Geodesic
Iterative solution of saddle-point SLAEs
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 135-150

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The paper considers preconditioned iterative methods in Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with a saddle point arising from grid approximations of three dimensional boundary-value problems of various types describing filtration flows of a two-phase incompressible fluid. A comparative analysis of up-to-date approaches to block preconditioning of SLAEs under consideration, including issues of scalable parallelization of algorithms on multiprocessor computing systems with distributed and hierarchical shared memory using hybrid programming tools, is presented. A regularized Uzawa algorithm using a two-level iterative process is proposed. Results of numerical experiments for the Dirichlet and Neumann model boundary-value problems are provided and discussed. 
@article{ZNSL_2019_482_a9,
     author = {V. P. Il'in and G. Yu. Kazantsev},
     title = {Iterative solution of saddle-point {SLAEs}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--150},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a9/}
}
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V. P. Il'in; G. Yu. Kazantsev. Iterative solution of saddle-point SLAEs. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 135-150. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a9/