Approximate incomplete cyclic reduction for systems which are tridiagonal and strictly diagonally dominant by rows

Authors:
Carl Christian Kjelgaard Mikkelsen;Bo Kågström
Affiliations:
Department of Computing Science and HPC2N, Umeå University, Sweden;Department of Computing Science and HPC2N, Umeå University, Sweden
Venue:
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Year:
2012

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Abstract

Systems which are narrow banded and strictly diagonally dominant by rows can be solved in parallel using a variety of methods including incomplete block cyclic reduction. We show how to accelerate the algorithm by approximating the very first step. We derive tight estimates for the forward error and explain why our procedure is suitable for linear systems obtained by discretizing some common parabolic PDEs. An improved ScaLAPACK style algorithm is presented together with strong scalability results.