A new methodology for complex systems using n-dimensional finite elements

In this article a new methodology is developed, for the modelling of complex systems where the number of variables and relationships can be high. This methodology allows an efficient work on a n-dimensional hypercube and its computational implementation, a fact that was not possible through a generalisation of the 2-dimensional methodology developed in [10]. The methodology allows obtaining representation models of a function or relationship, z = u(x1, x2, …… , xn) obtained from the interpolation defined in an n  -dimensional finite element model. The interpolation function implies the use of some initial conditions, what in the defined methodology implies the coincidence between the values of the function in a finite number of points zi,xi1,xi2,xi3,……,xini=1,.2,…,p.As usually when a finite element model of representation is used, the function is obtained in a finite set of points, called nodes [22]. In this case, this is done by solving an optimisation problem based on the search of the minimum of an error function defined generically in any finite element model defined in the hypercube.The computational implementation of the methodology allows obtaining families of mathematical models that represent the relationships. From each obtained model several information parameters are also considered, as roughness and stability.