Flexible Multiple Semicoarsening for Three-Dimensional Singularly Perturbed Problems

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Abstract
We present robust parallel multigrid-based solvers for 3D scalar partial differential equations. The robustness is obtained by combining multiple semicoarsening strategies, matrix-dependent transfer operators, and a Krylov subspace acceleration. The basis for the 3D preconditioner is a 2D method with multiple semicoarsened grids based on the MG-S method 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 dimensions with a line smoother in the third dimension. The method based on semicoarsening has been parallelized with the grid partitioning technique [J. Linden, B. Steckel, and K. Stüben, Parallel Comput., 7(1988), pp. 461--475], [O. A. McBryan et al., Impact Comput. Sci. Engrg., 3(1991), 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 volume and finite difference discretizations of 3D anisotropic diffusion equations and convection-dominated convection-diffusion problems.

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