P3M explained

Particle–Particle–Particle–Mesh (P³M) is a Fourier-based Ewald summation method^{[1] [2]} to calculate potentials in N-body simulations.^{[3] [4] [5]}

The potential could be the electrostatic potential among N point charges i.e. molecular dynamics, the gravitational potential among N gas particles in e.g. smoothed particle hydrodynamics, or any other useful function. It is based on the particle mesh method, where particles are interpolated onto a grid, and the potential is solved for this grid (e.g. by solving the discrete Poisson equation). This interpolation introduces errors in the force calculation, particularly for particles that are close together. Essentially, the particles are forced to have a lower spatial resolution during the force calculation. The P³M algorithm attempts to remedy this by calculating the potential through a direct sum for particles that are close, and through the particle mesh method for particles that are separated by some distance.

References

1. Web site: Fourier-based Ewald Summation Methods (Web Version). https://web.archive.org/web/20090821085337/http://people.ee.duke.edu/~ayt/ewaldpaper/node15.html#SECTION00041000000000000000. dead. 2009-08-21. 2009-03-01.
2. 10.1016/0010-4655(96)00016-1. Fourier-based Ewald Summation Methods (Published Version) . 1996CoPhC..95...73T . Toukmaji . Abdulnour Y. . Board . John A. . Computer Physics Communications . 1996 . 95 . 2 . 73 .
3. 10.1016/S0010-4655(84)82783-6. P3M3DP-the three-dimensional periodic particle-particle/particle-mesh program. 1984. 1984CoPhC..35..618E . Eastwood. J.W.. Hockney. R.W.. Lawrence. D.N.. Computer Physics Communications. 35.
4. Web site: How to mesh up Ewald sums. II. An accurate error estimate for the particle–particle–particle-mesh algorithm . 2009-03-01.
5. N-body simulations, section P3M and PM Tree Codes. Scholarpedia . 20 May 2008 . 3 . 5 . 3930 . 10.4249/scholarpedia.3930 . free . Trenti . Michele . Hut . Piet . 2008SchpJ...3.3930T .

Further reading

• Book: Computer simulation using particles. Roger W. Hockney. James W. Eastwood. Particle-Particle-Particle-Mesh (P³M) Algorithms. 267 - 304. CRC Press. 1988. 9780852743928. https://archive.org/details/computersimulati0000hock/page/267.
• Book: Molecular Simulation of Fluids. 1999. limited. R. J. Sadus. 162 - 169. Elsevier Science. Amsterdam. Particle-Particle and Particle-Mesh (PPPM) Methods. 9780444823052 .
• Book: Some New Directions in Science on Computers. Gyan Bhanot . Shiyi Chen . Philip Seiden . 286 - 287. Applications of N-body Methods to Studies of Large Scale Structure Formation in the Universe. Randall Splinter . S. Bhavsar . amp . World Scientific Publishing Co.. 1997. 981-02-3196-2.