An Efficient Iterative Method for the Formulation of Flow Networks

We propose an efficient iterative convolution thresholding method for the formulation of flow networks where thefluid is modeled by the Darcy–Stokesflow with the presence of volume sources.The method is based on the minimization of the dissipation power in thefluid region with a Darcy term.Theflow network is represented by its characteristic function and the energy is approximated under this representation.The minimization problem can then be approximately solved by alternating:1)solving a Brinkman equation to model the Darcy–Stokesflow and 2)updating the characteristic function by a simple convolution and thresholding step.The proposed method is simple and easy to implement.We prove mathematically that the iterative method has the total energy decaying property.Numerical experiments demonstrate the performance and robustness of the proposed method and interesting structures are observed.