4.10.3 Benchmarks

To test the parallel efficiency, the surface evolution was calculated for a sphere expanding at constant speed. The calculation was performed using 1, 2, 4, 8, and 16 cores of AMD Opteron 8435 processors clocking at $\SI {2.6}{\giga \hertz }$ . The corresponding average calculation times for a single time step and for different sphere diameters ${d}$ (measured in grid spacings) are listed together with the parallel efficiency in Table 4.4.

Table 4.4: Benchmarks for a time integration step of a sphere expanding with constant speed. The computation times as well as the parallel efficiency are given for varying sphere diameters ${{d}}$ and number of used CPUs.

$\parbox{\textwidth}{ \small \begin{tabular}{ S S[tabformat=2.1] S[ta... ...percent} & 51\,\si{\second} & 78.5\,\si{\percent}\\ \bottomrule \end{tabular}}$

According to Amdahl's law [9] the parallel efficiency decreases with the number of CPUs due to sequentially processed parts of the program. In case of 16 cores a parallel efficiency of approximately $\SI{78}{\percent}$ could be achieved except for the smallest sphere diameter ${d}=100$ . For smaller structures the overhead due to thread synchronization is more relevant, which results in a worse efficiency. Table 4.4 also shows the good scalability with surface size. If the diameter is multiplied by 10, the surface of the sphere is increased by a factor of 100, which is well reproduced by the listed runtimes.