Advances of the meccano method for isogeometric analysis of irregular planar domains

[EN]We present advances of the meccano method for T-spline modelling and analysis of complex geometries. We consider a planar domain composed by several irregular sub-domains. These sub-regions are defined by their boundaries and can represent different materials. The bivariate T-spline representation of the whole physical domain is constructed from a square. In this procedure, a T-mesh optimization method is crucial. We show results of an elliptic problem by using a quadtree local T-mesh refinement technique…

Adaptive T-spline refinement for isogeometric analysis in planar geometries

[EN]We present a new strategy, based on the meccano method [1, 2, 3], to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithm obtains, as a result, high quality parametric transformation between 2D objects and the parametric domain, the unit square. The key of the method lies in defining an isomorphic transformation between the parametric and physical T-mesh finding the optimal position of the interior nodes by applying a new T-mesh untangling and smoothing procedure. Bivariate T-spline representation is calculated by imposing the interpolation conditions on points sited both on the interior and on the boundary of the geometry…

Mesh Generation and Isogeometric Analysis

[EN]We present advances of the meccano method [1,2] for tetrahedral mesh generation and volumetric parameterization of solids. The method combines several former procedures: a mapping from the meccano boundary to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing. The key of the method lies in defining a one-to-one volumetric transformation between the parametric and physical domains. Results with adaptive finite elements will be shown for several engineering problems. In addition, the application of the method to T-spline modelling and isogeometric analysis [3,4] of complex geometries will be introduced…

Three-dimensional simulation of wind fields and air pollution over complex terrain

[EN]In this talk we introduce a new methodology for wind field simulation or forecasting over complex terrain. The idea is to use wind measurements or predictions of the HARMONIE mesoscale model as the input data for an adaptive finite element mass consistent wind model [1,2]. The method has been recently implemented in the freely-available Wind3D code [3]. A description of the HARMONIE Non-Hydrostatic Dynamics can be found in [4]. The results of HARMONIE (obtained with a maximum resolution about 1 Km) are refined by the finite element model in a local scale (about a few meters). An interface between both models is implemented such that the initial wind field approximation is obtained by a suitable interpolation of the HARMONIE results…

Crisis de fundamentos en las Matemáticas Españolas a finales del siglo XIX

Se estudia el estado de las Matemáticas en España a finales del siglo XIX, en especial la influencia de algunas interpretaciones metafíscas de los números complejos (Rey Heredia)