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 the OhtaKawasaki 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 typically three orders of magnitude more efficient than the commonly used gradient flow approach. The regularity and the first-order condition of minimizers are carefully 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.