Vesicle shape deformation using a discontinuous Galerkin method

Tae Yeon Kim; Wen Jiang; Sung Mun Lee; Jeong Hoon Song; Eun Jae Park

Vesicle shape deformation using a discontinuous Galerkin method

Tae Yeon Kim, Wen Jiang, Sung Mun Lee, Jeong Hoon Song, Eun Jae Park

Department of Computational Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This work concerns the development of a finite-element algorithm to discretize the phase-field model for the shape deformation of a vesicle based on the idea of discontinuous Galerkin method. The phase-field model originated from minimization of Canham-Helfrich elastic bending energy involves fourth-order gradients and thus C¹-basis functions are required for the standard conforming Galerkin formulation. We introduce a relatively inexpensive, nonconforming method based on C⁰-basis functions. We present the variational form of the method including additional terms to weakly enforce continuity of the derivatives across interelement boundaries and its stabilization is achieved via Nitsche's method. Numerical tests for the equilibrium shape of a single component vesicle are performed to demonstrate the performance of the proposed variational formulation.

Original language	English
Title of host publication	Proceedings of the 6th European Conference on Computational Mechanics
Subtitle of host publication	Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
Editors	Roger Owen, Rene de Borst, Jason Reese, Chris Pearce
Publisher	International Centre for Numerical Methods in Engineering, CIMNE
Pages	1886-1895
Number of pages	10
ISBN (Electronic)	9788494731167
Publication status	Published - 2020
Event	6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 - Glasgow, United Kingdom Duration: 2018 Jun 11 → 2018 Jun 15

Publication series

Name	Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018

Conference

Conference	6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
Country/Territory	United Kingdom
City	Glasgow
Period	18/6/11 → 18/6/15

Bibliographical note

Publisher Copyright:
copyright © Crown copyright (2018).All right reserved.

All Science Journal Classification (ASJC) codes

Computer Science Applications
Computational Theory and Mathematics
Mechanics of Materials
Mechanical Engineering

Cite this

Kim, T. Y., Jiang, W., Lee, S. M., Song, J. H., & Park, E. J. (2020). Vesicle shape deformation using a discontinuous Galerkin method. In R. Owen, R. de Borst, J. Reese, & C. Pearce (Eds.), Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 (pp. 1886-1895). (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018). International Centre for Numerical Methods in Engineering, CIMNE.

Kim, Tae Yeon ; Jiang, Wen ; Lee, Sung Mun et al. / Vesicle shape deformation using a discontinuous Galerkin method. Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. editor / Roger Owen ; Rene de Borst ; Jason Reese ; Chris Pearce. International Centre for Numerical Methods in Engineering, CIMNE, 2020. pp. 1886-1895 (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018).

@inproceedings{a569de4a48f143889afff15dc15686cc,

title = "Vesicle shape deformation using a discontinuous Galerkin method",

abstract = "This work concerns the development of a finite-element algorithm to discretize the phase-field model for the shape deformation of a vesicle based on the idea of discontinuous Galerkin method. The phase-field model originated from minimization of Canham-Helfrich elastic bending energy involves fourth-order gradients and thus C1-basis functions are required for the standard conforming Galerkin formulation. We introduce a relatively inexpensive, nonconforming method based on C0-basis functions. We present the variational form of the method including additional terms to weakly enforce continuity of the derivatives across interelement boundaries and its stabilization is achieved via Nitsche's method. Numerical tests for the equilibrium shape of a single component vesicle are performed to demonstrate the performance of the proposed variational formulation.",

author = "Kim, {Tae Yeon} and Wen Jiang and Lee, {Sung Mun} and Song, {Jeong Hoon} and Park, {Eun Jae}",

note = "Publisher Copyright: copyright {\textcopyright} Crown copyright (2018).All right reserved.; 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 ; Conference date: 11-06-2018 Through 15-06-2018",

year = "2020",

language = "English",

series = "Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018",

publisher = "International Centre for Numerical Methods in Engineering, CIMNE",

pages = "1886--1895",

editor = "Roger Owen and {de Borst}, Rene and Jason Reese and Chris Pearce",

booktitle = "Proceedings of the 6th European Conference on Computational Mechanics",

}

Kim, TY, Jiang, W, Lee, SM, Song, JH & Park, EJ 2020, Vesicle shape deformation using a discontinuous Galerkin method. in R Owen, R de Borst, J Reese & C Pearce (eds), Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018, International Centre for Numerical Methods in Engineering, CIMNE, pp. 1886-1895, 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018, Glasgow, United Kingdom, 18/6/11.

Vesicle shape deformation using a discontinuous Galerkin method. / Kim, Tae Yeon; Jiang, Wen; Lee, Sung Mun et al.
Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. ed. / Roger Owen; Rene de Borst; Jason Reese; Chris Pearce. International Centre for Numerical Methods in Engineering, CIMNE, 2020. p. 1886-1895 (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Vesicle shape deformation using a discontinuous Galerkin method

AU - Kim, Tae Yeon

AU - Jiang, Wen

AU - Lee, Sung Mun

AU - Song, Jeong Hoon

AU - Park, Eun Jae

PY - 2020

Y1 - 2020

N2 - This work concerns the development of a finite-element algorithm to discretize the phase-field model for the shape deformation of a vesicle based on the idea of discontinuous Galerkin method. The phase-field model originated from minimization of Canham-Helfrich elastic bending energy involves fourth-order gradients and thus C1-basis functions are required for the standard conforming Galerkin formulation. We introduce a relatively inexpensive, nonconforming method based on C0-basis functions. We present the variational form of the method including additional terms to weakly enforce continuity of the derivatives across interelement boundaries and its stabilization is achieved via Nitsche's method. Numerical tests for the equilibrium shape of a single component vesicle are performed to demonstrate the performance of the proposed variational formulation.

AB - This work concerns the development of a finite-element algorithm to discretize the phase-field model for the shape deformation of a vesicle based on the idea of discontinuous Galerkin method. The phase-field model originated from minimization of Canham-Helfrich elastic bending energy involves fourth-order gradients and thus C1-basis functions are required for the standard conforming Galerkin formulation. We introduce a relatively inexpensive, nonconforming method based on C0-basis functions. We present the variational form of the method including additional terms to weakly enforce continuity of the derivatives across interelement boundaries and its stabilization is achieved via Nitsche's method. Numerical tests for the equilibrium shape of a single component vesicle are performed to demonstrate the performance of the proposed variational formulation.

UR - http://www.scopus.com/inward/record.url?scp=85081044618&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85081044618&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85081044618

T3 - Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018

SP - 1886

EP - 1895

BT - Proceedings of the 6th European Conference on Computational Mechanics

A2 - Owen, Roger

A2 - de Borst, Rene

A2 - Reese, Jason

A2 - Pearce, Chris

PB - International Centre for Numerical Methods in Engineering, CIMNE

T2 - 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018

Y2 - 11 June 2018 through 15 June 2018

ER -

Kim TY, Jiang W, Lee SM, Song JH, Park EJ. Vesicle shape deformation using a discontinuous Galerkin method. In Owen R, de Borst R, Reese J, Pearce C, editors, Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018. International Centre for Numerical Methods in Engineering, CIMNE. 2020. p. 1886-1895. (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018).

Vesicle shape deformation using a discontinuous Galerkin method

Abstract

Publication series

Conference

Bibliographical note

All Science Journal Classification (ASJC) codes

Other files and links

Fingerprint

Cite this