In this note we present a reconstructive algorithm for solving the cross-sectional pipe area from boundary measurements in a tree network with one inaccessible end.This is equivalent to reconstructing the first order perturbation to a wave equation on a quantum graph from boundary measurements at all network ends except one.The method presented here is based on a time reversal boundary where to buy gruvi control method originally presented by Sondhi and Gopinath for one dimensional problems and later by Oksanen to higher dimensional manifolds.The algorithm wx gloves is local, so is applicable to complicated networks if we are interested only in a part isomorphic to a tree.Moreover the numerical implementation requires only one matrix inversion or least squares minimization per discretization point in the physical network.
We present a theoretical solution existence proof, a step-by-step algorithm, and a numerical implementation applied to two numerical experiments.