Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions

Jan Bouwe Van Den Berg, J. F. Williams

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Abstract

In this paper we develop a symmetry preserving method for the rigorous computation of stationary states of the Ohta-Kawasaki partial differential equation in three space dimensions. By preserving the relevant symmetries we achieve an enormous reduction in computational cost. This makes it feasible to construct computer-assisted proofs of complex three-dimensional structures. In particular, we provide the first existence proofs for both the double gyroid and body centered cubic packed sphere solutions to this problem.

Original languageEnglish
Pages (from-to)131-158
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume51
Issue number1
Early online date29 Jan 2019
DOIs
Publication statusPublished - Jan 2019

Keywords

  • 3D periodic structures
  • Computer-assisted proof
  • Otha-kawasaki problem
  • Partial differential equation
  • Symmetry preservation

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