Multigrid methods (MG) are known to be optimal solvers for elliptic
PDE's, i.e. they only require
Algebraic Multigrid methods (AMG) overcome this problem. These methods first employ a setup phase to create a hierarchy of meshes, transfer and coarse grid operators using with information from the matrix
While the parallelization of the solution phase is straightforward,
this is not true for the setup phase. Especially the classical
algorithm for the construction of the coarse grids is inherently
Different approaches to the parallelization have been proposed over the years. Some of them use the classical Ruge-Stüben coarsening scheme in the interior of each processor subdomain an a employ a special treatment at the boundaries to fix inconsistencies. Other algorithms employ parallel Maximal Independent Set techniques to create the coarse grid.
In our parallel coarsening scheme, the Coarse grid Classification (CGC) algorithm, we aim to keep the classical Ruge-Stüben coarsening scheme, which works excellent in the sequential case. Furthermore, we avoid inconsistencies at the subdomain boundaries instead of fixing them. We do so by first creating multiple candidate coarse grids on each processor subdomain. In a second stage, we assemble a consistent coarse grid, i.e. out of the candidate coarse grids we choose one coarse grid per processor subdomain such that they match at the interfaces.
The CGC coarsening algorithm is included in two software packages.
Singular phenomena and scaling in mathematical models
Project C2: Adaptive and robust multigrid methods for space time discretizations
|Development of CFD Code NaSt3DGP|
|High-Performance Parallel Computing|