Are some N-body algorithms intrinsically less collisional than others?

• Published in: The Astrophysical journal Vol. 349; no. 2; pp. 562 - 569
• Main Authors: HERNQUIST, L, BARNES, J. E
• Format: Journal Article
• Language: English
• Published: Chicago, IL University of Chicago Press 01.02.1990
• Subjects: ALGORITHMS; Astronomy; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY; Earth, ocean, space; Exact sciences and technology; Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations; MANY-BODY PROBLEM; MATHEMATICAL LOGIC; MATHEMATICAL MODELS; MOTION; Observation and data reduction techniques. Computer modeling and simulation; PHYSICAL PROPERTIES 640102 > Astrophysics & Cosmology > Stars & Quasi-Stellar, Radio & X-Ray Sources; SPHERICAL HARMONICS; STARS; TESTING; Spherical harmonic; N body system; Numerical method; Numerical algorithmics; Direct summation; Hierarchical tree method; Stellar dynamics; Self gravitating system
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1086/168343

Empirical tests are used to measure relaxation rates in direct summation, hierarchical tree, and spherical harmonic N-body codes. We find that these methods suffer from comparable levels of relaxation for the same particle number and effective spatial resolution. This conclusion is counter to the wide-spread belief that expansion techniques are intrinsically less collisional than other methods. In fact, any algorithm which represents the density field using discrete particles will be subject to fluctuations in the potential, resulting in departures from the mean-field limit. Given appropriate resources, direct summation and hierarchical tree methods are valid approaches for simulating collisionless systems. The suitability of a given technique for studying collisionless processes is determined only by considerations of efficiency. 42 refs.