Subdivision based finite elements for lipid membranes

In this thesis we study numerical methods for simulating mechanical deformations of cell membranes. Such models are given in terms of fourth order partial di erential equations. In order to enable comparisons of the models predictions to experimental results, the equations must be solved on arbitrary cell geometries. A Finite Element Method based on subdivision surfaces, which is capable of discretizing the partial di erential equations, is implemented in a C++ computer program. An integral part of cell membranes models are constraints, enforcing the conservation of the cells surface, volume and integrated mean curvature. The discretized equations can not exactly ful ll these constraints. Instead one introduces harmonic potentials of the quantities to be conserved. This allows for an approximate conservation. Several Rosenbrock methods for the solution of the resulting sti ordinary di erential equations are tested. Virtual experiments in which cells are aspirated into micropipettes are carried out as a benchmark for the performance of the simulation.