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IETI – Isogeometric Tearing and Interconnecting

Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (No...

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Detalles Bibliográficos
Autores principales: Kleiss, Stefan K., Pechstein, Clemens, Jüttler, Bert, Tomar, Satyendra
Formato: Online Artículo Texto
Lenguaje:English
Publicado: North-Holland Pub. Co 2012
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3914259/
https://www.ncbi.nlm.nih.gov/pubmed/24511167
http://dx.doi.org/10.1016/j.cma.2012.08.007
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author Kleiss, Stefan K.
Pechstein, Clemens
Jüttler, Bert
Tomar, Satyendra
author_facet Kleiss, Stefan K.
Pechstein, Clemens
Jüttler, Bert
Tomar, Satyendra
author_sort Kleiss, Stefan K.
collection PubMed
description Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requires to represent the computational domain as a collection of several NURBS geometries. Since there is a natural decomposition of the computational domain into several subdomains, NURBS-based IGA is particularly well suited for using FETI methods. This paper proposes the new IsogEometric Tearing and Interconnecting (IETI) method, which combines the advanced solver design of FETI with the exact geometry representation of IGA. We describe the IETI framework for two classes of simple model problems (Poisson and linearized elasticity) and discuss the coupling of the subdomains along interfaces (both for matching interfaces and for interfaces with T-joints, i.e. hanging nodes). Special attention is paid to the construction of a suitable preconditioner for the iterative linear solver used for the interface problem. We report several computational experiments to demonstrate the performance of the proposed IETI method.
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spelling pubmed-39142592014-02-05 IETI – Isogeometric Tearing and Interconnecting Kleiss, Stefan K. Pechstein, Clemens Jüttler, Bert Tomar, Satyendra Comput Methods Appl Mech Eng Article Finite Element Tearing and Interconnecting (FETI) methods are a powerful approach to designing solvers for large-scale problems in computational mechanics. The numerical simulation problem is subdivided into a number of independent sub-problems, which are then coupled in appropriate ways. NURBS- (Non-Uniform Rational B-spline) based isogeometric analysis (IGA) applied to complex geometries requires to represent the computational domain as a collection of several NURBS geometries. Since there is a natural decomposition of the computational domain into several subdomains, NURBS-based IGA is particularly well suited for using FETI methods. This paper proposes the new IsogEometric Tearing and Interconnecting (IETI) method, which combines the advanced solver design of FETI with the exact geometry representation of IGA. We describe the IETI framework for two classes of simple model problems (Poisson and linearized elasticity) and discuss the coupling of the subdomains along interfaces (both for matching interfaces and for interfaces with T-joints, i.e. hanging nodes). Special attention is paid to the construction of a suitable preconditioner for the iterative linear solver used for the interface problem. We report several computational experiments to demonstrate the performance of the proposed IETI method. North-Holland Pub. Co 2012-11-01 /pmc/articles/PMC3914259/ /pubmed/24511167 http://dx.doi.org/10.1016/j.cma.2012.08.007 Text en © 2012 Elsevier B.V. https://creativecommons.org/licenses/by-nc-nd/3.0/ Open Access under CC BY-NC-ND 3.0 (https://creativecommons.org/licenses/by-nc-nd/3.0/) license
spellingShingle Article
Kleiss, Stefan K.
Pechstein, Clemens
Jüttler, Bert
Tomar, Satyendra
IETI – Isogeometric Tearing and Interconnecting
title IETI – Isogeometric Tearing and Interconnecting
title_full IETI – Isogeometric Tearing and Interconnecting
title_fullStr IETI – Isogeometric Tearing and Interconnecting
title_full_unstemmed IETI – Isogeometric Tearing and Interconnecting
title_short IETI – Isogeometric Tearing and Interconnecting
title_sort ieti – isogeometric tearing and interconnecting
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3914259/
https://www.ncbi.nlm.nih.gov/pubmed/24511167
http://dx.doi.org/10.1016/j.cma.2012.08.007
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