A numerical method for solving parabolic equations based on the use of a multigrid techniques (Q2896260)

The authors present a new efficient method for the numerical solution of 2D parabolic equations discretized on detailed spatial grids. A generalization of this method for 3D parabolic equations is also presented. For several model problems, both theoretical and numerical investigations have shown the stability and accuracy which is typical for the fully implicit scheme. As was shown by numerical examples, the solution of problems with discontinuous coefficients has less accuracy as compared to the case of constant or smoothly varying coefficients.NEWLINENEWLINEThe results of theoretical investigation of the conservation property are given for a model problem solved by the new method with \(L = 2\) grid levels. The new method allows to reduce substantially the computational expenses as compared to the use of the fully implicit scheme or the explicit scheme on the finest grid. If the number of grid levels, \(L\), is sufficiently large, then the number of arithmetic operations on each time-step is proportional to the number of nodes of the finest grid. Application of the proposed method can be advantageous in the cases when the splitting by physical processes is used for the whole problem, and one of the arising computational subproblems is a solution of parabolic type equations.