Topological derivatives for elliptic problems on graphs

Günter Leugering (1) , Jan Sokolowski (2)

1 Chair of Applied mathematics 2
2 IECN - Institut Élie Cartan de Nancy

We consider elliptic problems on graphs under given loads. We ask the question which graph is best suited to sustain the loads. More precisely, given a cost function we may look at a multiple node of the graph ans ask as to whether that node should be resolved into a number of nodes of edge degree 3, in order to devrease the cost. Thus, we are looking into the topological gradient of an elliptic problem on a graph.

Mots clés: Topological derivative; shape optimization; aymptotic analysis; graph theory; singular perturbations; topology optimization

Domaines: Equations aux dérivées partielles [math.AP]

Günter Leugering, Jan Sokolowski. Topological derivatives for elliptic problems on graphs. 2006. ⟨hal-00105955⟩