An Efficient Implementation of the Thomas-Algorithm for Block Penta-diagonal Systems on Vector Computers

Authors:
Katharina Benkert;Rudolf Fischer
Affiliations:
High Performance Computing Center Stuttgart (HLRS), University of Stuttgart, 70569 Stuttgart, Germany;NEC High Performance Computing Europe GmbH, Prinzenallee 11, 40549 Duesseldorf, Germany
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Year:
2007

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Abstract

In simulations of supernovae, linear systems of equations with a block penta-diagonal matrix possessing small, dense matrix blocks occur. For an efficient solution, a compact multiplication scheme based on a restructured version of the Thomas algorithm and specifically adapted routines for LU factorization as well as forward and backward substitution are presented. On a NEC SX-8 vector system, runtime could be decreased between 35% and 54% for block sizes varying from 20 to 85 compared to the original code with BLAS and LAPACK routines.