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

Jan Bouwe Van Den Berg, J. F. Williams

Research output: Contribution to JournalArticleAcademicpeer-review

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

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Stationary States
Partial differential equations
Three-dimension
Computer-assisted Proof
Symmetry
Computing
Computational Cost
Costs
Partial differential equation
Three-dimensional

Keywords

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

Cite this

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Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions. / Van Den Berg, Jan Bouwe; Williams, J. F.

In: SIAM Journal on Mathematical Analysis, Vol. 51, No. 1, 01.2019, p. 131-158.

Research output: Contribution to JournalArticleAcademicpeer-review

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