RECENT DEVELOPMENT IN COMPUTATIONAL SCIENCE

ISCS 2011 Selected Papers Vol.2 Time Benchmarks for the OpenMP and GPU
Elapsed time (sec)
5
4
3
2
1
FFTW
CUFFT(DOUBLE)
CUFFT(SINGLE)
0.02
0.01
0
0 50 100
0
0 100 200 300 400
Transform Size (N^3)
Figure 8: The computational times with respect to the
various sizes for the CUFFT routine of 3D-FFT (GPU)
in M2.
Elapsed time (sec)
70
60
50
40
30
20
10
MPI + GPU
MPI(BLAS+FFTW)
MPI(CUBLAS+CUFFT)
MPI(CUBLAS+FFTW)
0
0 1 2 3 4 5 6
Num.of Processors
Figure 10: Conputational times (single CPMD iteration
in second) with respect to the number of MPI
threads for MPI+GPU (Tesla C1060) version. The
single MPI thread can access to a single GPU in M2.
Speed Up Factor
16
14
12
10
8
6
4
2
6
4
2
MPI + OpenMP
MPI
0
0 2 4 6
0
0 2 4 6 8 10 12 14 16
Num.of Processors
Figure 9: Parallelization efficiency for the MPI and
Hybrid versions for BaTiO3 system.
Elapsed time (sec)
35
30
25
20
15
10
5
0
6.30
5.09
20.0
33.9
2.35
16.6
2.08
21.0
Other
FFT
Matrix
8.70
2.02
4.45
2.23
FFTW+BLAS CUFFT+CUBLAS FFTW+CUBLAS
Figure 11: Conputational times (single CPMD iteration
in second) of MM, FFT, and others for BaTiO3
by MPI+ GPU (Tesla C1060) version (3MPI+3GPU).
GPU calculation for the MM (CUBLAS) is improved considerably, whereas the FFT by CUFFT
is more time-consuming than the FFTW, as expected from the result in Fig. 8.
4.3 MPI+OpenMP+GPU
In the experience which is encountered in the previous sections, the FFT by GPU cannot be carried
out so high performance. Taking into account this, the MPI+OpenMP+GPU (hybrid+GPU)
version is organized with the MPI (k point parallelization), the MM by GPU, the FFT by OpenMP
(6 threads in OpenMP), and other minor parallelization. This is tested in the magnetic system
(Fe/MgO/Fe) with M3 (4 threads in the MPI and 2 GPUs). The result with the CUDA Toolkit
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