Robust multigrid technique

Abstract

A new robust multigrid technique for solving a large class of boundary value problems on structured grids is proposed. The technique is based on incorporation of adaption of equations to the technique, the control volume discretization and original multigrid solver into general algorithm. Special subgrids of the finest grid are generated to obtain the most powerful coarse grid correction strategy. Expanded robustness of the multigrid technique is a result of adaption of equations, extremely accurate formulation of the discrete problems on the coarse grids, original coarsening, the most powerful coarse grid correction strategy, construction of problem-independent transfer operators, and absence of pre-smoothing and interpolation. The paper represents the algorithm, estimation of computational work and results of numerical test performed. © Springer-Verlae Berlin Heidelberg 2003.