Schwarz Preconditioner with Face Based Coarse Space for Multiscale Elliptic Problems in 3D

We present a parallel preconditioner based on the domain decomposition for the finite element discretization of multiscale elliptic problems in 3D with highly heterogeneous coefficients. The proposed preconditioner is constructed using an abstract framework of the Additive Schwarz Method which is intrinsically parallel. The coarse space consists of multiscale finite element functions associated with the wire basket, and is enriched with functions based on solving carefully constructed generalized eigen value problem locally on each face. The convergence rate of the Preconditioned Conjugate Method with the proposed preconditioner is shown to be independent of the variations in the coefficients for sufficient number of eigenfunctions in the coarse space.