标题： 任意拉格朗日-欧拉有限元方法用于脂质膜 显示英文标题

标题： Arbitrary Lagrangian--Eulerian finite element method for lipid membranes

摘要： 这里提出了一种任意拉格朗日-欧拉有限元方法及其数值实现，用于弯曲和变形的脂质膜。 膜表面配备了一个网格，其平面内运动无需依赖脂质的平面内流动。 相反，平面内网格动力学可以任意指定。 引入了一类新的网格运动，其中网格速度满足用户指定的二维材料的动力学方程。 一个拉格朗日乘子约束膜和网格的平面外速度相等，从而使网格和材料始终保持重叠。 随之出现一种相关的数值inf-sup不稳定性，并通过适应流体有限元分析中的已建立技术来消除。 在我们的实现中，上述拉格朗日乘子被投影到分段线性函数的不连续空间中。 通过研究一个具有生物学重要性的典型数值基准来比较新的网格运动与已建立的拉格朗日和欧拉公式：从平坦区域拉出膜 tether 并随后进行横向移动。 显示英文摘要

摘要： 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.