A Cartesian treecode for screened coulomb interactions

A treecode algorithm is presented for evaluating electrostatic potentials in a charged particle system undergoing screened Coulomb interactions in 3D. The method uses a far-field Taylor expansion in Cartesian coordinates to compute particle–cluster interactions. The Taylor coefficients are evaluated...

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Bibliographic Details
Published in:Journal of computational physics 2009-06, Vol.228 (10), p.3858-3868
Main Authors: Li, Peijun, Johnston, Hans, Krasny, Robert
Format: Article
Language:English
Subjects:
65Z05
82-08
Cartesian treecode
Computational techniques
Exact sciences and technology
Mathematical methods in physics
Particle–cluster interaction
Physics
Recurrence relations
Screened coulomb potential
Yukawa potential
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Summary:A treecode algorithm is presented for evaluating electrostatic potentials in a charged particle system undergoing screened Coulomb interactions in 3D. The method uses a far-field Taylor expansion in Cartesian coordinates to compute particle–cluster interactions. The Taylor coefficients are evaluated using new recurrence relations which permit efficient computation of high order approximations. Two types of clusters are considered, uniform cubes and adapted rectangular boxes. The treecode error, CPU time and memory usage are reported and compared with direct summation for randomly distributed particles inside a cube, on the surface of a sphere and on an 8-sphere configuration. For a given order of Taylor approximation, the treecode CPU time scales as O(NlogN) and the memory usage scales as O(N), where N is the number of particles. Results show that the treecode is well suited for non-homogeneous particle distributions as in the sphere and 8-sphere test cases.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2009.02.022