Numerical Solution of Polymer Self-Consistent Field Theory

We propose efficient pseudospectral numerical schemes for solving the self-consistent, mean-field equations for inhomogeneous polymers. In particular, we introduce a robust class of semi-implicit methods that employ asymptotic small scale information about the nonlocal density operators. The relaxation schemes are further embedded in a multilevel strategy resulting in a method that can cut down the computational cost by an order of magnitude. Three illustrative problems are used to test the numerical methods: (i) the problem of finding the mean chemical potential field for a prescribed inhomogeneous density of homopolymers; (ii) an incompressible melt blend of two chemically distinct homopolymers; and (iii) an incompressible melt of AB diblock copolymers.