On the minimal residual methods for solving diffusionconvection SLAEs

V. P. Il'in, D. I. Kozlov, A. V. Petukhov

Research output: Contribution to journalConference articlepeer-review


The objective of this research is to develop and to study iterative methods in the Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with non-symmetric sparse matrices of high orders arising in the approximation of multi-dimensional boundary value problems on the unstructured grids. These methods are also relevant in many applications, including diffusion-convection equations. The considered algorithms are based on constructing ATA - orthogonal direction vectors calculated using short recursions and providing global minimization of a residual at each iteration. Methods based on the Lanczos orthogonalization, AT - preconditioned conjugate residuals algorithm, as well as the left Gauss transform for the original SLAEs are implemented. In addition, the efficiency of these iterative processes is investigated when solving algebraic preconditioned systems using an approximate factorization of the original matrix in the Eisenstat modification. The results of a set of computational experiments for various grids and values of convective coefficients are presented, which demonstrate a sufficiently high efficiency of the approaches under consideration.

Original languageEnglish
Article number012005
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 13 Dec 2021
EventInternational Conference on Marchuk Scientific Readings 2021, MSR 2021 - Novosibirsk, Virtual, Russian Federation
Duration: 4 Oct 20218 Oct 2021




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