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Parallel solution of saddle point systems with nested iterative solvers based on the Golub-Kahan Bidiagonalization
We present a scalability study of Golub-Kahan bidiagonalization for the
parallel iterative solution of symmetric indefinite linear systems with a 2x2
block structure. The algorithms have been implemented within the parallel
numerical library PETSc. Since a nested inner-outer iteration strategy may be
necessary, we investigate different choices for the inner solvers, including
parallel sparse direct and multigrid accelerated iterative methods. We show the
strong and weak scalability of the Golub-Kahan bidiagonalization based
iterative method when applied to a two-dimensional Poiseuille flow and to two-
and three-dimensional Stokes test problems