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

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.