José Manuel Cascón

A New Meccano Technique for Adaptive 3-D Triangulations

This paper introduces a new automatic strategy for adaptive tetrahedral mesh generation. A local refinement/derefinement algorithm for nested triangula-tions and a simultaneous untangling and smoothing procedure are the main involved techniques. The mesh generator is applied to 3-D complex domains whose boundaries are projectable on external faces of a coarse object meccano composed of cuboid pieces. The domain surfaces must be given by a mapping between meccano surfaces and object boundary. This mapping can be defined by analytical or discrete functions. At present we have fixed mappings with orthogonal , cylindrical and radial projections, but any other one-to-one projection may be considered. The mesh generator starts from a coarse tetrahedral mesh which is automatically obtained by the subdivision of each hexahedra, of a meccano hexahedral mesh, into six tetrahedra. The main idea is to construct a sequence of nested meshes by refining only those tetrahedra which have a face on the meccano boundary. The virtual projection of meccano external faces defines a valid triangulation on the domain boundary. Then a 3-D local refinement/derefinement is carried out such that the approximation of domain surfaces verifies a given precision. Once this objective is reached, those nodes placed on the meccano boundary are really projected on their corresponding true boundary, and inner nodes are relocated using a suitable mapping. As the mesh topology is kept during node movement, poor quality or even inverted elements could appear in the resulting mesh. For this reason, we finally apply a mesh optimization procedure. The efficiency of the proposed technique is shown with several applications to complex objects.

The Meccano Method for Automatic Tetrahedral Mesh Generation of Complex Genus-Zero Solids

In this paper we introduce an automatic tetrahedral mesh generator for complex genus-zero solids, based on the novel meccano technique. Our method only demands a surface triangulation of the solid, and a coarse approximation of the solid, called meccano, that is just a cube in this case. The procedure builds a 3-D triangulation of the solid as a deformation of an appropriate tetrahedral mesh of the meccano. For this purpose, the method combines several procedures: an automatic mapping from the meccano boundary to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing. A volume parametrization of the genus-zero solid to a cube (meccano) is a direct consequence. The efficiency of the proposed technique is shown with several applications.

Space-Time adaptive algorithm for the mixed parabolic problem

In this paper we present an a-posteriori error estimator for the mixed formulation of a linear parabolic problem, used for designing an efficient adaptive algorithm. Our space-time discretization consists of lowest order Raviart-Thomas finite element over graded meshes and discontinuous Galerkin method with variable time step. Finally, several examples show that the proposed method is efficient and reliable.

The meccano method for isogeometric solid modeling and applications

We present a new method to construct a trivariate T-spline representation of complex solids for the application of isogeometric analysis. We take a genus-zero solid as a basis of our study, but at the end of the work we explain the way to generalize the results to any genus solids. The proposed technique only demands a surface triangulation of the solid as input data. The key of this method lies in obtaining a volumetric parameterization between the solid and the parametric domain, the unitary cube. To do that, an adaptive tetrahedral mesh of the parametric domain is isomorphically transformed onto the solid by applying a mesh untangling and smoothing procedure. The control points of the trivariate T-spline are calculated by imposing the interpolation conditions on points sited both on the inner and on the surface of the solid. The distribution of the interpolating points is adapted to the singularities of the domain to preserve the features of the surface triangulation. We present some results of the application of isogeometric analysis with T-splines to the resolution of Poisson equation in solids parameterized with this technique.

A new method for T-spline parameterization of complex 2D geometries

We present a new strategy, based on the idea of the meccano method and a novel T-mesh optimization procedure, 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. First, we define a parametric mapping between the input boundary of the object and the boundary of the parametric domain. Then, we build a T-mesh adapted to the geometric singularities of the domain to preserve the features of the object boundary with a desired tolerance. 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 in the interior and on the boundary of the geometry. The efficacy of the proposed technique is shown in several examples. Also we present some results of the application of isogeometric analysis in a geometry parameterized with this technique.

A unifying model to measure consensus solutions in a society

Abstract In this work, we contribute to the formal and computational analysis of the measurement of consensus in a society. We propose a unifying model that generates a consistent decision in terms of the individual preferences and then measures the consensus that arises from it. We focus our inspection on two relevant and specific cases: the Borda and the Copeland rules under a Kemeny-type measure. A computational analysis of these two proposals serves us to compare their respective performances.

Comparison of the meccano method with standard mesh generation techniques

The meccano method is a novel and promising mesh generation technique for simultaneously creating adaptive tetrahedral meshes and volume parameterizations of a complex solid. 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. In this paper we present the main advantages of our method against other standard mesh generation techniques. We show that our method constructs meshes that can be locally refined using the Kossaczky bisection rule and maintaining a high mesh quality. Finally, we generate volume T-mesh for isogeometric analysis, based on the volume parameterization obtained by the method.

Sensitivity analysis and parameter adjustment in a simplified physical wildland fire model

A simplified physical 2D wildland fire model is summarized.Some aspects of the numerical techniques used to solve the model are outlined.The simplicity of the model and the numerical techniques proposed allow very competitive computational times.The model is applied to a well measured experimental example.A global sensitivity analysis of the model is performed in order to validate the simplications proposed.A parameter adjustment of the model applied to the experimental example is carried out. A global sensitivity analysis and parameter adjustment of a simplified physical fire model applied to a well measured experimental example is developed in order to validate the model. The fire model is a simplified physical 2D wildland fire model with some 3D effects that takes into account the wind, the slope of the orography, the fuel load and type, the moisture content, the energy lost in the vertical direction and the radiation from the flames. The simplicity of the model and the numerical techniques proposed allow very competitive computational times.

Implementation in ALBERTA of an Automatic Tetrahedral Mesh Generator

This paper introduces a new automatic tetrahedral mesh generator on the adaptive finite element ALBERTA code. The procedure can be applied to 3D domains with boundary surfaces which are projectable on faces of a cube. The generalization of the mesh generator for complex domains which can be split into cubes or hexahedra is straightforward. The domain surfaces must be given as analytical or discrete functions. Although we have worked with orthogonal and radial projections, any other one-to-one projection may be considered. The mesh generator starts from a coarse tetrahedral mesh which is automatically obtained by the subdivision of each cube into six tetrahedra. The main idea is to construct a sequence of nested meshes by refining only the tetrahedra which have a face on the cube projection faces. The virtual projection of external faces defines a triangulation on the domain boundary. The 3-D local refinement is carried out such that the approximation of domain boundary surfaces verifies a given precision. Once this objective is achieved reached, those nodes placed on the cube faces are projected on their corresponding true boundary surfaces, and inner nodes are relocated using a linear mapping. As the mesh topology is kept during node movement, poor quality or even inverted elements could appear in the resulting mesh. For this reason, a mesh optimization procedure must be applied. Finally, the efficiency of the proposed technique is shown with several applications.

Consensus and the Act of Voting

In this article we are concerned with assessing the cohesiveness of a society whose individual preferences are known. We analyse the axiomatic properties of a general proposal to measure aggregate satisfaction in terms of coherence of the expressed opinions, that relies on the consensus with reference to a select social preference. The formal concept of referenced consensus measures that we introduce permits to produce a numerical social evaluation from purely ordinal individual information. A referenced consensus measure can be specialized via two ways: the specification of the representative agent, or from a practical point of view, the choice of a voting mechanism; and the measure of agreement between profiles of orderings and individual orderings. Introducing a fictitious agent, or the result of the act of voting, as a reference is fit for the common case of actual social choices. We carry out a descriptive analysis of the formal properties of referenced consensus measures with an emphasis on two relevant cases whose explicit constructions are detailed.