New Robust Multigrid Method for 2D Convection-Diffusion Problems

摘要

In this paper we introduce a new multigrid approach for solving 2D convection-diffusion problems. As in the hierarchical basis multigrid method, we use a transformed matrix with a relatively low generalized condition number. The transformation we use is not based on the nesting of the coarse and fine grid only, but uses more information from the matrix. After transforming back to the original matrix, this results in a robust multigrid algorithm with matrix-dependent prolongations and restrictions.