Sparse tensor-product fokker-planck-based methods for Nonlinear bead-spring chain models of dilute polymer solutions

In this paper we present a spectral method for the solution of a high-dimensional Fokker-Planck equation describing the evolution of the configuration probability density function for a dilute solution of idealized polymer chains. The numerical method draws on ideas found in the literature on sparse grids and allows solutions to be obtained at much lower cost, for comparable accuracy, than using a full tensor-product of one-dimensional basis functions. Numerical results for homogeneous shear flow serve to illustrate the attractive features of the new method.