2018/11/30 by Facca, Enrico, Cardin, Franco, Putti, Mario
#35J #35J70 #49K20 #49M25 #49M29 #65 #65N #65N30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1811.12691
Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based L1-optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that volves proportionally to the transported flux. In this paper we present an extension of this model that considers a time derivative of the conductivity that grows as a power law of the transport flux with exponent β>0. A sub-linear growth (01) favors flux intensity and promotes concentrated transport, leading to the emergence of steady-state "singular" and "fractal-like" configurations that resemble those of Branched Transport Problems. We derive a numerical discretization of the proposed model that is accurate, efficient, and robust for a wide range of scenarios. For β>1 the numerical model is able to reproduce highly irregular and fractal-like formations without any a-priory structural assumption.