TELESCOPING FAST MULTIPOLE METHODS USING CHEBYSHEV ECONOMIZATION

Chebyshev polynomials of the first kind are applied to telescope both the far-field multipole expansions and the near-field Taylor series ex pansions used in solving large N-body problems via fast multipole meth ods. The technique is demonstrated for pairwise-additive, 1/r interpar ticle potentials in Cartesian coordinates, and a general Mathematica(R ) package is provided to derive the modified expansion coefficients sy mbolically. Accelerated convergence and more uniform error can be achi eved without additional computations during runtime. Hence the telesco ped series require fewer expansion terms for a given accuracy requirem ent, saving considerable computational expense over conventional fast multipole implementations. (C) 1995 Academic Press, Inc.