Hydrodynamic interactions in long chain polymers: Application of the Chebyshev polynomial approximation in stochastic simulations

We have simulated Brownian bead-spring chains of up to 125 units with fluct uating hydrodynamic and excluded volume interactions using the Chebyshev po lynomial approximation proposed by Fixman [Macromolecules 19, 1204 (1986)] for the square root of the diffusion tensor. We have developed a fast metho d to continuously determine the validity of the eigenvalue range used in th e polynomial approximation, and demonstrated how this range may be quickly updated when necessary. We have also developed a weak first order semiimpli cit time integration scheme which offers increased stability in the presenc e of steep excluded volume potentials. The full algorithm scales roughly as O(N-2.25) and offers substantial computational savings over the standard C holesky decomposition. The above algorithm was used to obtain scaling expon ents for various static and zero shear rate dynamical properties, which are found to be consistent with theoretical and/or experimental predictions. ( C) 2000 American Institute of Physics. [S0021-9606(00)51431-7].