Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains
In this article we consider the application of Schwarz-type domain decomposition preconditioners for discontinuous Galerkin finite element approximations of elliptic partial differential equations posed on complicated domains, which are characterized by small details in the computational domain or m...
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| Format: | Article |
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Springer
2014
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| Online Access: | https://eprints.nottingham.ac.uk/29666/ |
| _version_ | 1848793825737179136 |
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| author | Antonietti, Paola F. Giani, Stefano Houston, Paul |
| author_facet | Antonietti, Paola F. Giani, Stefano Houston, Paul |
| author_sort | Antonietti, Paola F. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we consider the application of Schwarz-type domain decomposition preconditioners for discontinuous Galerkin finite element approximations of elliptic partial differential equations posed on complicated domains, which are characterized by small details in the computational domain or microstructures. In this setting, it is necessary to define a suitable coarse-level solver, in order to guarantee the scalability of the preconditioner under mesh refinement. To this end, we exploit recent ideas developed in the so-called composite finite element framework, which allows for the definition of finite element methods on general meshes consisting of agglomerated elements. Numerical experiments highlighting the practical performance of the proposed preconditioner are presented. |
| first_indexed | 2025-11-14T19:06:27Z |
| format | Article |
| id | nottingham-29666 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:06:27Z |
| publishDate | 2014 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-296662020-05-04T20:13:51Z https://eprints.nottingham.ac.uk/29666/ Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains Antonietti, Paola F. Giani, Stefano Houston, Paul In this article we consider the application of Schwarz-type domain decomposition preconditioners for discontinuous Galerkin finite element approximations of elliptic partial differential equations posed on complicated domains, which are characterized by small details in the computational domain or microstructures. In this setting, it is necessary to define a suitable coarse-level solver, in order to guarantee the scalability of the preconditioner under mesh refinement. To this end, we exploit recent ideas developed in the so-called composite finite element framework, which allows for the definition of finite element methods on general meshes consisting of agglomerated elements. Numerical experiments highlighting the practical performance of the proposed preconditioner are presented. Springer 2014-07 Article PeerReviewed Antonietti, Paola F., Giani, Stefano and Houston, Paul (2014) Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains. Journal of Scientific Computing, 60 (1). pp. 203-227. ISSN 0885-7474 Composite finite element methods Discontinuous Galerkin methods Domain decomposition Schwarz preconditioners http://link.springer.com/article/10.1007%2Fs10915-013-9792-y doi:10.1007/s10915-013-9792-y doi:10.1007/s10915-013-9792-y |
| spellingShingle | Composite finite element methods Discontinuous Galerkin methods Domain decomposition Schwarz preconditioners Antonietti, Paola F. Giani, Stefano Houston, Paul Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains |
| title | Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_full | Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_fullStr | Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_full_unstemmed | Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_short | Domain decomposition preconditioners for discontinuous Galerkin methods for elliptic problems on complicated domains |
| title_sort | domain decomposition preconditioners for discontinuous galerkin methods for elliptic problems on complicated domains |
| topic | Composite finite element methods Discontinuous Galerkin methods Domain decomposition Schwarz preconditioners |
| url | https://eprints.nottingham.ac.uk/29666/ https://eprints.nottingham.ac.uk/29666/ https://eprints.nottingham.ac.uk/29666/ |