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Investigation of the convergence rate of the multigrid method on quasinested adaptive grids

In this paper, we investigate the convergence rate of the multigrid method for solving the Helmholtz equation with boundary Dirichlet conditions for a sequence of quasinested adaptive grids. The symmetrical Gauss–Seidel method is used as smoothing. There is made a comparison with the method based on the fast discrete Fourier transform in application scenarios. Earlier there was investigated the convergence of the multigrid method in which the smoothing Jacobi and Richardson operators were used. We give the results of numerical experiments that show the higher convergence rate of the algorithm proposed.