Benchmarking and scalability

DFTB+ has an internal timer for various significant parts of its calculations. This can be enabled by adding the following option to the input:

Options {
  TimingVerbosity = 2

This will activate the timers for the most significant stages of a calculation. Higher values increase the verbosity of timing, while a value of -1 activates all available timers.

The typical output of running the code with timers enabled for a serial calculation will end with lines that look something like

DFTB+ running times                          cpu [s]             wall clock [s]
Pre-SCC initialisation                 +     3.46  (  5.8%)      3.45  (  5.8%)
SCC                                    +    47.34  ( 79.6%)     47.34  ( 79.6%)
  Diagonalisation                           44.79  ( 75.3%)     44.79  ( 75.3%)
  Density matrix creation                    2.21  (  3.7%)      2.21  (  3.7%)
Post-SCC processing                    +     8.68  ( 14.6%)      8.68  ( 14.6%)
  Energy-density matrix creation             0.55  (  0.9%)      0.55  (  0.9%)
  Force calculation                          7.74  ( 13.0%)      7.74  ( 13.0%)
  Stress calculation                         0.94  (  1.6%)      0.94  (  1.6%)
Missing                                +     0.00  (  0.0%)      0.00  (  0.0%)
Total                                  =    59.48  (100.0%)     59.47  (100.0%)

This shows the computing time (cpu) and real time (wall clock) times of major parts of the calculation.

An alternative method to obtain total times is by using the built-in shell command time when running the DFTB+ binary

time dftb+ > output

In the above example, at the termination of the code timings will be printed:

real    0m59.518s
user    0m59.430s
sys     0m0.092s

More advanced timing is possible by using profiling tools such as gprof.


Shared memory parallelism

The strong scaling for the OpenMP parallel code for some example inputs is shown here

Strong scaling for some SiC supercells.

These results were calculated on an old Xeon workstation (E5607 @ 2.27GHz) and are a self-consistent calculation of forces for different sized SiC supercells with 1 k-point and s and p shells of orbitals on the atoms. Timings and speed-ups come from data produced from the code’s reported total wall clock time.

There are several points to note

  1. The parallel scalability improves for the larger problems, going from ~68% to ~79% on moving from 512 atoms to 1728. This is a common feature, that larger problems give sufficient material for parallelism to work better.
  2. The gain in throughput for these particular problems is around a factor of 2 when using 4 processors, and raises to around 3 on 8 processors for the largest problem.
  3. From Amdhal’s law we can estimate the saturating limits for large numbers of processors as ~3.1 and ~4.8 for the smallest and largest problems respectively. This implies that there is not much value in using more than ~4 processors for the smallest calculation, since this has already gained around 2/3 of its theoretical maximum speed up. Adding a 5th or 6th processor will only improve performance by ~5% each, so is probably a waste of resources. Similarly for the largest calculation in this example, 6 processors gives around a factor of 3 speed up compared to serial operation, but adding 7th processors will only speed the calculation up by ~6%.
  4. The experimental data does not align exactly with the Amdahl curves, this could be due to competing processes taking resources (this is a shared memory machine with other jobs running) or the problem may run anomalously well for a particular number of processes. In this example 4 processors consistently ran slightly better, perhaps due to the cache sizes on this machine allowing the problem to be stored higher in the memory hierarchy for 4 processors compared to 3 (thus saving some page fetching).
  5. The weak scaling (increasing the number of processors proportional to the number of atoms) shows an approximately \(O(N^2)\) growth in time. A serial solution of these problems would increase as \(O(N^3)\) in the number of atoms.
  6. These timings are for this specific hardware and these particular problems, so you should test the case you are interested in before deciding on a suitable choice of parallel resources.

Weak scaling from the same data set is shown here

Weak scaling for some SiC supercells.

Distributed memory parallelism

This section coming soon!

Topics to be discussed:

  • Parallel scaling of simple examples.
  • Parallel efficiency.
  • Use of the Groups keyword in DFTB+ to improve scaling and efficiency for calculations with spin polarisation and/or k-points.
  • Effects of latency on code performance.