AuthorsP. E. Farrell and J. W. Pearson
TitleA Preconditioner for the Ohta--Kawasaki Equation
AfilliationScientific Computing
Project(s)Center for Biomedical Computing (SFF)
StatusPublished
Publication TypeJournal Article
Year of Publication2017
JournalSIAM Journal on Matrix Analysis and Applications
Volume38
Number1
Pagination217-225
PublisherSIAM
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 1 billion degrees of freedom.


 

DOI10.1137/16M1065483
Citation Key25493