accedaCRIShttps://accedacris.ulpgc.es/jspuiThe accedaCRIS digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 23 Mar 2023 20:24:10 GMT2023-03-23T20:24:10Z50131A simple strategy for defining polynomial spline spaces over hierarchical T-meseshttp://hdl.handle.net/10553/16442Title: A simple strategy for defining polynomial spline spaces over hierarchical T-meses
Authors: Brovka, Marina; López, J. I.; Escobar Sánchez, José María; Montenegro Armas, Rafael; Cascón Barbero, José Manuel
Abstract: We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision schemes. The proposed technique includes some simple rules for inferring local knot vectors to define -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced mesh. The straightforward implementation of the proposed strategy can make it an attractive tool for its use in geometric design and isogeometric analysis. In this paper we give a detailed description of our technique and illustrate some examples of its application in isogeometric analysis performing adaptive refinement for 2D and 3D problems.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10553/164422016-01-01T00:00:00ZConstruction of polynomial spline spaces over quadtree and octree T-mesheshttp://hdl.handle.net/10553/16837Title: Construction of polynomial spline spaces over quadtree and octree T-meshes
Authors: Brovka, M.; López, J. I.; Escobar, J. M.; Cascón Barbero, José Manuel; Montenegro, R.
Abstract: We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10553/168372014-01-01T00:00:00ZRanking intervals in complex stochastic Boolean systems using intrinsic orderinghttp://hdl.handle.net/10553/44518Title: Ranking intervals in complex stochastic Boolean systems using intrinsic ordering
Authors: González, Luis
Abstract: Many different phenomena, arising from scientific, technical or social areas, can be modeled by a system depending on a certain number n of random Boolean variables. The so-called complex stochastic Boolean systems (CSBSs) are characterized by the ordering between the occurrence probabilities Pr{u} of the 2 n associated binary strings of length n, i.e., u=(u 1,…,u n ) ∈ {0,1} n . The intrinsic order defined on {0,1} n provides us with a simple positional criterion for ordering the binary n-tuple probabilities without computing them, simply looking at the relative positions of their 0s and 1s. For every given binary n-tuple u, this paper presents two simple formulas – based on the positions of the 1-bits (0-bits, respectively) in u – for counting (and also for rapidly generating, if desired) all the binary n-tuples v whose occurrence probabilities Pr{v} are always less than or equal to (greater than or equal to, respectively) Pr{u}. Then, from these formulas, we determine the closed interval covering all possible values of the rank (position) of u in the list of all binary n-tuples arranged by decreasing order of their occurrence probabilities. Further, the length of this so-called ranking interval for u, also provides the number of binary n-tuples v incomparable by intrinsic order with u. Results are illustrated with the intrinsic order graph, i.e., the Hasse diagram of the partial intrinsic order.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10553/445182010-01-01T00:00:00ZA new method for T-spline parameterization of complex 2D geometrieshttp://hdl.handle.net/10553/16399Title: A new method for T-spline parameterization of complex 2D geometries
Authors: Brovka, Marina; López, J. I.; Escobar Sánchez, José María; Cascón Barbero, José Manuel; Montenegro Armas, Rafael
Abstract: 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 in order 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.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10553/163992014-01-01T00:00:00ZWind forecasting based on the HARMONIE model and adaptive finite elementshttp://hdl.handle.net/10553/45229Title: Wind forecasting based on the HARMONIE model and adaptive finite elements
Authors: Oliver, Albert; Rodriguez, Eduardo; Escobar Sánchez, José M; Montero, Gustavo; Hortal, Mariano; Calvo, Javier; Cascón, José Manuel; Montenegro, Rafael
Abstract: In this paper, we introduce a new method for wind field forecasting over complex terrain. The main idea is to use the predictions of the HARMONIE meso-scale model as the input data for an adaptive finite element mass-consistent wind model. The HARMONIE results (obtained with a maximum resolution of about 1 km) are refined in a local scale (about a few metres). An interface between both models is implemented in such a way that the initial wind field is obtained by a suitable interpolation of the HARMONIE results. Genetic algorithms are used to calibrate some parameters of the local wind field model in accordance to the HARMONIE data. In addition, measured data are considered to improve the reliability of the simulations. An automatic tetrahedral mesh generator, based on the meccano method, is applied to adapt the discretization to complex terrains. The main characteristic of the framework is a minimal user intervention. The final goal is to validate our model in several realistic applications on Gran Canaria island, Spain, with some experimental data obtained by the AEMET in their meteorological stations. The source code of the mass-consistent wind model is available online at http://www.dca.iusiani.ulpgc.es/Wind3D/.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10553/452292015-01-01T00:00:00ZComplex sochastic Boolean systems: new properties of the intrinsic order graphhttp://hdl.handle.net/10553/16415Title: Complex sochastic Boolean systems: new properties of the intrinsic order graph
Authors: González Sánchez, Luis
Abstract: A complex stochastic Boolean system (CSBS) is a system depending on an arbitrary number n of stochastic Boolean variables. The analysis of CSBSs is mainly based on the intrinsic order: a partial order relation defined on the set f0; 1gn of binary n-tuples. The usual graphical representation for a CSBS is the intrinsic order graph: the Hasse diagram of the intrinsic order. In this paper, some new properties of the intrinsic order graph are studied. Particularly, the set and the number of its edges, the degree and neighbors of each vertex, as well as typical properties, such as the symmetry and fractal structure of this graph, are analyzed…
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10553/164152011-01-01T00:00:00ZPartitioning the intrinsic order graph for complex stochastic Boolean systemshttp://hdl.handle.net/10553/44517Title: Partitioning the intrinsic order graph for complex stochastic Boolean systems
Authors: González, Luis
Abstract: Many different problems in Engineering and Computer Science can be modeled by a complex system depending on a certain number n of stochastic Boolean variables: the so-called complex stochastic Boolean system (CSBS). The most useful graphical representation of a CSBS is the intrinsic order graph (IOG). This is a symmetric, self-dual diagram on 2(n) nodes (denoted by I-n) that displays all the binary n-tuples in decreasing order of their occurrence probabilities. In this paper, two different ways of partitioning the IOG -with applications to the analysis of CSBSs- are presented. The first one is based on the successive bisections of this graph into smaller and smaller equal-sized subgraphs. The second one consists of decomposing the graph I-n, into totally ordered subsets (chains) of the set {0,1}(n) of all binary n-tuples.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10553/445172010-01-01T00:00:00ZIntrinsic ordering, combinatorial numbers and reliability engineeringhttp://hdl.handle.net/10553/16353Title: Intrinsic ordering, combinatorial numbers and reliability engineering
Authors: González Sánchez, Luis
Abstract: A new algorithm for evaluating the top event probability of large fault trees (FTs) is presented. This algorithm does not require any previous qualitative analysis of the FT. Indeed, its efficiency is independent of the FT logic, and it only depends on the number n of basic system components and on their failure probabilities. Our method provides exact lower and upper bounds on the top event probability by using new properties of the intrinsic order relation between binary strings. The intrinsic order enables one to select binary n-tuples with large occurrence probabilities without necessity to evaluate them. This drastically reduces the complexity of the problem from exponential (2n binary n-tuples) to linear (n Boolean variables). Our algorithm
is mainly based on a recursive formula for rapidly computing the sum
of the occurrence probabilities of all binary n-tuples with weight m whose
1s are placed among the k right-most positions. This formula, as well as the
balance between accuracy and computational cost, is closely related to the
famous Pascal’s triangle.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10553/163532013-01-01T00:00:00ZIntrinsic order, lexicographic order, vector order and hamming weighthttp://hdl.handle.net/10553/44514Title: Intrinsic order, lexicographic order, vector order and hamming weight
Authors: González, Luis
Abstract: To compare binary n-tuple probabilities with no need to compute them, we have defined a partial order relation on the set {0, 1}n of all binary n-tuples: The so-called intrinsic order relation. In this paper, some properties of the intrinsic ordering are derived. These properties involve the lexicographic (truth-table) order in {0, 1}n, the vector order defined between the vectors of positions of 1-bits of the binary n-tuples, and the number of 1-bits in the binary n-tuples (i.e., the Hamming weights). These results are illustrated through simple examples and the intrinsic order graph.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10553/445142012-01-01T00:00:00ZEdges, chains, shadows, neighbors and subgraphs in the intrinsic order graphhttp://hdl.handle.net/10553/44515Title: Edges, chains, shadows, neighbors and subgraphs in the intrinsic order graph
Authors: Gonźalez, Luis
Abstract: Many different scientific, technical or social phenomena can be modeled by a complex system depending on a large number n of random Boolean variables. Such systems are called complex stochastic Boolean systems (CSBSs). The most useful representation of a CSBS is the intrinsic order graph. This is a symmetric digraph on 2 n nodes, with a characteristic fractal structure. In this paper, different properties of the intrinsic order graph are studied, namely those dealing with its edges; chains; shadows, neighbors and degrees of its vertices; and some relevant subgraphs, as well as the natural isomorphisms between them.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10553/445152012-01-01T00:00:00ZNormalized Frobenius condition number of the orthogonal projections of the identityhttp://hdl.handle.net/10553/16394Title: Normalized Frobenius condition number of the orthogonal projections of the identity
Authors: Suárez Sarmiento, Antonio F.; González Sánchez, Luis
Abstract: This paper deals with the orthogonal projection (in the Frobenius sense) AN of the identity matrix I onto the matrix subspace AS (A ? Rn×n, S being an arbitrary subspace of Rn×n). Lower and upper bounds on the normalized Frobenius condition number of matrix AN are given. Furthermore, for every matrix subspace S ? Rn×n, a new index bF (A, S), which generalizes the normalized Frobenius condition number of matrix A, is defined and analyzed...
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10553/163942013-01-01T00:00:00ZComparison of the meccano method with standard mesh generation techniqueshttp://hdl.handle.net/10553/16392Title: Comparison of the meccano method with standard mesh generation techniques
Authors: Cascón, J. M.; Rodriguez, E.; Escobar, J. M.; Montenegro, R.
Abstract: 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 by 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…
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10553/163922013-01-01T00:00:00ZThe effect of parallelization on a tetrahedral mesh optimization methodhttp://hdl.handle.net/10553/45228Title: The effect of parallelization on a tetrahedral mesh optimization method
Authors: Rodríguez, Eduardo; Benítez Díaz, Domingo; Escobar Sánchez, José María; Montenegro Armas, Rafael
Abstract: A parallel algorithm for simultaneous untangling and smoothing of tetrahedral meshes is proposed in this paper. This algorithm is derived from a sequential mesh optimization method. We provide a detailed analysis of its parallel scalability and efficiency, load balancing, and parallelism bottlenecks using six benchmark meshes. In addition, the influence of three previously-published graph coloring techniques on the performance of our parallel algorithm is evaluated. We demonstrate that the proposed algorithm is highly scalable when run on a shared-memory computer with up to 128 Itanium 2 processors. However, some parallel deterioration is observed. Here, we analyze its main causes using a theoretical performance model and experimental results.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10553/452282014-01-01T00:00:00Z