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

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