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)
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Official URL: http://dx.doi.org/10.1137/16M1065483 |
Abstract
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 |
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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 (https://ror.org/0439y7842) |
Depositing User: | John Pearson |
Date Deposited: | 20 Jan 2016 17:21 UTC |
Last Modified: | 04 Mar 2024 16:30 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/53812 (The current URI for this page, for reference purposes) |
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