Topological derivatives for networks of elastic strings

G. Leugering (1) , J. Sokolowski (2)

1 Department Mathematik [Erlangen]
2 IECN - Institut Élie Cartan de Nancy

We consider second order problems on metric graphs under given boundary and nodal conditions. We consider the problem of changing the topology of the underlying graph in that we replace a multiple node by an imported subgraph, or, in reverse, concentrate a subgraph to a single node or delete or add edges, respectively. We wish to do so in some optimal fashion. More precisely, given a cost function we may look at such operations in order to find an optimal topology of the graph. Thus, finally we are looking into the topological gradient of an elliptic problem on a graph.

Mots clés: wave equation on graph; optimal topology of graph; topological derivative

Domaines: Equations aux dérivées partielles [math.AP]

G. Leugering, J. Sokolowski. Topological derivatives for networks of elastic strings. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2011, 91 (12), pp.926-943. ⟨10.1002/zamm.201000067⟩. ⟨hal-00463693⟩