Parallel solution of elasticity problems using overlapping aggregations
Applications of Mathematics (2018)
- Volume: 63, Issue: 6, page 603-628
- ISSN: 0862-7940
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topKohut, Roman. "Parallel solution of elasticity problems using overlapping aggregations." Applications of Mathematics 63.6 (2018): 603-628. <http://eudml.org/doc/294876>.
@article{Kohut2018,
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.},
author = {Kohut, Roman},
journal = {Applications of Mathematics},
keywords = {conjugate gradients; aggregation; Schwarz method; finite element method; geotechnical application; elasticity},
language = {eng},
number = {6},
pages = {603-628},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Parallel solution of elasticity problems using overlapping aggregations},
url = {http://eudml.org/doc/294876},
volume = {63},
year = {2018},
}
TY - JOUR
AU - Kohut, Roman
TI - Parallel solution of elasticity problems using overlapping aggregations
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 6
SP - 603
EP - 628
AB - 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.
LA - eng
KW - conjugate gradients; aggregation; Schwarz method; finite element method; geotechnical application; elasticity
UR - http://eudml.org/doc/294876
ER -
References
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