Page 145 - Computational Fluid Dynamics for Engineers

4.5 Finite-Difference Methods for Elliptic Equations 131

Ih

Ah
Fig. 4.12. W-cycle on four
8/z level grids.

Fig. 4.13. FMV-cycle on
four level grids.

Another popular procedure is the so-called full multigrid V-cycle (FMV)
method described below. In this procedure, the calculations begin on the coars-
est grid which provides a good initial guess by interpolation for the next fine
grid. On this fine grid, the V-Cycle method is applied (see Fig. 4.13).

Full multigrid V-cycle (FMV) Method.
/
U ^ F M V / l ( U \ F / l )
h
2 /
2h
1. Initialize U>\ U \ ...; F , F ,...
Solve or relax on coarsest grid
jj4h = V4h + I*hu*h
U 4h <- MV 4 / l (U 4 / l ,F 4 / l )
V2h = jj2h + ^h^h
2 / l 2 / l 2 / l
\j2h ^_ MV (U ,F )

h
h
h
U h <-MV (U ,F )
On the finest grid, then use the following procedure
1. If f?h = coarsest grid, then go to 3.
1
ElseF 2 h = / / ^ ( F ^ - A f c U ' )
2h
V = 0
2 /
jjih <_ FMV 2 / l (U \F 2 / l )
2. Correct U^ = U' 1 + I^ hV 2h
h
h
h
3. U h <- MV (V , F ) n 2 times