2012/03/19 by Yunfei Ma, Ma, Yunfei, Petter E. Bjørstad +5
Computer Science · Engineering · #65N55 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1203.4044
openalex publication_date 2012/03/19 · openalex created_date 2017/07/14 · openalex updated_date 2026/07/28
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.