A Note on Optimal Spectral Bounds for Nonoverlapping Domain Decomposition Preconditioners for Hp-Version Discontinuous Galerkin Methods
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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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