# Physics:P3M

**Particle–Particle–Particle–Mesh** (**P ^{3}M**) is a Fourier-based Ewald summation method

^{[1]}

^{[2]}to calculate potentials in N-body simulations.

^{[3]}

^{[4]}

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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 P^{3}M 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

- ↑ "Fourier-based Ewald Summation Methods (Web Version)". http://people.ee.duke.edu/~ayt/ewaldpaper/node15.html#SECTION00041000000000000000. Retrieved 2009-03-01.
- ↑
*Fourier-based Ewald Summation Methods (Published Version)*. doi:10.1016/0010-4655(96)00016-1. Bibcode: 1996CoPhC..95...73T. - ↑
*P3M3DP-the three-dimensional periodic particle-particle/particle-mesh program*. doi:10.1016/S0010-4655(84)82783-6. Bibcode: 1984CoPhC..35..618E. - ↑ "How to mesh up Ewald sums. II. An accurate error estimate for the particle–particle–particle-mesh algorithm". http://link.aip.org/link/?JCPSA6/109/7694/1. Retrieved 2009-03-01.
- ↑ "N-body simulations, section P3M and PM Tree Codes". http://www.scholarpedia.org/article/N-body_simulations#P3M_and_PM-Tree_codes. Retrieved 2009-03-01.

## Further reading

- Roger W. Hockney; James W. Eastwood (1988). "Particle-Particle-Particle-Mesh (P
^{3}M) Algorithms".*Computer simulation using particles*. CRC Press. pp. 267–304. ISBN 9780852743928. https://archive.org/details/computersimulati0000hock/page/267. - R. J. Sadus. "Particle-Particle and Particle-Mesh (PPPM) Methods".
*Molecular Simulation of Fluids*. Amsterdam: Elsevier Science. pp. 162–169. - Randall Splinter & S. Bhavsar (1997). "Applications of N-body Methods to Studies of Large Scale Structure Formation in the Universe".
*Some New Directions in Science on Computers*. World Scientific Publishing Co.. pp. 286–287. ISBN 981-02-3196-2.

Original source: https://en.wikipedia.org/wiki/ P3M.
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