Volume 13, Issue 4
A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for Hp-Version Discontinuous Galerkin Methods

P. F. Antonietti, P. Houston & I. Smears

Int. J. Numer. Anal. Mod., 13 (2016), pp. 513-524

Published online: 2016-07

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  • Abstract
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 p²H/(qh) for the hp-version of the discontinuous Galerkin method.
  • Keywords

Schwarz preconditioners hp-discontinuous Galerkin methods

  • AMS Subject Headings

65N30 65N55 65F08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-513, author = {}, title = {A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for Hp-Version Discontinuous Galerkin Methods}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {4}, pages = {513--524}, abstract = {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 p²H/(qh) for the hp-version of the discontinuous Galerkin method.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/450.html} }
TY - JOUR T1 - A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for Hp-Version Discontinuous Galerkin Methods JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 513 EP - 524 PY - 2016 DA - 2016/07 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/450.html KW - Schwarz preconditioners KW - hp-discontinuous Galerkin methods AB - 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 p²H/(qh) for the hp-version of the discontinuous Galerkin method.
P. F. Antonietti, P. Houston & I. Smears. (1970). A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for Hp-Version Discontinuous Galerkin Methods. International Journal of Numerical Analysis and Modeling. 13 (4). 513-524. doi:
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