Introduction to Robust Multigrid Technique
Part A: Structured Grids

S.I. Martynenko
Central Institute of Aviation Motors
Moscow, Russia


Robust Multigrid Technique is intended to be a computational core of black box software for solving physically meaningful problems on structured grids. To overcome problem of robustness for a sufficiently large class of the partial differential equations, the technique consists of two parts: ``analytical'' part (adaption of the boundary volume problems to the technique) and ``computational'' part (control volume discretization and solution of discretized problems by original multigrid solver). Interpolation and pre-smoothing are eliminated from the ``computational'' part. In addition, the most powerful coarse grid correction strategy used in the technique makes task of the smoother the least demanding. 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 preprint reports the essential principles of the robust multigrid technique (Chapter 1), application to handle model problems (Chapter 2), multigrid software (Chapter 3 and 4) and parallel implementation (Chapter 5).

Contributed October 2, 2001.