Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific and Statistical Computing
A hybrid difference scheme on a Shishkin mesh for linear convection-diffusion problems
Applied Numerical Mathematics
Some numerical experiments with multigrid methods on Shishkin meshes
Journal of Computational and Applied Mathematics
Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
Hi-index | 0.00 |
Solving the algebraic linear systems proceeding from the discretization on some condensed meshes of 2D singularly perturbed problems, is a difficult task. In this work we present numerical experiments obtained with the multigrid method for this class of linear systems. On Shishkin meshes, the classical multigrid algorithm is not convergent. We see that modifying only the restriction operator in an appropriate form, the algorithm is convergent, the CPU time increases linearly with the discretization parameter and the number of cycles is independent of the mesh sizes.