论文标题
全球收敛的修改牛顿方法，用于直接最小化Ohta-Kawasaki能量，并将其应用于二嵌段共聚物的定向自组装
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
论文作者
论文摘要
我们提出了一个快速稳固的方案，用于直接最小化Ohta-kawasaki能量，该能量表征了二嵌段共聚物熔体的微相分离。该方案采用线条搜索采用了全球收敛的修改牛顿方法，该方法被证明是质量保守，能量降级，渐近上四次收敛，并且比常用的梯度流动方法高三个数量级。分析了最小化器的规律性和一阶条件。提供了基于新型聚合物 - 基底相互作用模型和提出的方案的二嵌段共聚物熔体的定向自组装的数值研究。
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.
