Solving parabolic equations on locally refined grids
O. Yu. Milyukova, V. F. Tishkin
Institute for Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia
An implicit finite difference scheme for solving the heat conduction equation on locally refined grids in a rectangular domain is considered. To solve the resulting system of equations, the conjugate gradient method with preconditioning is used. This method is a variant of the incomplete Cholesky decomposition or modified incomplete Cholesky decomposition. A modification of the computation of the preconditioning matrix for the variant of the incomplete Cholesky-conjugate gradient method for the case of the numerical solution of heat conduction equations with a rapidly varying thermal conductivity coefficient is proposed. Variants of the above-mentioned method designed for use on parallel computer systems with MIMD architecture are proposed. The solution of model problems on a moderate number of processors is used to examine the rate of convergence and the efficiency of the proposed methods.
parabolic equation, grid method, incomplete Cholesky decomposition, parallel computing.
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Computational Mathematics and Mathematical Physics, 2005, 45:11, 1952–1964
O. Yu. Milyukova, V. F. Tishkin, “Solving parabolic equations on locally refined grids”, Zh. Vychisl. Mat. Mat. Fiz., 45:11 (2005), 2031–2043; Comput. Math. Math. Phys., 45:11 (2005), 1952–1964
Citation in format AMSBIB
\by O.~Yu.~Milyukova, V.~F.~Tishkin
\paper Solving parabolic equations on locally refined grids
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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