A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods
In this article, we consider the derivation of hp-optimal spectral bounds for a class of domain decomposition preconditioners based on the Schwarz framework for discontinuous Galerkin finite element approximations of second-order elliptic partial differential equations. In particular, we improve the...
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| Format: | Article |
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Institute for Scientific Computing and Information
2015
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| Online Access: | https://eprints.nottingham.ac.uk/30303/ |
| _version_ | 1848793959402307584 |
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| author | Antonietti, Paola F. Houston, Paul Smears, Iain |
| author_facet | Antonietti, Paola F. Houston, Paul Smears, Iain |
| author_sort | Antonietti, Paola F. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article, we consider the derivation of hp-optimal spectral bounds for a class of domain decomposition preconditioners based on the Schwarz framework for discontinuous Galerkin finite element approximations of second-order elliptic partial differential equations. In particular, we improve the bounds derived in our earlier article [P.F. Antonietti and P. Houston, J. Sci. Comput., 46(1):124--149, 2011] in the sense that the resulting bound on the condition number of the preconditioned system is not only explicit with respect to the coarse and fine mesh sizes H and h, respectively, and the fine mesh polynomial degree p, but now also explicit with respect to the polynomial degree q employed for the coarse grid solver. More precisely, we show that the resulting spectral bounds are of order p^2H/(qh) for the hp-version of the discontinuous Galerkin method. |
| first_indexed | 2025-11-14T19:08:35Z |
| format | Article |
| id | nottingham-30303 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:08:35Z |
| publishDate | 2015 |
| publisher | Institute for Scientific Computing and Information |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-303032020-05-04T20:10:29Z https://eprints.nottingham.ac.uk/30303/ A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods Antonietti, Paola F. Houston, Paul Smears, Iain In this article, we consider the derivation of hp-optimal spectral bounds for a class of domain decomposition preconditioners based on the Schwarz framework for discontinuous Galerkin finite element approximations of second-order elliptic partial differential equations. In particular, we improve the bounds derived in our earlier article [P.F. Antonietti and P. Houston, J. Sci. Comput., 46(1):124--149, 2011] in the sense that the resulting bound on the condition number of the preconditioned system is not only explicit with respect to the coarse and fine mesh sizes H and h, respectively, and the fine mesh polynomial degree p, but now also explicit with respect to the polynomial degree q employed for the coarse grid solver. More precisely, we show that the resulting spectral bounds are of order p^2H/(qh) for the hp-version of the discontinuous Galerkin method. Institute for Scientific Computing and Information 2015 Article NonPeerReviewed Antonietti, Paola F., Houston, Paul and Smears, Iain (2015) A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods. International Journal of Numerical Analysis and Modeling . ISSN 1705-5105 (Submitted) Schwarz preconditioners hp–discontinuous Galerkin methods http://www.math.ualberta.ca/ijnam/contents.htm |
| spellingShingle | Schwarz preconditioners hp–discontinuous Galerkin methods Antonietti, Paola F. Houston, Paul Smears, Iain A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods |
| title | A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods |
| title_full | A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods |
| title_fullStr | A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods |
| title_full_unstemmed | A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods |
| title_short | A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods |
| title_sort | note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous galerkin methods |
| topic | Schwarz preconditioners hp–discontinuous Galerkin methods |
| url | https://eprints.nottingham.ac.uk/30303/ https://eprints.nottingham.ac.uk/30303/ |