Vesicle shape deformation using a discontinuous Galerkin method

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

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationProceedings of the 6th European Conference on Computational Mechanics
Subtitle of host publicationSolids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
EditorsRoger Owen, Rene de Borst, Jason Reese, Chris Pearce
PublisherInternational Centre for Numerical Methods in Engineering, CIMNE
Pages1886-1895
Number of pages10
ISBN (Electronic)9788494731167
Publication statusPublished - 2020 Jan 1
Event6th 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 112018 Jun 15

Publication series

NameProceedings 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

Conference6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018
CountryUnited Kingdom
CityGlasgow
Period18/6/1118/6/15

All Science Journal Classification (ASJC) codes

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

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  • 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.