  The thesis is about an application of the shape optimization to the
morphological evolution of Golgi stack. Golgi stack consists of multiple layers
of cisternae. It is an organelle in the biological cells. Inspired by the
Helfrich Model \cite{Helfrich}, which is a model for vesicles typically applied
to biological cells, a new model specially designed for Golgi stack is
developed and then implemented using FEM in this thesis.
  In the Golgi model, each cisternae of the Golgi stack is viewed as a closed
vesicle without topological changes, and our model is adaptable to both
single-vesicle case and multiple-vesicle case. The main idea of the math model
is to minimize the elastic energy(bending energy) of the vesicles, with some
constraints designed regarding the biological properties of Golgi stack. With
these constraints attached to the math model, we could extend this model to an
obstacle-type problem. Hence, in the thesis, not only the simulations of Golgi
stack are shown, but some interesting examples without biological meanings are
also demonstrated. Also, as multiple cisternaes are considered as a whole, this
is also a model handling multiple objects.
  A set of numerical examples is shown to compare with the observed shape of
Golgi stack, so we can lay down some possible explanations to the morphological
performance of trans-Golgi cisternae.
