Adaptive grids as parametrized scale-free networks

Abstract

In this paper we present a possible model of adaptive grids for numerical resolution of differential problems, using physical or geometrical properties, as viscosity or velocity gradient of a moving fluid. The relation between the values of grid step and these entities is based on the mathematical scheme offered by the model of scale-free networks, due to Barabasi, so that the step can be connected to the other variables by a constitutive relation. Some examples and an application are discussed, showing that this approach can be further developed for treatment of more complex situations.