Farrell, Patrick E, Pearson, John W (2017) A preconditioner for the OhtaKawasaki equation. SIAM Journal on Matrix Analysis and Applications, 38 (1). pp. 217225. ISSN 08954798. EISSN 10957162. (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 OhtaKawasaki equation, a nonlocal CahnHilliard equation that describes the evolution of diblock copolymer melts. We devise a computable approximation to the inverse of the Schur complement of the coupled secondorder 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 threedimensional 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:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics 
Depositing User:  John Pearson 
Date Deposited:  20 Jan 2016 17:21 UTC 
Last Modified:  29 May 2019 16:54 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/53812 (The current URI for this page, for reference purposes) 
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