Parallel solvers for three-dimensional parabolic equations are required for scalable simulation of diffusion and heat conduction on supercomputers with a large number of processors. Two parallel schemes of numerical integration are studied in this paper. The first one is the implicit scheme, resolved by the multigrid. The second one is based on explicit Chebyshev iterations. The results of numerical experiments are given for model problems including case of discontinuous coefficients. Computations show these techniques provide high parallel efficiency and allow to overcome scalability challenges in preparation for exascale.

three-dimensional parabolic equations, multigrid, Chebyshev's iterations, parallel implementation

Mathematical problems and theory of numerical methods