Title: A Level-set Method for Shape and Topology Optimization


		         Gregoire Allaire
              28 rue du Ranelagh, 75016 Paris, France
	         gregoire.allaire@polytechnique.fr
	     http://www.cmap.polytechnique.fr/~allaire


Abstract:
Together with F. Jouve and A.-M. Toader we introduced a new method of shape 
and topology optimization for elastic structures based on the level-set method
of Osher and Sethian. It is based on a combination of the classical shape 
derivative and of the level-set method for front propagation. We implemented 
this method in two and three space dimensions for a model of linear or 
non-linear elasticity and with various objective functions (compliance, 
least-square criteria, eigenfrequency, multiple loads). The shape derivative 
is computed by an adjoint method. The cost of our numerical algorithm is 
moderate since the shape is captured on a fixed Eulerian mesh. Although this 
method can easily handle topology changes, it does not relax the problem which
is well-known to be ill-posed. Thus, the resulting optimal shape is strongly 
dependent on the initial guess. Various 2-d and 3-d examples are discussed.