Topological derivatives for networks of elastic strings - Leugering, Günter; Sokolowski, J. (ZAMM - Zeitschrift für angewandte Mathematik und Mechanik, 2011)
We consider linear second order differential equations on metric graphs under given boundary and nodal conditions. We are interested in the problem of changing the topology of the underlying graph in that we replace a multiple node by a subgraph or concentrate a subgraph to a single node. We wish to do so in an optimal fashion. More precisely, given a cost function we may look for its sensitivity with respect to these operations in order to find an optimal topology of the graph. Thus, in essence, we are looking for the topological gradient for linear second order problems on metric graphs.