T. Washio et Cw. Oosterlee, FLEXIBLE MULTIPLE SEMICOARSENING FOR 3-DIMENSIONAL SINGULARLY PERTURBED PROBLEMS, SIAM journal on scientific computing (Print), 19(5), 1998, pp. 1646-1666
We present robust parallel multigrid-based solvers for 3D scalar parti
al differential equations. The robustness is obtained by combining mul
tiple semicoarsening strategies, matrix-dependent transfer operators,
and a Krylov subspace acceleration. The basis for the 3D preconditione
r is a 2D method with multiple semicoarsened grids based on the MG-S m
ethod from [C. W. Oosterlee, Appl. Numer. Math., 19(1995), pp. 115-128
] and [T. Washio and C. W. Oosterlee, GMD Arbeitspapier 949, GMD, St.
Augustin, Germany, 1995]. The 2D method is generalized to three dimens
ions with a line smoother in the third dimension. The method based on
semicoarsening has been parallelized with the grid partitioning techni
que [J. Linden, B. Steckel, and K. Stuben, Parallel Comput., 7(1988),
pp. 461-475], [O. A. McBryan et al., Impact Comput. Sci. Engrg., 3(199
1), pp. 1-75] and is evaluated as a solver and as a preconditioner on
a MIMD machine. The robustness of the 3D method is shown for finite vo
lume and finite difference discretizations of 3D anisotropic diffusion
equations and convection-dominated convection-diffusion problems.