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

DOI10.1137/20M1378119zbMath1480.49027arXiv2010.15271OpenAlexW3095693631MaRDI QIDQ5022488

Lianghao Cao, Omar Ghattas, J. Tinsley Oden

Publication date: 19 January 2022

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.15271

zbMATH Keywords

Newton methodOhta-Kawasaki modelHessian approximationblock copolymernonlocal Cahn-Hilliard modeldirected self-assembly

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Newton-type methods (49M15) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21)

Related Items (4)

Bayesian model calibration for diblock copolymer thin film self-assembly using power spectrum of microscopy data and machine learning surrogate ⋮ Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm ⋮ Residual-based error corrector operator to enhance accuracy and reliability of neural operator surrogates of nonlinear variational boundary-value problems ⋮ A scalable framework for multi-objective PDE-constrained design of building insulation under uncertainty

Uses Software

• FEniCS
• hIPPYlib

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compatibility conditions for Dirichlet and Neumann problems of Poisson's equation on a rectangle
• Calculus on normed vector spaces
• A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation
• On energy minimizers of the diblock copolymer problem
• On the derivation of a density functional theory for microphase separation of diblock copolymers
• Elliptic partial differential equations of second order
• A note on preconditioner for the Ohta-Kawasaki equation
• Emergence of nontrivial minimizers for the three-dimensional Ohta-Kawasaki energy
• Sufficient conditions for global minimality of metastable states in a class of non-convex functionals: a simple approach via quadratic lower bounds
• Automating the finite element method
• On global minimizers for a variational problem with long-range interactions
• On the Phase Diagram for Microphase Separation of Diblock Copolymers: An Approach via a Nonlocal Cahn–Hilliard Functional
• The Global Dynamics of Discrete Semilinear Parabolic Equations
• Matching Schur Complement Approximations for Certain Saddle-Point Systems
• The Equilibrium Theory of Inhomogeneous Polymers
• On the Finite Element Solution of the Pure Neumann Problem
• Validation of the bifurcation diagram in the 2D Ohta–Kawasaki problem
• A Preconditioner for the Ohta--Kawasaki Equation
• 2D Phase Diagram for Minimizers of a Cahn–Hilliard Functional with Long-Range Interactions
• A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion

This page was built for publication: 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