System-size scaling

As mentioned in chapter 7, there are several steps in the calculation which are not strictly ${\cal O}(N)$, such as the calculation of the structure factor, the calculation of the ion-ion interaction energy (by Ewald's method [175,176,177,178]) and possibly the calculation of the energy correction. All of these operations need only be performed once for each ionic configuration, and so do not contribute significantly to the total computational effort. However, there are a number of FFTs within the method which require an effort which scales as ${\cal O}(N \log_m N)$. To verify that these operations do not spoil the linear-scaling of the rest of the method, we plot the CPU time required per iteration in figure 9.8 and see that it is indeed linear with respect to system-size as required.

Figure 9.8: Variation of computational effort with system-size.