  We propose a new preconditioner for the Ohta--Kawasaki equation, a nonlocal
Cahn--Hilliard equation that describes the evolution of diblock copolymer
melts. We devise a computable approximation to the inverse of the Schur
complement of the coupled second-order formulation via a matching strategy. The
preconditioner achieves mesh independence: as the mesh is refined, the number
of Krylov iterations required for its solution remains approximately constant.
In addition, the preconditioner is robust with respect to the interfacial
thickness parameter if a timestep criterion is satisfied. This enables the
highly resolved finite element simulation of three-dimensional diblock
copolymer melts with over one billion degrees of freedom.
