The monograph describes the theoretical foundations and practical aspects of the geometric multigrid methods. The main attention is paid to construction of the robust multigrid algorithm with the least number of the problem-dependent components for solving the (non)linear boundary value problems on the structured grids. The detailed description of the basic components, the convergence proof, the complexity and the parallelization are given. The monograph contains examples of the multigrid algorithms for solving the Navier-Stokes equations. It is shown the opportunity of solving a wide class of the applied problems by the unified multigrid method. The monograph is intended for senior students of the technical universities, graduate students and engineers. The book will be useful for the software developers for modeling of the physical processes in aviation and rocket engineering, plant and chemical engineering and other branches of the mechanical engineering.

robust multigrid, structured grids, boundary value problems, Navier-Stokes equations

Mathematical problems and theory of numerical methods