# Parallel solution of saddle point systems with nested iterative solvers based on the Golub-Kahan Bidiagonalization

arXiv: https://arxiv.org/abs/2001.10424 · HTML: https://mlsanity.com/paper/2001.10424/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [Automated Grammar-based Algebraic Multigrid Design With Evolutionary Algorithms](https://mlsanity.com/paper/2603.17641/) (2026)

## Abstract (arXiv)

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.