  In this study, we evaluate the performance of feedback control-based time
step adaptivity schemes for the nonlocal Cahn-Hilliard equation derived from
the Ohta-Kawasaki free energy functional. The temporal adaptivity scheme is
recast under the linear feedback control theory equipped with an error
estimation that extrapolates the solution obtained from an energy-stable, fully
implicit time marching scheme. We test three time step controllers with
different properties: a simple Integral controller, a complete
Proportional-Integral-Derivative controller, and the PC11 predictive
controller. We assess the performance of the adaptive schemes for the nonlocal
Cahn-Hilliard equation in terms of the number of time steps required for the
complete simulation and the computational effort measured by the required
number of nonlinear and linear solver iterations. We also present numerical
evidence of mass conservation and free energy decay for simulations with the
three different time step controllers. The PC11 predictive controller is the
best in all three-dimensional test cases.
