论文标题
形状的牛顿方案，用于将壳变形壳，并应用于毛细管桥
A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges
论文作者
论文摘要
我们提出了一个二阶数值方案，以最大程度地减少所有接口的总能量，以在任意固体之间计算毛细管桥。从理论的角度来看，这种方法可以解释为使用Shape Hessian的牛顿 - 奇语计算最小表面的计算。特别是，我们为涉及正常矢量的壳上的功能的形状Hessian提供了明确表示，而无需恢复到体积公式或近似曲率。从算法的角度来看，我们通过液体的三角形表面结合了一个分辨的界面，并为由任意几何形状引起的约束的水平设置描述。然后，通过Fenics环境提供的有限元来计算毛细管桥的实际形状，从而最大程度地降低了总界面能的形状导数。
We present a second order numerical scheme to compute capillary bridges between arbitrary solids by minimizing the total energy of all interfaces. From a theoretical point of view, this approach can be interpreted as the computation of generalized minimal surfaces using a Newton-scheme utilizing the shape Hessian. In particular, we give an explicit representation of the shape Hessian for functionals on shells involving the normal vector without reverting back to a volume formulation or approximating curvature. From an algorithmic perspective, we combine a resolved interface via a triangulated surface for the liquid with a level set description for the constraints stemming from the arbitrary geometry. The actual shape of the capillary bridge is then computed via finite elements provided by the FEniCS environment, minimizing the shape derivative of the total interface energy.
