Test Case 1

The system simulated is a hydrogen defect in 32 atoms of palladium. It uses 10 k-points and the PBE exchange correlation functional ([27]-[28]).

Table: Scaling of Test Case 1.

Test Case 1	Cores	Time (secs)	Speedup
VASP 5.2.2	64	298.187	1
KPAR=2	128	159.982	1.863
KPAR=5	320	75.357	3.956
KPAR=10	640	47.795	6.239

Table () shows that the k-point parallelized code scales satisfactorily to 320 cores, where it is twice as fast as the original code at the same number of cores (see Table ()).

Table: The optimal NPAR for the original code is 4, 8, 32, and 32 for 64, 128, 320 and 640 cores respectively. For the k-point parallelized code the optimal NPAR is 4 for any number of cores, provided one k-group consists of 64 cores.

Test Case 1	Cores	Time (secs)	Speedup
VASP 5.2.2	128	206.517	1
KPAR=2	128	158.686	1.301
VASP 5.2.2	320	146.197	1
KPAR=5	320	75.201	1.944
VASP 5.2.2	640	147.606	1
KPAR=10	640	47.795	3.088

Figure 1: Speedup for Test Case 1 (where Speedup is taken to be 1 for 64 cores).