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Short time observables

Table i compares the accuracy of force calculations achieved by the approximation schemes SAMM, FAMUSAMM/DC-1d and FAMUSAMM/linear, respectively. As accuracy measures the table displays the time averages tex2html_wrap_inline1417 and standard deviations tex2html_wrap_inline1427 of the rms errors tex2html_wrap_inline1419 given by eq. (7). These values have been extracted from trajectories of 0.4ps duration. In addition, the values for the average energy drifts tex2html_wrap_inline1433 as calculated from trajectories of tex2html_wrap_inline1479ps duration, are given.

  table440
Table: Approximation errors of force calculation for various methods as measured by the time average tex2html_wrap_inline1417 of the rms error, eq. (7), and by its standard deviation tex2html_wrap_inline1427; also given are average energy drifts tex2html_wrap_inline1433 reflecting algorithmic noise.

As can be seen, the average rms errors tex2html_wrap_inline1417 of force approximation are of about the same size (1%) for all three methods. The tex2html_wrap_inline1417 values of the FAMUSAMM algorithms are only slightly larger than that of SAMM. Thus, the multiple-time-step extrapolation procedures do not seem to sizably reduce the quality of force approximation achieved by SAMM. In contrast, as shown in ref. [19], cutoff methods exhibit errors tex2html_wrap_inline1417 which are larger by at least a factor of ten. Thus, as far as the quality of force approximation is concerned, the FAMUSAMM procedures essentially preserve the advantageous properties of SAMM.

But considering the fluctuations tex2html_wrap_inline1427 of the error tex2html_wrap_inline1419, a distinct difference between SAMM and the FAMUSAMM schemes becomes apparent. Due to the application of the multiple-time-step extrapolation procedures, for FAMUSAMM the fluctuations tex2html_wrap_inline1427 are tenfold larger than for SAMM. Thus the question arises, whether the slightly larger values of tex2html_wrap_inline1417 and the drastically increased values of tex2html_wrap_inline1427 for the FAMUSAMM methods are accompanied by comparable increases of algorithmic noise.

Consideration of the associated values for the energy drifts in Table i reveals a slight increase for FAMUSAMM/DC-1d as compared to SAMM which is in line with the corresponding increase of tex2html_wrap_inline1417. In contrast, a dramatically enhanced algorithmic noise is apparent for the FAMUSAMM/linear approach although in that case tex2html_wrap_inline1417 is nearly as small as for SAMM. Hence, the superiority of the DC-1d scheme as compared to the linear extrapolation is actually preserved despite the fact, that in FAMUSAMM extrapolations are applied to local Taylor expansion coefficients representing approximated forces instead to explicitly calculated exact forces. Finally note, that the tex2html_wrap_inline1427 values are uncorrelated to the observed algorithmic noise; this finding underlines the validity of the respective arguments presented in refs. [16] and [20].


next up previous
Next: Long time observables Up: Results of quality assessment Previous: Results of quality assessment

Helmut Grubmueller
Wed Apr 30 15:40:09 MET DST 1997