Rt. Farouki et S. Hamaguchi, SPLINE APPROXIMATION OF EFFECTIVE POTENTIALS UNDER PERIODIC BOUNDARY-CONDITIONS, Journal of computational physics, 115(2), 1994, pp. 276-287
The use of spline functions to approximate the ''effective'' inter-par
ticle potentials that result from taking into account all image partic
les in periodic-boundary-condition Monte Carlo or molecular dynamics s
imulations is described. Such approximations are intrinsically very ''
smooth,'' easy to construct, relatively inexpensive to evaluate, and c
an provide a high degree of accuracy. The asymptotic properties of sys
tems governed by long-range interactions may thus be determined using
relatively small particle numbers. A number of implementation issues a
re discussed in detail, including the choice of end conditions, econom
ical storage of the spline coefficients, conversion to B-spline form,
and efficient evaluation procedures. Applied to the problem of locatin
g the melting temperature T-m of a Yukawa system by means of molecular
dynamics simulations, we observe values for T-m that are virtually in
dependent of the particle number N if the pair potential includes the
spline correction term and N greater than or similar to 250, whereas u
sing only the ''minimum image'' method gives T-m values that systemati
cally decrease and attain the asymptotic value only for N greater than
or similar to 5000. (C) 1994 Academic Press, Inc.