

Michael Bader : Total Semicoarsening: Multigrid Methods for Convection Problems
Current multigrid methods that are used to solve convection problems usually use
techniques where either the coarse grids (includes AMG methods) or the smoothers are adapted to the
flow field. Both approaches can make the parallel implementation of the resulting methods a difficult
job. In this talk, we would like to present a method that retains the rectangular structure of
the coarse grids, but still uses interpolation and coarse grid operators that are problem or
matrixdependent.
The respective multigrid method is based on total semicoarsening. Total semicoarsening is a coarsening
technique that places the coarse grid points not only on the corners of the course grid cells, but
also on the faces. The resolution of the course grid points on the faces may be that of the
finest grid, but can also be chosen such that a certain balance between the influence of convection
and diffusion is achieved.
For the 2D and 3D case, we will discuss data structures required for using total semicoarsening grids,
and techniques to construct the interpolation and coarse grid operators. Numerical results will
be given for some test problems.
