TY - GEN

T1 - 3D multigrid on partially ordered sets of grids

AU - Hemker, P.W.

AU - Koren, B.

AU - Noordmans, J.

PY - 1997

Y1 - 1997

N2 - 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
rectangular) grids.
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.

AB - 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
rectangular) grids.
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.

M3 - Conference contribution

T3 - VKI LS

BT - Proceedings of the 28th Computational Fluid Dynamics; 3-7 March 1997, Von Karman Institute for Fluid Dynamics Rhode-Saint Genese

A2 - Deconinck, H.

PB - Von Karman Institute for Fluid Dynamics

CY - Rhode-Saint-Genèse

ER -