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

Article

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.

Keywords

parabolic equations multigrid methods speed of convergence of an iterative method 

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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

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