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The efficiency was compared by adjusting the number of sub-areas and performing calculations using the same number of time-steps on the same quad-core personal computer (PC) (2,000 time-steps in this case). The speedup S is defined as S=Ts/Tp, where Ts is the execution time of the sequential algorithm, and Tp is the execution time of the parallel algorithm. The speedup value and the sub-area numbers represent the single-zone efficiency. This means that the efficiency is calculated in a single processor (where each sub-area has its own processor). The test results for the sub-areas are presented in Table 6. Table 7 summarizes the differences between the different calculation methods.

Table 6

Comparing the calculation time and speedup in sub-areas

Sub-area NCalculation time (s)Speedup SSingle-zone efficiency S/N
2,489 
1,248 1.99 0.995 
883 2.82 0.705 
996 2.50 0.417 
Sub-area NCalculation time (s)Speedup SSingle-zone efficiency S/N
2,489 
1,248 1.99 0.995 
883 2.82 0.705 
996 2.50 0.417 
Table 7

Calculation results with different calculation approaches (t= 0.5)

XActual (10–3)Proposed scheme (10–3)Literature (Zhang & Shen 2002) (10–3)This study (10–3)Diff (%)
0.1 2.2224 2.3654 2.3409 2.3731 6.78 
0.3 5.8184 6.1928 6.1266 6.2088 6.71 
0.5 7.1919 7.6547 7.5670 7.6623 6.54 
0.7 5.8184 6.1928 6.1266 6.2088 6.71 
0.9 2.2224 2.3654 2.3409 2.3731 6.78 
XActual (10–3)Proposed scheme (10–3)Literature (Zhang & Shen 2002) (10–3)This study (10–3)Diff (%)
0.1 2.2224 2.3654 2.3409 2.3731 6.78 
0.3 5.8184 6.1928 6.1266 6.2088 6.71 
0.5 7.1919 7.6547 7.5670 7.6623 6.54 
0.7 5.8184 6.1928 6.1266 6.2088 6.71 
0.9 2.2224 2.3654 2.3409 2.3731 6.78 

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