I am looking into implementation of Ewald summation techniques for a number of point charges in periodic 3D space (i.e. a molecular simulation box with periodic boundary conditions). The “mainstream” Ewald-type techniques I know are:

  • original Ewald scheme
  • particle-mesh Ewald (PME)
  • smooth particle-mesh Ewald (SPME)

However, while I can find papers describing each of those, I have not been able to find a comprehensive article/white paper/technique note comparing their implementations and their CPU timings on a typical dense system (liquid, protein in solvent, whatever…). What resources do you know of on this topic?

  • 2
    $\begingroup$ Why not give it a go and just benchmark it? I know DLPOLY Classic implements Ewald and SPME. Run some of their test ensembles with both and see how it behaves and scales $\endgroup$ Sep 9 '12 at 4:56

I also unsuccessfully tried to look for such a paper in the past but below are some useful resources I've found. The only definitive answer I can give you is that traditional Ewald summation will be slower than a particle-mesh technique for any relevant system sizes (this is backed up in several of the references below).

Chapter 4.9 of the GROMACS user manual has some very nice discussion on their various implemenations of long-range electrostatics and appropriate references.

The LAMMPS documentation also has quite a few references and some bits of helpful discussion.

You can also try digging through the AMBER manual which uses a PME implementation but I haven't read any of this myself.

Also here you can find implementation details for the PPPM method in HOOMD (helpful if you're interested in GPGPU implementations).

I think the most relevant bit of discussion is probably this excerpt in the GROMACS manual:

The Particle-Particle Particle-Mesh methods of Hockney & Eastwood can also be applied in GROMACS for the treatment of long range electrostatic interactions [99]. Although the P3M method was the first efficient long-range electrostatics method for molecular simulation, the smooth PME (SPME) method has largely replaced P3M as the method of choice in atomistic simulations. One performance disadvantage of the original P3M method was that it required 3 3D-FFT back transforms to obtain the forces on the particles. But this is not required for P3M and the forces can be derived through analytical differentiation of the potential, as done in PME. The resulting method is termed P3M-AD. The only remaining difference between P3M-AD and PME is the optimization of the lattice Green influence function for error minimization that P3M uses. However, in 2012 it has been shown that the SPME influence function can be modified to obtain P3M [100]. This means that the advantage of error minimization in P3M-AD can be used at the same computational cost and with the same code as PME, just by adding a few lines to modify the influence function. However, at optimal parameter setting the effect of error minimization in P3M-AD is less than 10%. P3M-AD does show large accuracy gains with interlaced (also known as staggered) grids, but that is not supported in GROMACS (yet).

If you're really looking to dive in, you can look at the source code for these packages (I believe you need a license for AMBER) to see the actual implementations.


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.