Formalization of Computations at Numerical Solution of Boundary Value Problems

The paper represents a new robust multigrid technique for solving boundary value problems in black box manner. To overcome problem of robustness, the technique was based on incorporating the adaptation of boundary value problems to numerical methods, control volume discretisation and a new multigrid solver into a united computational algorithm. Special multiple coarse grid correction strategy makes it possible to obtain problem-independent transfer operators. As a result, the most of the modes are approximated on coarse grids in order to ensure the problem of smoothing on the finest grid to be the least demanding. Detailed description of the robust multigrid technique and examples of application for solving benchmark problems are given in the paper.