Error Analysis of the GRAPE1 SpecialPurpose NBody Machine
Abstract
We discuss the numerical accuracy of GRAPE1, a specialpurpose computer for astrophysical Nbody calculations. The word length is the primary factor that determines the construction cost of such a specialpurpose computer. Regarding GRAPE1, we adopted the minimal word length with which we can obtain physically correct results. We used 16bit fixedpoint numbers for the positions of particles, 48bit fixedpoint numbers for the accumulation of force, and 8bit floatingpoint numbers for all other force calculations. The theoretical accuracy of the force calculated by GRAPE1 is ~ 0.4% for a homogeneous sphere with a softening parameter of the order of the average interparticle distance, independent of the number of particles, except for very small N (such as N <~ 100). The integration error for a typical particle caused by this roundoff error scales as a twobody relaxation effect, and is roughly 10100 times smaller than the relaxation effect itself. This implies that the numerical accuracy of GRAPE1 is sufficient for collisionless calculations, since twobody relaxation dominates the numerical error of collisionless Nbody calculations. The results of calculations on the GRAPE1 system support our theoretical estimate.
 Publication:

Publications of the Astronomical Society of Japan
 Pub Date:
 October 1990
 Bibcode:
 1990PASJ...42..717M
 Keywords:

 COLLISIONLESS SYSTEMS;
 NUMERICAL SIMULATION;
 SPECIALPURPOSE COMPUTER;
 STELLAR DYNAMICS