Iterative Solution of Saddle-Point Systems of Linear Equations

V. P. Il’in, G. Y. Kazantcev

Research output: Contribution to journalArticlepeer-review

Abstract

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 threedimensional 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. Bibliography: 15 titles.

Original languageEnglish
Pages (from-to)199-208
Number of pages10
JournalJournal of Mathematical Sciences (United States)
Volume249
Issue number2
DOIs
Publication statusPublished - 1 Aug 2020

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