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JOURNALS // Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Vychislitelnaya Matematika i Informatika" // Archive

Vestn. YuUrGU. Ser. Vych. Matem. Inform., 2013 Volume 2, Issue 3, Pages 92–105 (Mi vyurv95)

This article is cited in 1 paper

Computational Mathematics

Parallel algebraic solvers library Krylov

D. S. Butyuginab, Ya. L. Guryevaa, V. P. Il'ina, D. V. Perevozkina, A. V. Petukhova, I. N. Skopina

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS (Novosibirsk, Russian Federation)
b Novosibirsk State University

Abstract: Article describes functional capabilities and software implementation peculiarities of parallel algorithms library Krylov, which is oriented on the solution of large systems of linear algebraic equations with sparse symmetric and unsymmetric matrices (positive definite and semi-definite) obtained from discrete approximations of multidimensional boundary value problems for partial differential equations on unstructured meshes. The library includes two-level iterative methods in Krylov subspaces; preconditioning of the latter is based on the balanced decomposition of the computational domain with variable sizes of subdomain overlapping and different boundary conditions on interfacing boundaries. Program implementations use typical compressed sparse matrix data formats. Results of numerical experiments are presented which demonstrate the efficiency of parallelization for typical ill-conditioned problems.

Keywords: preconditioned iterative algorithms; Krylov subspaces; domain decomposition methods; sparse algebraic systems; numerical experiments.

UDC: 519.612

Received: 14.06.2013

DOI: 10.14529/cmse130307



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