Parallel Solution of Elasticity Problems using Aggregations

0429488 - ÚGN 2015 CZ eng A - Abstract
Kohut, Roman
Parallel Solution of Elasticity Problems using Aggregations.
Modelling 2014. Ostrava: Ústav geoniky AV ČR, 2014 - (Blaheta, R.; Starý, J.; Sysalová, D.). s. 56-56. ISBN 978-80-86407-47-0.
[Modelling 2014. 02.06.2014-06.06.2014, Rožnov pod Radhoštěm]
Institutional support: RVO:68145535
Keywords : elasticity problems * parallel solution * aggregations
Subject RIV: BA - General Mathematics

The contribution is devoted to a FE solution of elasticity problems. For the solution of the corresponding system of linear equations we use preconditioned CG method with overlapping Schwarz type preconditioners. The efficiency of the preconditioner decreases with an increasing number of subproblems and for avoiding this problem it is necessary to involve a coarse mesh correction. We use the algebraic coarse space created by aggregation. The aggregation used in the contribution is based on the idea that the basis functions for the coarse grid space are given by a linear combination of the basis functions for the fine grid space in the case of fully compatible FE spaces. The corresponding coefficients are given by the function values of the coarse grid basis function in the corresponding fine grid nodes. Using these relations between basis functions for the coarse grid and the fine grid spaces we obtain formulae for relations between the coarse matrix elements and the fine matrix elements.
Permanent Link: http://hdl.handle.net/11104/0234594