Arbitrary Lagrangian--Eulerian finite element method for lipid membranes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918348577570816 |
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| author | Sahu, Amaresh |
| author_facet | Sahu, Amaresh |
| contents | An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the in-plane flow of lipids. Instead, in-plane mesh dynamics can be specified arbitrarily. A new class of mesh motions is introduced, where the mesh velocity satisfies the dynamical equations of a user-specified two-dimensional material. A Lagrange multiplier constrains the out-of-plane membrane and mesh velocities to be equal, such that the mesh and material always overlap. An associated numerical inf--sup instability ensues, and is removed by adapting established techniques in the finite element analysis of fluids. In our implementation, the aforementioned Lagrange multiplier is projected onto a discontinuous space of piecewise linear functions. The new mesh motion is compared to established Lagrangian and Eulerian formulations by investigating a preeminent numerical benchmark of biological significance: the pulling of a membrane tether from a flat patch, and its subsequent lateral translation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arbitrary Lagrangian--Eulerian finite element method for lipid membranes Sahu, Amaresh Computational Physics Soft Condensed Matter Biological Physics An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the in-plane flow of lipids. Instead, in-plane mesh dynamics can be specified arbitrarily. A new class of mesh motions is introduced, where the mesh velocity satisfies the dynamical equations of a user-specified two-dimensional material. A Lagrange multiplier constrains the out-of-plane membrane and mesh velocities to be equal, such that the mesh and material always overlap. An associated numerical inf--sup instability ensues, and is removed by adapting established techniques in the finite element analysis of fluids. In our implementation, the aforementioned Lagrange multiplier is projected onto a discontinuous space of piecewise linear functions. The new mesh motion is compared to established Lagrangian and Eulerian formulations by investigating a preeminent numerical benchmark of biological significance: the pulling of a membrane tether from a flat patch, and its subsequent lateral translation. |
| title | Arbitrary Lagrangian--Eulerian finite element method for lipid membranes |
| topic | Computational Physics Soft Condensed Matter Biological Physics |
| url | https://arxiv.org/abs/2412.07596 |