A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-Version Discontinuous Galerkin methods
Keywords
Advanced Numerical Methods for Scientific Computing
Code:
44/2015
Title:
A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-Version Discontinuous Galerkin methods
Date:
Sunday 20th September 2015
Author(s):
Antonietti, P.F.; Houston, P.; Smears, I.
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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.