On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion

On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion

We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the di...

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Bibliographic Details
Main Authors: Styahar Andriy, Savula Yarema
Format: Article
Language:English
Published: Sciendo 2015-03-01
Series:Acta Mechanica et Automatica
Subjects:
elasticity theory
timoshenko shell theory
steklov-poincare operator
domain decomposition
Online Access:https://doi.org/10.1515/ama-2015-0006
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spelling doaj-d7551e64735f4782b8c8a7891bac8a502021-09-06T19:39:46ZengSciendoActa Mechanica et Automatica 2300-53192015-03-0191273210.1515/ama-2015-0006On The Convergence of Domain Decomposition Algorithm for The Body with Thin InclusionStyahar Andriy0Savula Yarema1Faculty of Applied Mathematics and Informatics, Department of Applied Mathematics, Ivan Franko Lviv National University, Universytetska,1, 79000, Lviv, UkraineFaculty of Applied Mathematics and Informatics, Department of Applied Mathematics, Ivan Franko Lviv National University, Universytetska,1, 79000, Lviv, UkraineWe consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the dimension of the problem inside the inclusion is decreased by one. For the numerical solution of this problem we propose an iterative domain decomposition algorithm (Dirichlet-Neumann scheme). This approach allows us to decouple problems in both parts and preserve the structure of the corresponding matrices. We investigate the convergence of the aforementioned algorithm and prove that the problem is well-posed.https://doi.org/10.1515/ama-2015-0006elasticity theorytimoshenko shell theorysteklov-poincare operatordomain decomposition
collection DOAJ
language English
format Article
sources DOAJ
author Styahar Andriy
Savula Yarema
spellingShingle Styahar Andriy
Savula Yarema
On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion
Acta Mechanica et Automatica
elasticity theory
timoshenko shell theory
steklov-poincare operator
domain decomposition
author_facet Styahar Andriy
Savula Yarema
author_sort Styahar Andriy
title On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion
title_short On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion
title_full On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion
title_fullStr On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion
title_full_unstemmed On The Convergence of Domain Decomposition Algorithm for The Body with Thin Inclusion
title_sort on the convergence of domain decomposition algorithm for the body with thin inclusion
publisher Sciendo
series Acta Mechanica et Automatica
issn 2300-5319
publishDate 2015-03-01
description We consider a coupled 3D model that involves computation of the stress-strain state for the body with thin inclusion. For the description of the stress-strain state of the main part, the linear elasticity theory is used. The inclusion is modelled using Timoshenko theory for shells. Therefore, the dimension of the problem inside the inclusion is decreased by one. For the numerical solution of this problem we propose an iterative domain decomposition algorithm (Dirichlet-Neumann scheme). This approach allows us to decouple problems in both parts and preserve the structure of the corresponding matrices. We investigate the convergence of the aforementioned algorithm and prove that the problem is well-posed.
topic elasticity theory
timoshenko shell theory
steklov-poincare operator
domain decomposition
url https://doi.org/10.1515/ama-2015-0006
work_keys_str_mv AT styaharandriy ontheconvergenceofdomaindecompositionalgorithmforthebodywiththininclusion
AT savulayarema ontheconvergenceofdomaindecompositionalgorithmforthebodywiththininclusion
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