Particle mesh Ewald method for acceleration of solving pairwise interaction by long range forces (electrostatic, gravitational ... ) seem to be very general and easy to implement. The basic principle is well described in many sources.

What is harder to find is how exactly split the potential kernel ( say $V(r)=1/r = V_{SR}(r) + V_{LR}$ ) into short range and long range part. In other words:

  • How should I choose short range part $V_{SR}(r)$ so that the long range part $V_{LR} = V(r) - V_{SR}(r)$ is easy to express in Fourier space as some analytic function fast to evaluate numerically.
  • It would be nice to use similar splitting in all dimension ( 1D, 2D, 3D ).

e.g. somewhere I read that often is used Yukawa-like potential $V_{SR} = \exp(-\beta r )/r$ or Gaussian like damping $V_{SR} = \exp(-\beta r^2 )/r$.

But how to evaluate Fourier transform of long range $V_{LR}(r)$ efficintly in such case? Or is there any better choice of $V_{SR}$.


Check out:

Nijboer, B. R. A., & De Wette, F. W. (1957). On the calculation of lattice sums. Physica, 23(1-5), 309–321. doi:10.1016/S0031-8914(57)92124-9

There they make the case for using a splitting based on the incomplete Gamma function. That splitting generalizes the choice of the error function to arbitrary dimensions.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.