Numerical algorithm for solving diffusion-type equations on the basis of multigrid methods
Tóm tắt
A new numerical algorithm based on multigrid methods is proposed for solving equations of the parabolic type. Theoretical error estimates are obtained for the algorithm as applied to a two-dimensional initial-boundary value model problem for the heat equation. The good accuracy of the algorithm is demonstrated using model problems including ones with discontinuous coefficients. As applied to initial-boundary value problems for diffusion equations, the algorithm yields considerable savings in computational work compared to implicit schemes on fine grids or explicit schemes with a small time step on fine grids. A parallelization scheme is given for the algorithm.
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