Optimal transportation networks via a phase field approximation of the generalized urban planning problem

General information

The code implements the method proposed in [1], for solving the generalized urban planning problem [2] via a phase field approximation approach.

The problem was implemented using Matlab, Version R2018b.

Run example

To run the code, open Matlab and execute Example.m. This will compute a simple example of transport from one point source to two point sinks with equal mass. For an other example or a different setting, the following parameters can be changed within the example file:

n: Image size (n by n grid) 
savename: Savename 
epsilonStart: Initial epsilon 
epsilonEnd: Final epsilon 
maxIter: Maximal number of iterations
tol: Iteration error tolerance  
a0: Parameter a0
a: Parameter a 
b: Parameter b 
example: Example (see getExample.m)
initSol: Initial solution given (true or false)
savenameInit: Filename of initial solution (filename/savename of given initial solution)

[1] Luca Ferrari, Carolin Rossmanith, and Benedikt Wirth. Phase field approximations of branched transportation problems. Preprint, 2018.

[2] Alessio Brancolini and Giuseppe Buttazzo. Optimal networks for mass transportation problems. ESAIM Control Optim. Calc. Var., 11(1):88-101 (electronic), 2005.