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.

中文翻译：

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基于 Golub-Kahan 双对角化的带有嵌套迭代求解器的鞍点系统的并行求解

我们针对具有 2x2 块结构的对称不定线性系统的并行迭代解决方案提出了 Golub-Kahan 双对角化的可扩展性研究。这些算法已在并行数值库 PETSc 中实现。由于嵌套的内外迭代策略可能是必要的，我们研究了内部求解器的不同选择，包括并行稀疏直接和多重网格加速迭代方法。当应用于二维泊肃叶流以及二维和三维斯托克斯测试问题时，我们展示了基于 Golub-Kahan 双对角化的迭代方法的强和弱可扩展性。