A comparison of iterative multi-level finite element solvers

A comparison is made of two iterative algorithms: Preconditioned Conjugate Gradients (PCG) and Multigrid methods (MG), applying them to a series of test problems of plane elasticity. These problems are discretized by multilevel finite element meshes, that is, a coarse mesh whose elements are success...

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Detalles Bibliográficos
Publicado: 1998
Materias:
Algorithms
Computational geometry
Computer simulation
Convergence of numerical methods
Elasticity
Finite element method
Iterative methods
Multigrid methods
Preconditioned conjugate gradients (PCG)
Structural analysis
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00457949_v69_n5_p655_Jouglard
http://hdl.handle.net/20.500.12110/paper_00457949_v69_n5_p655_Jouglard
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00457949_v69_n5_p655_Jouglard
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spelling paper:paper_00457949_v69_n5_p655_Jouglard2023-06-08T15:05:21Z A comparison of iterative multi-level finite element solvers Algorithms Computational geometry Computer simulation Convergence of numerical methods Elasticity Finite element method Iterative methods Multigrid methods Preconditioned conjugate gradients (PCG) Structural analysis A comparison is made of two iterative algorithms: Preconditioned Conjugate Gradients (PCG) and Multigrid methods (MG), applying them to a series of test problems of plane elasticity. These problems are discretized by multilevel finite element meshes, that is, a coarse mesh whose elements are successively refined to obtain a fine mesh. In particular, uniform refinement was adopted in conjunction with triangular finite element discretizations, to obtain the hierarchy of meshes needed by the multilevel algorithms. A numerical analysis is made of convergence criteria based on the energy variation of the incremental correction to the solution through the iterative process, which seems to be a more convenient choice to the usual criteria based on the norm of the residual. Performance comparisons are made using diagonal and hierarchical preconditioners, and in all the examples tested the hierarchical PCG is found to be faster than the multigrid solvers. © 1998 Elsevier Science Ltd. All rights reserved. 1998 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00457949_v69_n5_p655_Jouglard http://hdl.handle.net/20.500.12110/paper_00457949_v69_n5_p655_Jouglard
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Algorithms
Computational geometry
Computer simulation
Convergence of numerical methods
Elasticity
Finite element method
Iterative methods
Multigrid methods
Preconditioned conjugate gradients (PCG)
Structural analysis
spellingShingle Algorithms
Computational geometry
Computer simulation
Convergence of numerical methods
Elasticity
Finite element method
Iterative methods
Multigrid methods
Preconditioned conjugate gradients (PCG)
Structural analysis
A comparison of iterative multi-level finite element solvers
topic_facet Algorithms
Computational geometry
Computer simulation
Convergence of numerical methods
Elasticity
Finite element method
Iterative methods
Multigrid methods
Preconditioned conjugate gradients (PCG)
Structural analysis
description A comparison is made of two iterative algorithms: Preconditioned Conjugate Gradients (PCG) and Multigrid methods (MG), applying them to a series of test problems of plane elasticity. These problems are discretized by multilevel finite element meshes, that is, a coarse mesh whose elements are successively refined to obtain a fine mesh. In particular, uniform refinement was adopted in conjunction with triangular finite element discretizations, to obtain the hierarchy of meshes needed by the multilevel algorithms. A numerical analysis is made of convergence criteria based on the energy variation of the incremental correction to the solution through the iterative process, which seems to be a more convenient choice to the usual criteria based on the norm of the residual. Performance comparisons are made using diagonal and hierarchical preconditioners, and in all the examples tested the hierarchical PCG is found to be faster than the multigrid solvers. © 1998 Elsevier Science Ltd. All rights reserved.
title A comparison of iterative multi-level finite element solvers
title_short A comparison of iterative multi-level finite element solvers
title_full A comparison of iterative multi-level finite element solvers
title_fullStr A comparison of iterative multi-level finite element solvers
title_full_unstemmed A comparison of iterative multi-level finite element solvers
title_sort comparison of iterative multi-level finite element solvers
publishDate 1998
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00457949_v69_n5_p655_Jouglard
http://hdl.handle.net/20.500.12110/paper_00457949_v69_n5_p655_Jouglard
_version_ 1768545087466242048

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