The Improved Robustness of Multigrid Elliptic Solvers Based on Multiple Semicoarsened Grids

Multigrid convergence rates degenerate on problems with stretched grids or anisotropic operators, unless one uses line or plane relaxation. For three-dimensional problems, only plane relaxation suffices, in general. While line and plane relaxation algorithms are efficient on sequential machines, they are quite awkward and inefficient on parallel machines. This paper presents a new multigrid algorithm, based on the use of multiple coarse grids, that eliminates the need for line or plane relaxation in anisotropic problems. This algorithm is developed, and the standard multigrid theory is extended to establish rapid convergence for this class of algorithms. The new algorithm uses only point relaxation, allowing easy and efficient parallel implementation, yet achieves robustness and convergence rates comparable to line and plane relaxation multigrid algorithms.The algorithm described here is a variant of Mulder’s multigrid algorithm [W. Mulder, J. Compact. Phys., 83 (1989), pp. 303–323] for hyperbolic problem...