Alfredo Buttari and Salvatore Filippone
University of Rome "Tor Vergata"
Rome, Italy
and
Pasqua D'Ambra,
Institute for High-Performance Computing and Networking - CNR
Naples, Italy
email: pasqua.dambra@na.icar.cnr.it
and
Daniela di Serafino
Second University of Naples
Caserta, Italy
Effective numerical simulations in many application fields, such as Computational Fluid Dynamics, require fast and reliable numerical software modules to perform Sparse Linear Algebra computations.
The PSBLAS library was designed to provide basic operations needed to build iterative methods for the solution of sparse linear systems on distributed-memory parallel computers [1]. PSBLAS includes parallel versions of most of the computational kernels proposed in [2]. Furthermore, the library provides a set of auxiliary routines for the creation and management of distributed sparse matrix structures, whose functionalities are close to the ones required by the recent Sparse BLAS standard [3]. Both computational and auxiliary PSBLAS routines appeared to be powerful and flexible in restructuring a complex CFD code, in order to improve accuracy and efficiency in the solution of the sparse linear systems and in the so-called boundary data exchange arising in the numerical simulation process [4].
In this work we focus on the exploitation of the PSBLAS library for building additive Schwarz preconditioners, that are well suited for parallel iterative solution of linear systems arising from PDE discretizations. These preconditioners can be implemented by an appropriate sequence of existing PSBLAS routines, with no changes to the data type definitions; the preconditioner build phase is implemented by extending the auxiliary routine set. Experiments to analyze the performance of the PSBLAS-based Schwarz preconditioners with Krylov solvers have been carried out on test matrices arising from automotive engine simulations; some comparisons with widely used sparse linear algebra packages have also been performed.
References:
[1]S. Filippone, M. Colajanni, PSBLAS: A Library for Parallel Linear Algebra
Computation on Sparse Matrices, ACM Transactions on Mathematical Software,
26 (4) (2000).
[2]I. Duff, M. Marrone, G. Radicati, C. Vittoli, Level 3 Basic Linear
Algebra Subprograms for Sparse Matrices: a User Level Interface,
ACM Transactions on Mathematical Software, 23 (3) (1997).
[3]I. Duff, M. Heroux, R. Pozo, An Overview of the Sparse Basic Linear
Algebra Subprograms: The New Standard from the BLAS Technical Forum,
ACM Transactions on Mathematical Software, 28 (2) (2002).
[4]S. Filippone, P. D'Ambra, M. Colajanni, Using a Parallel Library
of Sparse Linear Algebra in a Fluid Dynamics Applications Code on Linux
Clusters, in Parallel Computing - Advances & Current Issues,
G. Joubert, A. Murli, F. Peters, M. Vanneschi eds., Imperial College Press
Pub. (2002).