Test Case 2

The system simulated is a unit cell of Litharge (a-PbO), a total of 4 atoms. 108 k-points are used.

Table: Scaling of Test Case 2.

Test Case 2	Cores	Time (secs)	Speedup
VASP 5.2.2	144	2141.206	1
KPAR=2	288	1097.981	1.950
KPAR=3	432	766.196	2.794
KPAR=4	576	607.69	3.524
KPAR=6	864	410.018	5.222
KPAR=9	1296	278.585	7.686
KPAR=12	1728	215.757	9.924
KPAR=18	2592	150.177	14.258
KPAR=27	3888	105.563	20.284
KPAR=36	5184	87.569	24.452
KPAR=54	7776	65.332	32.774
KPAR=108	15552	41.055	52.154

Table () shows that the k-point parallelized code scales rather satisfactorily to 3888 cores, and at 1738 cores it is 7 times faster than the original code at the same number of cores (see Table ()).

Table: The optimal NPAR for the original code is 18, 18, 18, 36, 36, 36 and 36 for 144, 288, 432, 576, 864, 1296 and 1728 cores respectively. For the k-point parallelized code the optimal NPAR is 18 for any number of cores, provided one k-group consists of 144 cores.

Test Case 2	Cores	Time (secs)	Speedup
VASP 5.2.2	288	1530.244	1
KPAR=2	288	1097.981	1.394
VASP 5.2.2	432	1348.436	1
KPAR=3	432	766.196	1.76
VASP 5.2.2	576	1473.4	1
KPAR=4	576	607.69	2.425
VASP 5.2.2	864	1562.76	1
KPAR=6	864	410.018	3.811
VASP 5.2.2	1296	1899.499	1
KPAR=9	1296	278.585	6.818
VASP 5.2.2	1728	1532.32	1
KPAR=12	1728	215.757	7.1021

Figure 2: Speedup for Test Case 2 (where Speedup is taken to be 1 for 144 cores).