On application of multigrid and explicit-iterative methods to solution of the parabolic equations with anisotropic discontinuous coefficients

The research and development of multigrid and explicit-iterative methods for solving actual 3D applied problems based on optimal properties of Chebyshev polynomials. The implicit scheme for parabolic equation based on the multigrid is studied. The new elements are construction of intergrid transfer operators for case of discontinuous coefficients and adaptation to the boundary of high frequency spectrum of the discrete operator. The adaptation is performed in the multigrid iterations and it increases the efficiency of the method. Explicit-iterative scheme with Chebyshev parameters is studied as a competitor of the multigrid scheme. For these schemes the results of comparison on the model problems are demonstrated. Both schemes provide a high performance; they scale well and allow overcoming difficulties in achieving exaflops performance.