Topological derivatives for elliptic problems on graphs
Résumé
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.
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