A preconditioner for the Ohta-Kawasaki equation

Patrick E. Farrell, John Pearson

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.
Original languageEnglish
Pages (from-to)217-225
Number of pages9
JournalSIAM Journal on Matrix Analysis and Applications
Issue number1
Publication statusPublished - 21 Mar 2017


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