We present an iterative method based on a generalization of the Golub-Kahan bidiagonalization for solving indefinite matrices with a 2×2 block structure. We focus in particular on our recent imple- mentation of the algorithm using the parallel numerical library PETSc. Since the algorithm is a nested solver, we investigate different choices for parallel inner solvers and show its strong scalability for two Stokes test problems. The algorithm is found to be scalable for large sparse problems.
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