A Computational Algorithm For System Modelling Based On Bi-dimensional Finite Element Techniques

摘要

This paper develops a modelling methodology for studying relations defined a priori in two dimensions, z = u(x,y), for which experimental data are known. An innovation is that the methodology is based on bi-dimensional finite element techniques, in which the model's value consists of a finite number of points, making it possible to obtain its value at any point. Its application permits obtaining representational models of the relation. A computational algorithm is presented; its program has been called Finit Trap 2D, which generates families of models. It has defined criteria for model selection based on information parameters. This scientific research technique complements those existing in scientific literature for generating mathematical models based on experimental data [Cortes M, Villacampa Y, Mateu J, Uso, JL. A new methodology for modelling highly structured systems. Environmental modelling and software 2000;15(5):461-70, S-PLUS 2000. Guide to statistics, vosl. 1-2. Mathsoft Inc.; 1999, SPSS 12.0. Guide to statistics, Mathsoft Inc.; 2003, Verdu F. Un algoritmo para la construccion multiple de modelos matematicos no lineales y el estudio de su estabilidad, Thesis Doctoral, Universidad de Alicante; 2001, Verdu F, Villacampa Y. A computational algorithm for the multiple generation of nonlinear mathematical models and stability study. Advances in Engineering Software 2008;39(5):430-7, Villacampa Y, Cortes M, Vives F, Uso JL, Castro MA. A new computational algorithm to construct mathematical models. In: Ecosystems and sustainable development II. Advances in ecological sciences, vol. 2, WIT Press: Southampton, Boston; 1999], and will be useful in the effort to simplify the model.rnIt should be emphasised that representational models have been generated from bi-dimensional finite element models. This will naturally lead to their future application in processes described by partial differential equation whose coefficients are functions, A(x,y) for which only experimental data are known.