# Speed-up

2d model :

 processors number algorithm RCB algorithm RIB algorithm RGB 1 56.5s 56.5s 56.5s 2 28.7s 28.88s 28.99s 4 14.75s 14.86s 15.5s 6 10.15s 10.13s 10.38s 8 8.23s 8.02s 8.61s 10 6.84s 6.94s 6.74s 12 5.92s 5.85s 6.05s 14 5.2s 5.52s 5.51s 16 4.81s 4.77s 4.94s
Computation time (1000 iterations)

It seems that there is not difference between the algorithms

3d model :

 processors number algorithm RCB algorithm RIB algorithm RGB 1 957s 957s 957s 2 464s 465s 784s 4 233.5s 238s 403s 6 156s 158s 192s 8 113.5s 119s 119s 10 88.5s 95.5s 97.5s 12 72.5s 76.5s 79.5s 14 62.5s 65.5s 66.5s 16 55s 57.5s 58s
Computation time (250 iterations)

There is a great difference with RGB algorithm. The computational time is  more important. The reason seems to be : With RGB algorithm, frontier is generated near wall of the profil. So, because of unstructured refined grid,  there is a lot of nodes in the frontier.

Comparaison between 2d and 3d models:

The 3D model has a better speedup than the 2D model. An hypothesis concerning this result is that the number of nodes inside a zone compared to the number of nodes of the frontier is greater in 3D thab in 2D.

Considering a 2D square and a 3D cube, the number of nodes for a side contining n+1 nodes are :

 3D 2D inside (n-1)**3 (n-1)**2 frontier 6n**2 4n

The ratio between the number of nodes on the zone's frontier and the nmber of nodes inside it can be calculated, and it can be observed that the 2D ratio is 4/6*(n-1) greater than the 3D ration. The hypothesis concerning the amount of data transfered seems good.