NPAC Technical Report SCCS-738
Application of Parallel Multigrid Methods to Unsteady Flow: A Performance Evaluation
Ammar Degani, Geoffrey Fox
Submitted September 15 1995
Abstract
The parallel multigrid time-accurate calculation of the unsteady incompressible
Navier-Stokes equations is carried out using both explicit and implicit schemes.
In the explicit solution method, a `lumped' scheme is employed at the coarsest
multigrid levels where all the processors solve the same problem. On the other
hand, in the implicit method, in which the equations are solved in a
fully-coupled mode, a `semi-distributive' scheme is used where the effective
number of active processors decreases logarithmically with each coarsening of
the mesh at the coarsest levels. Both V and W cycles are implemented in the
explicit method and the convergence rates and execution times are compared.
It is demonstrated that good speedups are obtained for the implicit scheme and
the slight degradation in parallel efficiency, relative to calculations
performed on the finest grid, is dominated by increased convergence rates.