Topological derivative

Topological derivative

In the field of shape optimization, a topological derivative is, conceptually, a derivative of a function of a region with respect to small changes in its topology, such as adding a small hole.

Shape optimization concerns itself with finding an optimal shape. That is, find Omega to minimize some scalar-valued objective function, J(Omega). Neglecting changes in topology, an initial guess can be improved by perturbing the shape of Omega by methods of calculus of variations and functional analysis. However, this does not permit a discrete operation such as making a hole in Omega.

External links

* Allaire et al. [http://www.cmap.polytechnique.fr/~jouve/papers/toplev.pdf Structural optimization using topological and shape sensitivity via a level set method]


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