Applications of Mathematics

, Volume 63, Issue 6, pp 603–628 | Cite as

Parallel solution of elasticity problems using overlapping aggregations

  • Roman Kohut


The finite element (FE) solution of geotechnical elasticity problems leads to the solution of a large system of linear equations. For solving the system, we use the preconditioned conjugate gradient (PCG) method with two-level additive Schwarz preconditioner. The preconditioning is realised in parallel. A coarse space is usually constructed using an aggregation technique. If the finite element spaces for coarse and fine problems on structural grids are fully compatible, relations between elements of matrices of the coarse and fine problems can be derived. By generalization of these formulae, we obtain an overlapping aggregation technique for the construction of a coarse space with smoothed basis functions. The numerical tests are presented at the end of the paper.


conjugate gradients aggregation Schwarz method finite element method geotechnical application elasticity 

MSC 2010

65F08 74S05 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Institute of GeonicsAcademy of Sciences of the Czech RepublicOstravaCzech Republic

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