Formalisation of the multigrid computations (Q2452133)

Summary: The paper represents a robust multigrid algorithm for solving a large class of applied problems (from Poisson equation to Navier-Stokes equations) on the structured grids. The algorithm consists of the robust multigrid technique (variant of the geometric multigrid methods with the problem-independent transfer operators) and the smoothing procedure based on Gauss-Seidel iterations with block unknown ordering. Theoretical analysis and numerical experiments show that close-to-optimal convergence rate for many (non)linear problems is obtained with the same multigrid components. Proposed approach can be used in black box software.