Algebraic two-level preconditioners for the Schur complement method

The solution of elliptic problems is challenging on parallel distributed me mory computers since their Green's functions are global. To address this is sue, we present a set of preconditioners for the Schur complement domain de composition method. They implement a global coupling mechanism, through coa rse-space components, similar to the one proposed in [Bramble, Pasciak, and Shatz, Math. Comp., 47 (1986), pp. 103-134]. The definition of the coarse- space components is algebraic; they are defined using the mesh partitioning information and simple interpolation operators. These preconditioners are implemented on distributed memory computers without introducing any new glo bal synchronization in the preconditioned conjugate gradient iteration. The numerical and parallel scalability of those preconditioners are illustrate d on two-dimensional model examples that have anisotropy and/or discontinui ty phenomena.