Iterative solution of singular systems with applications

0430877 - ÚGN 2015 RIV DE eng C - Conference Paper (international conference)
Blaheta, Radim - Jakl, Ondřej - Starý, Jiří
Iterative solution of singular systems with applications.
Parallel Processing and Applied Mathematics. Berlin, Heidelberg: Springer-Verlag, 2014 - (Wyrzykowski, R.; Dongarra, J.; Karczewski, K.; Waśniewski, J.), s. 114-123. Lecture Notes in Computer Science, 8384, Part 1. ISBN 978-3-642-55223-6. ISSN 0302-9743.
[Parallel Processing and Applied Mathematics - International Conference PPAM 2013 /10./. Warsaw (PL), 08.09.2013-11.09.2013]
R&D Projects: GA MŠMT ED1.1.00/02.0070
Institutional support: RVO:68145535
Keywords : singular system * symmetric positive semidefinite problem * stabilized preconditioned conjugate gradient method * GEM software
Subject RIV: BA - General Mathematics

This paper deals with e cient solution of singular symmetric positive semidenite problems. Our motivation arises from the need to solve special problems of geotechnics, e.g. to perform upscaling analysis of geocomposites. In that and other applications we have to solve boundary problems with pure Neumann boundary conditions. We show that the stabilized PCG method with various preconditioners is a good choice for systems resulting from the numerical solution of Neumann problems, or more generally problems with a known small dimensional null space. We make use of this scenario to compare parallel implementations of the corresponding solvers, namely implementations in the in-house nite element software GEM and implementations employing components of the general Trilinos framework. The studies show that the solvers based on GEM are highly competitive with its recognized counterpart.
Permanent Link: http://hdl.handle.net/11104/0235543