Parallel Solution of 3D Ohta-Kawasaki Nonlocal Phase Field Model in FEniCS

Resumo

This study presents new results for the parallel solution of the 3D nonlocal Cahn-Hilliard equation
derived from the Ohta-Kawasaki free energy functional with adaptive time step control. 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 use three time-step controllers
with different properties: a simple Integral controller, a complete Proportional-Integral-Derivative controller, and
the PC11 predictive controller. We explore how different controllers affect the convergence of the nonlinear solver
for two values of the nonlocal parameter. The efficiency of the adaptive schemes for the nonlocal Cahn-Hilliard

equation is evaluated in terms of the number of time steps required for the complete simulation and the com-
putational effort measured by the required number of nonlinear and linear solver iterations. We show numerical

evidence of mass conservation and free energy decay for both nonlocal parameters.