  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.
