Efficient order-adaptive methods for polymer self-consistent field theory

Abstract

A highly accurate and memory-efficient approach for the solution of polymer self-consistent field theory (SCFT) is proposed. The central idea is to combine spectral integration in the polymer chain contour variable with a spectral deferred correction technique to solve the SCFT modified diffusion equations with arbitrarily high order of accuracy. The result is a robust method that achieves high accuracy with a minimal number of discrete contour nodes, which translates into vastly reduced memory requirements and increased computational efficiency. In particular, this spectral deferred correction method enables the computation of strongly segregated systems with unprecedented accuracy. Moreover, the framework of deferred corrections allows us to adaptively increase the order of accuracy during the outer saddle point iteration to drastically reduce the cost of a SCFT computation.