APRECONDITIONER FOR THE OHTA-KAWASAKI EQUATION

作者：Farrell Patrick E^*; Pearson John W

来源：SIAM Journal on Matrix Analysis and Applications, 2017, 38(1): 217-225.

DOI：10.1137/16M1065483

• Ohta-Kawasaki equation
• preconditioner
• Schur complement
• nonlocal Cahn-Hilliard equation

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 1 billion degrees of freedom.

• 出版日期2017