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A multigrid method for a heat equation with discontinuous coefficients with a special choice of grids

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Abstract

A new multigrid method is proposed for the solution of systems of linear algebraic equations obtained as a result of the discretization of the initial boundary-value problems for a heat equation with a discontinuous heat conduction coefficient. In the method, a special construction of the next level grid is used, with special treatment of subregions near the discontinuity lines of the heat conduction coefficient. The numerical experiments with a 2D model problem discretized on orthogonal grids demonstrated a high convergence rate for the method and weak dependence of the convergence on the discontinuity jump of the coefficient.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    O. Yu. Milyukova & V. F. Tishkin

Authors
  1. O. Yu. Milyukova
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  2. V. F. Tishkin
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Correspondence to O. Yu. Milyukova.

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Original Russian Text © O.Yu. Milyukova, V.F. Tishkin, 2015, published in Matematicheskoe Modelirovanie, 2015, Vol. 27, No. 9, pp. 17–32.

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Milyukova, O.Y., Tishkin, V.F. A multigrid method for a heat equation with discontinuous coefficients with a special choice of grids. Math Models Comput Simul 8, 118–128 (2016). https://doi.org/10.1134/S2070048216020101

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  • DOI: https://doi.org/10.1134/S2070048216020101

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