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

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