Algebraic domain decomposition solver for linear elasticity

Aleš Janka

Applications of Mathematics (1999)

  • Volume: 44, Issue: 6, page 435-458
  • ISSN: 0862-7940

Abstract

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We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.

How to cite

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Janka, Aleš. "Algebraic domain decomposition solver for linear elasticity." Applications of Mathematics 44.6 (1999): 435-458. <http://eudml.org/doc/33041>.

@article{Janka1999,
abstract = {We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.},
author = {Janka, Aleš},
journal = {Applications of Mathematics},
keywords = {algebraic multigrid; zero energy modes; convergence theory; finite elements; computational mechanics; iterative solvers; algebraic multigrid; overlapping Schwarz domain decomposition; zero-energy modes; convergence rate; structural mechanics},
language = {eng},
number = {6},
pages = {435-458},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Algebraic domain decomposition solver for linear elasticity},
url = {http://eudml.org/doc/33041},
volume = {44},
year = {1999},
}

TY - JOUR
AU - Janka, Aleš
TI - Algebraic domain decomposition solver for linear elasticity
JO - Applications of Mathematics
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 6
SP - 435
EP - 458
AB - We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.
LA - eng
KW - algebraic multigrid; zero energy modes; convergence theory; finite elements; computational mechanics; iterative solvers; algebraic multigrid; overlapping Schwarz domain decomposition; zero-energy modes; convergence rate; structural mechanics
UR - http://eudml.org/doc/33041
ER -

References

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