Parallelization issues

pw.x can run in principle on any number of processors (up to maxproc, presently fixed at 128 in PW/para.f90). The N_p processors can be divided into N_pk pools of N_pr processors, N_p = N_pk*N_pr . The k-points are divided across N_pk pools (``k-point parallelization''), while both R- and G-space grids are divided across the N<sub>pr</sub> processors of each pool (``PW parallelization''). A third level of parallelization, on the number of bands, is currently confined to the calculation of a few quantities that would not be parallelized at all otherwise. A fourth level of parallelization, on the number of NEB images, is available for NEB calculation only.

The effectiveness of parallelization depends on the size and type of the system and on a judicious choice of the N_pk and N_pr :

• k-point parallelization is very effective if N_pk is a divisor of the number of k-points (linear speedup guaranteed), but it does not reduce the amount of memory per processor taken by the calculation. As a consequence, large systems may not fit into memory. The same applies to parallelization over NEB images.
• PW parallelization works well if N_pr is a divisor of both dimensions along the z axis of the FFT grids, N₃ and Nr₃ (which may coincide). It does not scale so well as k-point parallelization, but it reduces both CPU time AND memory (the latter almost linearly).
• Optimal serial performances are achieved when the data are as much as possible kept into the cache. As a side effect, one can achieve better than linear scaling with the number of processors, thanks to the increase in serial speed coming from the reduction of data size (making it easier for the machine to keep data in the cache).

Note that for each system there is an optimal range of number of processors on which to run the job. A too large number of processors will yield performance degradation, or may cause the parallelization algorithm to fail in distributing properly R- and G-space grids.

Note also that Beowulf-style machines (PC clusters) may have disappointing parallelization performances unless they have a decent communication hardware (at least Gigabit ethernet). Do not expect good scaling with cheap hardware: plane-wave calculations are not at all an "embarrassing parallel" problem. Note that multiprocessor motherboards for Intel Pentium CPUs typically have just one memory bus for all processors. This dramatically slows down any code doing massive access to memory (as most codes in the Quantum-ESPRESSO package do) that runs on processors of the same motherboard.