A Geometric Model For The Generation Of Models Defined In Complex Systems
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Y. Villacampa, F. J. Navarro-González & J. Llorens
Y. Villacampa1, F. J. Navarro-González1 & J. Llorens2 1Departamento de Matemática Aplicada, Universidad de Alicante, Spain 2Departamento de Sistemas Informático y Computación, Universidad Politécnica de Valencia, Spain Abstract When studying and modelling Complex Systems where there can be a considerable number of variables and relations, it is very important to obtain methodologies that help us to model natural phenomena, these being phenomena present in the physical world and real life. Hypothetically, if we consider a relation defined by a set of variables, ( ) 1 2 , ,......, n y f x x x = , symbolic and numerical methodologies can be obtained. This article presents a model of n-dimensional finite elements that provides the basis for defining a numerical methodology for studying and modelling complex systems. The use of n-dimensional elements then allows us to represent the relation using the values of the same for a finite number of points, this being carried out by resolving an optimization problem. To obtain the geometric model it was necessary to use the correct data structure design and programming to allow effective management of the acquisition and storage of the elements, the nodes considered for each, as well as the functions and procedures needed to approach the problem of optimisation. Finally, we applied the methodology to determine the geometric model and the problem of optimization to study and model an environmental problem Keywords: modelling, finite elements, Complex Systems.
modelling, finite elements, Complex Systems