Carlos Amaral Holbig*,
Paulo Sergio Morandi Jr.**, Bernardo Frederes Kramer Alcalde**
Tiaraju Asmuz Diverio** and Dalcidio Moraes Claudio***
* Universidade de Passo Fundo and PPGC at UFRGS
Passo Fundo
Brazil
email: holbig@upf.br
** Instituto de Informatica and PPGC at UFRGS
Porto Alegre
Brazil
emails: {diverio,sergio,bfkalcalde}@inf.ufrgs.br
*** Faculdade de Informatica and PPGCC at PUCRS
Porto Alegre
Brazil
email: dalcidio@pucrs.br
Many different numerical algorithms contain the solution of linear equation systems as a subproblem. Because of these aspects, this work aims the development of solvers to linear systems (for dense and sparse matrices) with high accuracy on cluster computers using C-XSC library (a C++ class library for extended scientific computing - see details about this library in [1]). The integration between C-XSC and MPI libraries on cluster computer was necessary and essential for the implementation of our algorithms in this kind of environment. We want to join the high accuracy given by C-XSC with the computational gain provided by parallelization [2]. Actually, our software run on labtec cluster at UFRGS and the integration between C-XSC and MPI was done correctly [3]. Our tests show that the C-XSC library needs to be optimized to be efficient in a High Performance Environment. About the C-XSC programs executed on cluster, some changes were made in the programs for their correct use in this environment, mainly about how to manipulate dotprecisions variables (high accuracy variables). Nowadays we are working in the implementation of parallel versions of programs to solve linear systems (without and with high accuracy) and the optimization of C-XSC library on cluster computers.
This work is part of a international cooperation project between Brazilian and German universities (UFRGS, PUCRS, UPF, University of Wuppertal and University of Karlsruhe). This work is supported in part by CAPES and FAPERGS (Brazil) and DAAD and IB/DLR (Germany).
References:
[1]Hofschuster, W., Kramer, W., Wedner, S., Wiethoff, A.: C-XSC 2.0:
A C++ Class Library for Extended Scientific Computing. Universitat
Wuppertal, Preprint BUGHW - WRSWT 2001/1 (2001).
[2]Holbig, C.A., Diverio, T.A., Claudio, D.M., Kramer, W., Bohlender,
G.: Automatic Result Verification in the Environment of High
Performance Computing. In: IMACS/GAMM INTERNATIONAL SYMPOSIUM ON
SCIENTIFIC COMPUTING, COMPUTER ARITHMETIC AND VALIDATED NUMERICS,
2002, Paris. Extended abstracts, pg. 54-55 (2002).
[3]Holbig, C.A., Diverio, T.A., Kramer, W.: An Accurate and Efficient
Selfverifying Solver for Systems with Banded Coefficient Matrix. In
INTERNATIONAL PARALLEL COMPUTING, 2003, Dresden. Book of Resumes,
pg. 58 (2003).