Title: Almost optimal order approximate inverse based preconditioners for 3-d convection dominated problems on tensor-grids

Authors: J.M. Maubach

Addresses: Centre for Analysis Scientific Computing and Applications, Faculty of Mathematics and Computer Science, Technical University of Eindhoven, The Netherlands

Abstract: For a one-dimensional diffusion problem on an refined computational grid we present preconditioners based on the standard approximate inverse technique. Next, we determine its spectral condition number κ2 and perform numerical calculations which corroborate the theoretical results. Then we perform numerical calculations which show that the standard approximate inverse preconditioners and our modified versions behave in a similar manner. To finish with we show that a combination of the standard approximate inverse with an additional incomplete factorisation leads to an almost optimal order preconditioner in 1–3 dimensions on refined grids, with and without dominant convection.

Keywords: approximate preconditioners; almost optimal order preconditioners; condition number; finite difference convection; diffusion operators; tensor grids.

DOI: 10.1504/IJCSM.2007.016536

International Journal of Computing Science and Mathematics, 2007 Vol.1 No.2/3/4, pp.271 - 292

Published online: 07 Jan 2008 *

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