Shape optimization with a level set based mesh evolution method

In this article, we discuss an approach for geometry and topology optimization of structures which benefits from an accurate description of shapes at each stage of the iterative process–by means of a mesh amenable for mechanical analyses–while retaining the whole versatility of the level set method when it comes to accounting for their evolution. The key ingredients of this method are two operators for switching from a meshed representation of a domain to an implicit one, and conversely; this notably brings into play an algorithm for generating the signed distance function to an arbitrary discrete domain, and a mesh generation algorithm for implicitly-defined geometries.