An unconditionally gradient stable numerical method for the Ohta-Kawasaki model

Junseok Kim; Jaemin Shin

doi:10.4134/BKMS.b150980

An unconditionally gradient stable numerical method for the Ohta-Kawasaki model

Junseok Kim, Jaemin Shin

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We present a finite difference method for solving the Ohta- Kawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the Ohta- Kawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.

Original language	English
Pages (from-to)	145-158
Number of pages	14
Journal	Bulletin of the Korean Mathematical Society
Volume	54
Issue number	1
DOIs	https://doi.org/10.4134/BKMS.b150980
Publication status	Published - 2017

Bibliographical note

Funding Information:
The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827).

Publisher Copyright:
© 2017 Korean Mathematical Society.

Keywords

Block-copolymer
Ohta-kawasaki model
Solvability
Unconditionally gradient stability

ASJC Scopus subject areas

General Mathematics

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10.4134/BKMS.b150980

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title = "An unconditionally gradient stable numerical method for the Ohta-Kawasaki model",

abstract = "We present a finite difference method for solving the Ohta- Kawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the Ohta- Kawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.",

keywords = "Block-copolymer, Ohta-kawasaki model, Solvability, Unconditionally gradient stability",

author = "Junseok Kim and Jaemin Shin",

note = "Funding Information: The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). Publisher Copyright: {\textcopyright} 2017 Korean Mathematical Society.",

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AU - Shin, Jaemin

N1 - Funding Information: The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2014R1A2A2A01003683). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2009-0093827). Publisher Copyright: © 2017 Korean Mathematical Society.

PY - 2017

Y1 - 2017

N2 - We present a finite difference method for solving the Ohta- Kawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the Ohta- Kawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.

AB - We present a finite difference method for solving the Ohta- Kawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the Ohta- Kawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.

KW - Block-copolymer

KW - Ohta-kawasaki model

KW - Solvability

KW - Unconditionally gradient stability

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SP - 145

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JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

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ER -

An unconditionally gradient stable numerical method for the Ohta-Kawasaki model

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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