 
Summary: NUMERICAL SOLUTION OF
POLYMER SELFCONSISTENT FIELD THEORY
HECTOR D. CENICEROS AND GLENN H. FREDRICKSON
MULTISCALE MODEL. SIMUL. c 2004 Society for Industrial and Applied Mathematics
Vol. 2, No. 3, pp. 452474
Abstract. We propose efficient pseudospectral numerical schemes for solving the selfconsistent,
meanfield equations for inhomogeneous polymers. In particular, we introduce a robust class of
semiimplicit 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.
Key words. diblock coplymers, incompressible melt blend, semiimplicit methods, multilevel
relaxation
AMS subject classifications. 65K10, 65Z05
DOI. 10.1137/030601338
1. Introduction. Fieldtheoretic models and approaches have proven to be very
useful in the study of inhomogeneous polymer and complex fluid phases. The appli
cation of such methods to dense phases, such as melts and concentrated solutions
