Generalized shape optimization using XFEM and Level Set methods

This paper presents an intermediate approach between parametric shape optimization
and topology optimization. It is based on using the recent Level Set
description of the geometry and the novel eXtended Finite Element Method (XFEM).
The method takes benefit of the fixed mesh work using X-FEM and of
the curves smoothness of the Level Set description. Design variables are shape
parameters of basic geometric features. The number of design variables of this
formulation is small whereas various global and local constraints can be considered.
The Level Set description allows to modify the connectivity of the structure
as geometric features can merge or separate from each other. However no
new entity can be introduced. A central problem that is investigated here is the
sensitivity analysis and the way it can be carried out efficiently. Numerical applications
revisit the classical elliptical hole benchmark from shape optimization.