Efficient reformulation and solution of a nonlinear PDE-controlled flow network model
We consider a flow network where the flow of parts can be controlled at the vertices of the network. Based on a modified coarse grid discretization presented in Fugenschuh et al. (SIAM J Scientific Comput 30(3):1490-1507, 2008) we derive a mixed-integer program (MIP). Under suitable assumptions on the cost functional we prove that there exists an equivalent linear program (LP). We present numerical results concerning validity of our result and show the improvement of the computing times using the equivalent LP over the MIP.
flow networks networks conservation laws adjoint calculus