be symmetric positive definite. For the diffusion problem this preconditioner can be interpreted as a simple form of domain decomposition preconditioning. In order to solve each subdomain problem we analyse two solvers named Cyclic Reduction solver and Approximate Schur solver. Numerical results carried out on Cray Y-MP for a set of test-problems permit to evaluate the effectiveness of the parallel polynomial preconditioner.
Pubblicazioni consigliate
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris
