Domain Decomposition Preconditioners for a Discontinuous Galerkin Formulation of a Multiscale Elliptic Problem

Details Domain Decomposition Preconditioners for a Discontinuous Galerkin Formulation of a Multiscale Elliptic Problem Domain Decomposition Preconditioners for a Discontinuous Galerkin Formulation of a Multiscale Elliptic Problem

2012-03-19

arxiv.org/abs/1203.4044v1

Mathematics

Numerical Analysis

32pages, 5 figures

Scientific paper

In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on a discontinuous Galerkin formulation. We present both a nonoverlapping and an overlapping version of the method. We prove that the condition number bound of the preconditioned algebraic system in either case can be made independent of the coefficients under certain assumptions. Also, in our analysis, we do not need to assume that the coefficients are continuous across the coarse grid boundaries. The analysis and the condition number bounds are new, and contribute towards further extension of the theory for the discontinuous Galerkin discretization for multiscale problems.

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