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A preconditioner for the Ohta-Kawasaki equation

Farrell, Patrick E, Pearson, John W (2017) A preconditioner for the Ohta-Kawasaki equation. SIAM Journal on Matrix Analysis and Applications, 38 (1). pp. 217-225. ISSN 0895-4798. E-ISSN 1095-7162. (doi:10.1137/16M1065483) (KAR id:53812)


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.

Item Type: Article
DOI/Identification number: 10.1137/16M1065483
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Q Science > QD Chemistry > QD473 Physical properties in relation to structure
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders: Engineering and Physical Sciences Research Council (
Depositing User: John Pearson
Date Deposited: 20 Jan 2016 17:21 UTC
Last Modified: 04 Mar 2024 16:30 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Pearson, John W.

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