Parallel Subdomain-Based Preconditioner for the Schur Complement
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Preconditioned spectral multi-domain discretization of the incompressible Navier-Stokes equations
Journal of Computational Physics
Some inequalities for eigenvalues of Schur complements of Hermitian matrices
Journal of Computational and Applied Mathematics
Parallel scalability study of hybrid preconditioners in three dimensions
Parallel Computing
A Quasi-algebraic Multigrid Approach to Fracture Problems Based on Extended Finite Elements
SIAM Journal on Scientific Computing
Advances in Engineering Software
Advances in Engineering Software
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The solution of elliptic problems is challenging on parallel distributed memory computers since their Green's functions are global. To address this issue, we present a set of preconditioners for the Schur complement domain decomposition method. They implement a global coupling mechanism, through coarse-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 global synchronization in the preconditioned conjugate gradient iteration. The numerical and parallel scalability of those preconditioners are illustrated on two-dimensional model examples that have anisotropy and/or discontinuity phenomena.