Fluent Inc., 10 Cavendish Court, Lebanon, NH, 03766

Abstract

Selective multigrid has higher order of interpolation and
prolongation operators in comparison with standard aggregative
multigrid. These properties provide better convergence rate for
selective multigrid but come at price of a longer setup phase.
A question what solver is faster can't be answered without direct
comparison of both solvers under a specified convergence criteria.

The selective multigrid has been implemented following
J.W.Ruge and K.Stueben's works. The standard coarsening
scheme was used and the direct
and standard interpolations were tried. The standard
interpolation is more exact but more expensive in time
and memory.

The convergence and running time of the selective multigrid were
compared with that of the Weiss et al's
aggregative multigrid. Both solvers were applied to a
test problem based on a diffusivity
equation and to a few matrices built from a pressure
equation for some CFD problems. Their performance is
analyzed based on reduction of
residuals by one and six order of magnitude.

References:

Stueben K.,
*An Introduction to Algebraic Multigrid*, pp. 413-532 in
Trottenberg U., Oosterlee C.W., and Schuller A., Multigrid, Academic
Press, 2001.

Weiss J.M, Maruszewski J.P, Smith W.A.,
*Implicit
Solution of the Navier-Stokes Equations
on Unstructured Meshes*, 13th
AIAA CFD Conference, June 1997, Paper 97-2103