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844 Section 1
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Onconjugateresidualmethodsforsolvingnon.symmetricSLAEs
V. P. Il'in1,2, D. I. Kozlov1, A. V. Petukhov1
1Institute of Computational Mathematics and Mathematical Geophysics SBRAS 2Novosibirsk State University Email: ilin@sscc.ru
DOI 10.24412/cl.35065.2021.1.00.17
The aim of this work is to develop and study iterative methods in Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with non.symmetric sparse matrices of high orders arising in the approxima�tion of multidimensional boundary value problems on the unstructured grids and which are also relevant in many applications, including diffusion.convective equations. The considered algorithms are based on the con�struction ATA�orthogonal direction vectors calculated using short recursions and providing global minimiza�tion of the residual at each iteration. Methods based on Lanczos orthogonalization, AT�preconditioned conju�gate residuals algorithm, as well as left Gaussian transformation for the original SLAE are implemented. In ad�dition, the efficiency of these iterative processes was investigated when solving algebraic systems precondi�tioned 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.
AlgorithmforthenumericalsolutionofthepureNeumannprobleminfracturedporousmedia
M. I. Ivanov1, I. A. Kremer1,2, Yu. M. Laevsky1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS 2Novosibirsk State University Email:ivanov@sscc.ru, kremer@sscc.ru, laev@labchem.sscc.ru
DOI 10.24412/cl.35065.2021.1.00.20
The paper considers some variants of boundary value problems for the pressures and filtration rates of a liquid in fractured porous media [1]. For non.flow conditions at the external reservoir boundaries, the pres�sures inside the media are determined ambiguously. A variant of the pure Neumann problem arises [2]. For such a problem, the condition of unique solvability is derived. Classical and mixed generalized problem state�ments that include the constraint on the pressures explicitly are investigated. An algorithm for numerical solu�tion of the problem using the mixed finite element method is presented. The properties of the proposed algo�rithm are discussed on the examples of numerical solutions of modelproblems.
This work was supported by the RSF (grant 19.11.00048).
