Measuring relative performance improvements is not as straightforward as measuring the increase in peak performance of the fastest supercomputers because the scientific focus changes over the years. One has to find a problem that has been addressed on supercomputers over several decades and for which a performance measure can be defined that is independent of the particularities of the applied algorithms. One such problem, taken from computational magnetism, is the study of phase transitions and critical phenomena of the Ising model using Monte Carlo methods. The measure of relative performance is the effective number of independent Ising spin flips per CPU second. Three calculations performed in 1972, 1992, and 1995, respectively, are compared in the figure below with the speed of the computers they ran on (normalized to the machine in 1972). While the result may be different by an order of magnitude or two, depending on the problem one investigates, it is quite obvious that algorithmic and methodological improvements, not only result in best use of existing HPC resources, but actually multiply by several orders of magnitude the increase of in bare computer performance, as can be seen from the comparison to the development of peak performance (dashed line in the figure) of the fastest supercomputers in world. It is important to note, however, that the increase in computer speed remains a necessary condition for the algorithmic improvements, since the challenge to optimize a method on new architectures is what triggers algorithmic innovations in many cases.

Relative performance increase of Ising model simulations () compared the normalized speed of the computers (•) the simulations where executed on. The dashed line is a schematic of the increase in peak performance of the fastest supercomputers since 1972.