# 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

arXiv: https://arxiv.org/abs/2010.15271 · HTML: https://mlsanity.com/paper/2010.15271/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 2 of 2)

- [Bayesian model calibration for block copolymer self-assembly: Likelihood-free inference and expected information gain computation via measure transport](https://mlsanity.com/paper/2206.11343/) (2022)
- [Residual-Based Error Corrector Operator to Enhance Accuracy and Reliability of Neural Operator Surrogates of Nonlinear Variational Boundary-Value Problems](https://mlsanity.com/paper/2306.12047/) (2023)

## Abstract (arXiv)

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.