In this paper we discuss different possibilities of using partially ordered sets
of grids in multigrid algorithms. Because, for a classical sequence of regular grids
the number of degrees of freedom grows nmch faster with the refinement level for
3D than for 2D, it is more difficult to find sufficiently effective relaxation procedures.
Therefore, we study the possibility of using different families of (regular
Semi-coarsening is one technique in which a partially ordered set of grids is
used. In this case still a unique fine-grid discrete problem is solved. On the other
hand, sparse grid techniques are more efficient if we compare the accuracy obtained
with the number of degrees of fre(Ylom used. However, in the latter case it is not
always feasible to identify an appropriate discrete equation that should be solved.
The different approaches are compared.
The relation between the different approaches is described by looking at hierarchical
ba.c;es and by considering full approximation (FAS). We show that in
some ca.c:;es the 3D situation is essentially more difficult than the 2D ease. We also
describe different rnultigrid strategies. Numerical results are given for a transonir:
Euler-flow over the ONERA M6-winp;.
Note: In essence, this papP.r will be publiRhecl in the Pror.c:edinp;s of the Fifth
European Multigrid Conference, BirkhauRer, BaHel.
|Title of host publication||Proceedings of the 28th Computational Fluid Dynamics; 3-7 March 1997, Von Karman Institute for Fluid Dynamics Rhode-Saint Genese|
|Place of Publication||Rhode-Saint-Genèse|
|Publisher||Von Karman Institute for Fluid Dynamics|
|Publication status||Published - 1997|