A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.

Los SIG en el contexto del medio marino en la Región de Murcia

La aplicación de los Sistemas de Información Geográfica (SIG) se ha extendido en el mundo científico-técnico, donde se ha convertido en un instrumento de análisis y almacenamiento de información imprescindible. El uso de los SIG abarca casi cualquier aplicación en la que haya una componente espacial, como usos militares, aplicaciones en infraestructuras, planificación territorial, etc. En el medio marino se pueden aplicar para teledetección, cartografía digital, geoestadística, análisis y modelación espacial, Infraestructuras de Datos Espaciales (IDE), visores web, etc. En 1988, la Región de Murcia impulsó el proyecto de cartografía binómica del litoral murciano, siendo un instrumento que ha ido actualizándose hasta nuestros días. En comparación con otras regiones mediterráneas españolas, el litoral murciano es el tramo del litoral mediterráneo con la información cartográfica más completa y precisa, además del SIG marino más avanzado. Son numerosos los trabajos y aplicaciones en los que se ha utilizado como base la cartografía y los datos asociados, como la Red Natura 2000, ‘Programa de gestión integrada del litoral del Mar Menor y su zona de influencia’, caracterización ambiental para la propuesta de Reservas Marinas, diagnóstico medioambiental, etc.

Advanced interpretation of subsidence in Murcia (SE Spain) using A-DInSAR data – modelling and validation

Subsidence is a natural hazard that affects wide areas in the world causing important economic costs annually. This phenomenon has occurred in the metropolitan area of Murcia City (SE Spain) as a result of groundwater overexploitation. In this work aquifer system subsidence is investigated using an advanced differential SAR interferometry remote sensing technique (A-DInSAR) called Stable Point Network (SPN). The SPN derived displacement results, mainly the velocity displacement maps and the time series of the displacement, reveal that in the period 2004–2008 the rate of subsidence in Murcia metropolitan area doubled with respect to the previous period from 1995 to 2005. The acceleration of the deformation phenomenon is explained by the drought period started in 2006. The comparison of the temporal evolution of the displacements measured with the extensometers and the SPN technique shows an average absolute error of 3.9±3.8 mm. Finally, results from a finite element model developed to simulate the recorded time history subsidence from known water table height changes compares well with the SPN displacement time series estimations. This result demonstrates the potential of A-DInSAR techniques to validate subsidence prediction models as an alternative to using instrumental ground based techniques for validation.