# Institute of Mathematics

## Parallel solution of elasticity problems using overlapping aggregations

#### Roman Kohut

###### Received May 29, 2017.   Published online June 12, 2018.

Abstract:  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.
Keywords:  conjugate gradients; aggregation; Schwarz method; finite element method; geotechnical application; elasticity
Classification MSC:  65F08,74S05
DOI:  10.21136/AM.2018.0142-17

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Affiliations:   Roman Kohut, Institute of Geonics, Academy of Sciences of the Czech Republic, Studentská 17, 708 00 Ostrava, Czech Republic, e-mail: roman.kohut@ugn.cas.cz

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