A globally convergent modified Newton method for the direct minimization of the Ohta-Kawasaki energy with application to the directed self-assembly of diblock copolymers

Abstract

We propose a fast and robust scheme for the direct minimization of the Ohta-Kawasaki energy that characterizes the microphase separation of diblock copolymer melts. The scheme employs a globally convergent modified Newton method with line search which is shown to be mass-conservative, energy-descending, asymptotically quadratically convergent, and three orders of magnitude more efficient than the commonly-used gradient flow approach. The regularity and the first-order condition of minimizers are analyzed. A numerical study of the chemical substrate guided directed self-assembly of diblock copolymer melts, based on a novel polymer-substrate interaction model and the proposed scheme, is provided.

References in corpus (1)

• Density Functional Theory for Block Copolymer Melts and Blends

Cited by in corpus (3)

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• Optimal design of chemoepitaxial guideposts for directed self-assembly of block copolymer systems using an inexact-Newton algorithm
• Analysis and discretization of the Ohta-Kawasaki equation with forcing and degenerate mobility