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

siam journal on scientific computing

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