A Shape Newton Scheme for Deforming Shells with Application to Capillary Bridges

We present a second order numerical scheme to compute capillary bridges between arbitrary solids by minimizing the total energy of all interfaces. From theoretical point view, this approach can be interpreted as computation generalized minimal surfaces using Newton-scheme utilizing shape Hessian. In particular, we give an explicit representation Hessian for functionals on shells involving normal vector without reverting back volume formulation or approximating curvature. algorithmic perspective, combine resolved interface via triangulated surface liquid with level set description constraints stemming from geometry. The actual bridge is then computed finite elements provided FEniCS environment, derivative energy.