New Advances in the Study of Generalized Willmore Surfaces and Flow

Athukorallage, Bhagya; Aulisa, Eugenio; Bornia, Giorgio; Paragoda, Thanuja; Toda, Magdalena

doi:10.7546/giq-17-2016-133-142

VOL. 17 | 2016 New Advances in the Study of Generalized Willmore Surfaces and Flow

Bhagya Athukorallage, Eugenio Aulisa, Giorgio Bornia, Thanuja Paragoda, Magdalena Toda

Editor(s) Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka

Geom. Integrability & Quantization, 2016: 133-142 (2016) DOI: 10.7546/giq-17-2016-133-142

Abstract

In this paper we study a Generalized Willmore flow for graphs and its numerical applications.

First, we derive the time dependent equation which describes the geometric evolution of a Generalized Willmore flow in the graph case. This equation is recast in divergence form as a coupled system of second order nonlinear PDEs.

Furthermore, we study finite element numerical solutions for steady-state cases obtained with the help of the FEMuS library (Finite Element Multiphysics Solver). We use automatic differentiation (AD) tools to compute the exact Jacobian of the coupled PDE system subject to Dirichlet boundary conditions.