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Figure 3. Running time of hybrid MPI and OpenMP application
for computing of SHA and LSC. (a) broadcast time of
EGM2008 and the EGM2008-derived geoid heights, (b)
runtime for SHA of EGM2008, (c) runtime to find optimum
correlation length using LSC fitting, and (d) total computation
time.
As results, the broadcast time of EGM2008 and the EGM2008-
derived geoid heights needed approximately 4 seconds at 1
node (2 processors) and approximately 18 seconds for
maximum node (32 processors). The share (ratio) of broadcast
time in total computation time showed almost 096. This means
that although it has almost no influence upon total computation
time, it increased linearly depending on the number of nodes.
For SHA, the calculations were possible with approximately
3.6% of 1 processor. And LSC fitting was possible to be
calculated with approximately 3.8% of 1 processor. The total
computation time was approximately 6 hours and 40 minutes (0
node) and approximately 15 minutes (maximum node). This is
similar to the result of SHA research using supercomputer,
which means parallization modeling for SHA and LSC fitting
suggested by this paper is well executed in low-performance
cluster system (Xiao and lu, 2007).
6. CONCLUSION
In this paper, we proposed spherical harmonic analysis used to
evaluate suitability of GGMs and hybrid MP and OpenMP
approach to reduce data processing time for least-squares
collocation fitting.
Hybrid implementation using parallelization modeling showed
more advanced result in calculation speed than serial
implementation. Moreover, cluster system with low-
performance not high-performance computing (HPC) like
supercomputer performed SHA and LSC fitting more effectively.
7. REFERENCES
Bae, T.S., Lee, J., Kwon, J.H. and Hong, C.K., 2011. Update of
the precision geoid determination in Korea. Geophysical
Prospecting, 60(3). pp. 555-571.
Chandler, G. and Merry, C., 2010, The South African geoid
2010: SAGEOIDIO. PositionIT, pp. 29-33.
Chapman, B., Jost, G. and Van der Pas, R., 2007. Using
OpenMP. The MIT Press, Boston. pp. 1-34.
Chorley, M.J. and Walker, D.W., 2010. Performance analysis of
a hybrid MPI/OpenMP application on multi-core clusters.
Journal of Computational Science 1, pp. 168-174.
Daho, S.A.B., Fairhead, J.D., Zeggai, A., Ghezali, B., Derkaoui,
A., Gourine, B. and Khelifa, S., 2008. New investigation on the
choice of the tailored geopotential model for Algeria. Journal of
Geodynamics, 45, pp. 154-162.
Darbeheshti, N., 2009. Modification of the least-squares
collocation method for non-stationary gravity field modelling.
Ph.D. thesis, Curtin University of Technology, Perth, Western
Australia
Dawod, G.M., Mohamed, H.F. and Ismail, S.S., 2010.
Evaluation and adaptation of the EGM2008 geopotential model
along the Northern Nile Valley, Egypt: Case Study. Journal of
Surveying Engineering, 136, pp. 36-40.
Forsberg, R., Tscherning, C.C. and Knudsen, P., 2003. An
overview manual of the GRAVSOFT geodetic gravity field
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