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  • A surface mesh smoothing and untangling method independent of the CAD parameterization

     Gargallo Peiró, Abel; Roca Navarro, Xevi; Sarrate Ramos, Jose
    Computational Mechanics
    Vol. 53, num. 4, p. 587-609
    DOI: 10.1007/s00466-013-0920-1
    Date of publication: 2014-04-01
    Journal article

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    A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to check the quality and validity of a surface mesh. Then, we detail how to optimize any Jacobian-based distortion measure to obtain smoothed and untangled meshes with the nodes on the surface. We prove that this method is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations. The examples show that the method can optimize meshes composed by a large number of inverted elements. Finally, the method can be extended to obtain high-order meshes with the nodes on the CAD surfaces.

  • Validation and generation of curved meshes for high-order unstructured methods  Open access

     Gargallo Peiró, Abel
    Universitat Politècnica de Catalunya
    Theses

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    En aquesta tesis es presenta un nou marc per validar i generar malles corbes d¿alt ordre per models geomètrics complexos. La aplicació principal dels mètodes proposats és la generació de malles aptes per a realitzar anàlisis amb elements finits mitjançant mètodes d¿alt ordre no-estructurats. És important recalcar que la manca d¿un mallador robust i automàtic per malles corbes és un dels problemes principals que ha obstaculitzat la introducció dels mètodes d¿alt ordre a la indústria. Concretament, sense malles corbes d¿alt ordre composades per elements vàlids i tal que encaixi amb el contorn del domini, les taxes de convergència dels mètodes d¿alt ordre no es poden assolir. La motivació principal d¿aquest treball és, per tant, proporcionar un nou marc que corregeixi aquestes mancances.En primer lloc, proposem una nova mesura de distorsió (qualitat) per malles corbes de qualsevol grau polinòmic. Les mesures presentades permeten validar si una malla d¿alt ordre és apta per a l¿anàlisi d¿elements finits amb mètodes d¿alt ordre no-estructurats. En particular, donat un element d¿alt ordre, la mesura de qualitat assigna valor zero si l¿element és invàlid, i valor u si l¿element es correspon amb la configuració ideal triada (mida i distribució nodal desitjades). A més a més, demostrem que si la qualitat d¿un element és major que zero, la regió en la que el determinant de la Jacobiana de l¿element és no-positiva té mesura zero. Presentem diversos exemples per il¿lustrat que les mesures proposades poden ser usades per validar malles d¿alt ordre isotròpiques i de capa límit.En segon lloc, desenvolupem un mètode per suavitzar i desenredar malles d¿alt ordre. Específicament, proposem una minimització no-lineal global de la mesura de distorsió. La distorsió és regularitzada per tal de permetre desenredar malles que continguin elements invàlids. D¿altra banda, el procés d¿optimització preserva, quan és possible, diverses característiques geomètriques de la malla lineal (forma dels elements, costats rectes, i mida). Per mitjà de diversos exemples mostrem que la implementació del procés d¿optimització és robusta i capaç de lidiar amb configuracions en les que la malla inicial conté un gran nombre d¿elements invàlids. Considerem casos amb malles de fins a grau polinòmic deu, grans deformacions dels contorns corbs, contorns còncaus, i malles de capa límit amb un grans compressions.En tercer lloc, estenem la definició de mesura de distorsió i qualitat a malles corbes d¿alt ordre amb els nodes en superfícies parametritzades. Usant aquesta definició, proposem també un procediment de suavitat i desenredat per malles en superfícies CAD. Aquest procediment està expressat en termes de les coordenades paramètriques dels nodes de la malla per imposar que els nodes estiguin sempre sobre la geometria CAD. A la vegada, demostrem que el procediment és independent de la parametrització de la superfície. Per tant, el mètode pot optimitzar malles a superfícies CAD que estiguin definides per parametritzacions de baixa qualitat. Finalment, proposem un nou mètode per generar malles corbes d¿alt ordre, mitjançant un procediment a posteriori. El procediment consisteix en modificar una malla linear introduint primer nodes d¿alt ordre. En segon lloc, es desplacen els nodes de contorn per assegurar que estan exactament sobre la superfície CAD. I en tercer lloc, es suavitza i desenreda la malla per tal d¿obtenir una malla final d¿alt ordre corba que sigui vàlida. Finalment, incloem diversos exemples on mostrem que les malles generades són aptes per a realitzar anàlisis amb elements finits mitjançant mètodes no-estructurats d¿alt ordre.

    This thesis is divided into three separate volumes, which are consistent with the indifferent order in which they could be read. Two of them are dedicated to two masters of modern architecture, Mies and Utzon, who respectively personify two major architectural currents which share with unequal intensity the first half of the twentieth century: rationalism and realism or organic architecture. The third volume presents some important platforms of the architecture of Mesopotamia, Egypt and Greece, that shortlist of three architectural cultures which, according to Giedion, embodied the first spatial conception of architecture. This volume is presented here as an annex, as this thesis mainly analyzes various notions of platforms built during the twentieth century. But it was precisely from the reinterpretation of the platform, classical in essence, that those magnificent massive platforms of the antiquity rightly claimed their modern relevance. Both Mies and Utzon not only delimited their respective projects between two substantially horizontal layers, that of the ground and that of the roof, but also the formal characteristics of each of these episodes defined the key attributes and interests of their architecture. In both cases, however, it has been the plane of the roof which has raised more analysis and recognition: - In the case of Mies, his roofs, straight and flat without exception, have been the result of the evolution of certain structural typologies, in concrete and later on in steel, which also fulfilled a conception of programme that prioritized flexibility ahead of functionality . - In the case of Utzon, his deliberately wavy roofs, invariably of concrete, have been the most distinctive figurative feature of all his architecture, eclipsed under the impact of his most celebrated work, the Sydney Opera House. However, for the understanding of the architecture, of both Mies and Utzon, it would be erroneous not to put the episodes of their respective roofs in relation to their ground planes, mostly understood as platforms. It is necessary to believe therefore that the numerous essays that have focused on the top plane, that of the roof as the preferred objective of analysis or even as the only one, of their respective works, have done so knowing this dual relationship, assuming this reductionism as a strategy for a greater analytical depth. This work poses a similar license, focused in this case, however, on the other horizontal plane, the one underneath, the ground level, significantly less explored and, in the opinion of the author, equally relevant. From this reduction of the focal field, where the platform becomes the epicentre of the projects of both architects, this thesis has been carried out to state that: -Both in the case of Mies and in the one of Utzon, the use of the platform, far from being an isolated fact, became a constant in each of their respective careers. - Except for a few exceptions, determined by singular requirements of the environment or the programme, all of their respective platforms are massive, far from the light horizontal planes with which modern architecture was built. - Both in one case as in the other, the platform is systematically used as a mediation space, to interact with the environment and determine the limits of the project and as transition space (where one passes), to build the visual approach system of the compound. -Starting from a certain moment, corresponding to the mature stage of both architects, Platform and Access united an inseparable binomial, prevalent in the construction of ground floors of their respective architectures, which gave place to an episode, that of the elevated access, which characterized all of their work. The platform became the threshold of their architectures.

  • Preserving isotropic element size functions in adaptivity, quadrilateral and hexahedral mesh generation

     Ruiz Girones, Eloi; Roca Navarro, Xevi; Sarrate Ramos, Jose
    Advances in engineering software
    Vol. 65, p. 168-181
    Date of publication: 2013
    Journal article

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    In electric circuit theory, it is of great interest to compute the effective resistance between any pair of vertices of a network, as well as the Kirchhoff Index. During the last decade these parametres have been applied in Organic Chemistry as natural structural indexes different from the usual ones in order to achieve an improvement in the discrimination between different molecules which have similar structural behaviours. Moreover, a wide range of generalized Kirchhoff Indexes for some networks have been introduced. The objective of the present work is to obtain the Kirchhoff Index for a wide range of composite networks known as cluster networks

    In electric circuit theory, it is of great interest to compute the effective resistance between any pair of vertices of a network, as well as the Kirchhoff Index. During the last decade these parametres have been applied in Organic Chemistry as natural structural indexes different from the usual ones in order to achieve an improvement in the discrimination between different molecules which have similar structural behaviours. Moreover, a wide range of generalized Kirchhoff Indexes for some networks have been introduced. The objective of the present work is to obtain the Kirchhoff Index for a wide range of composite networks known as cluster networks.

  • Least-squares approximation of affine mappings for sweep mesh generation: Functional analysis and applications

     Roca Navarro, Xevi; Sarrate Ramos, Jose
    Engineering with computers
    Vol. 29, num. 1, p. 1-15
    DOI: 10.1007/s00366-012-0260-3
    Date of publication: 2013-01
    Journal article

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  • High-order mesh generation on CAD geometries

     Gargallo Peiró, Abel; Roca Navarro, Xevi; Peraire Guitart, Jaume; Sarrate Ramos, Jose
    International Conference on Adaptive Modeling and Simulation
    p. 301-312
    Presentation's date: 2013-06-04
    Presentation of work at congresses

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    We present a technique to extend Jacobian-based distortion (quality) measures for planar triangles to high-order isoparametric elements of any interpolation degree on CAD parameterized surfaces. The resulting distortion (quality) measures are expressed in terms of the parametric coordinates of the nodes. These extended distortion (quality) measures can be used to check the quality and validity of a high-order surface mesh. We also apply them to simultaneously smooth and untangle high-order surface meshes by minimizing the extended distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes. Thus, the nodes always lie on the surface. Finally, we include several examples to illustrate the application of the proposed technique.

    We present a technique to extend Jacobian-based distortion (quality) measures for planar triangles to high-order isoparametric elements of any interpolation degree on CAD parameterized surfaces. The resulting distortion (quality) measures are expressed in terms of the parametric coordinates of the nodes. These extended distortion (quality) measures can be used to check the quality and validity of a high-order surface mesh. We also apply them to simultaneously smooth and untangle high-order surface meshes by minimizing the extended distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes. Thus, the nodes always lie on the surface. Finally, we include several examples to illustrate the application of the proposed technique.

  • Meshing Maestro Poster Award 2012

     Gargallo Peiró, Abel; Sarrate Ramos, Jose
    Award or recognition

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  • SIMULACIONES NUMERICAS DE ALTA FIDELIDAD PARA UNA INGENIERIA ASISTIDA POR ORDENADOR FIABLE

     Fernandez Mendez, Sonia; Sarrate Ramos, Jose; Roca Navarro, Francisco Javier; Sala Lardies, Esther; Casoni Rero, Eva; Giorgiani, Giorgio
    Competitive project

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  • Untangling and smoothing of quadrilateral and hexahedral meshes

     Wilson, Tom; Sarrate Ramos, Jose; Roca Navarro, Xevi; Montenegro, Rafael; Escobar, José María
    International Conference on Engineering Computational Technology
    p. 36
    DOI: 10.4203/ccp.100.36
    Presentation's date: 2012-09-04
    Presentation of work at congresses

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  • Defining quality measures for mesh optimization on parameterized CAD surfaces

     Gargallo Peiró, Abel; Roca Navarro, Xevi; Peraire, Jaime; Sarrate Ramos, Jose
    International Meshing Roundtable
    p. 85-102
    DOI: 10.1007/978-3-642-33573-0_6
    Presentation's date: 2012-10-07
    Presentation of work at congresses

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    A new procedure to smooth and untangle meshes on parameterized surfaces  Open access

     Gargallo Peiró, Abel; Roca Navarro, Xevi; Sarrate Ramos, Jose
    European Congress on Computational Methods in Applied Sciences and Engineering
    p. 1-13
    Presentation's date: 2012-09-10
    Presentation of work at congresses

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    We present a technique to extend any distortion (quality) measure for planar meshes to meshes on parameterized surfaces. The resulting distortion (quality) measure is expressed in terms of the parametric coordinates of the nodes. This extended distortion (quality) measure can be used to check the quality and validity of both triangle and quadrilateral surface meshes. We also apply it to simultaneously smooth and untangle surface meshes by minimizing the extended distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes and therefore, the nodes always lie on the surface. Finally, we include several examples to illustrate the applicability of the proposed technique. Specifically, we extend several Jacobian-based measures, and we us them to smooth and untangle triangle and quadrilateral meshes on CAD surfaces.

    Postprint (author’s final draft)

  • Unstructures hexahedral mesh generation for esterior domains by the receding front method

     Ruiz Girones, Eloi; Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    Congreso en Métodos Numéricos em Engenharia
    p. 211-
    Presentation's date: 2011-06-15
    Presentation of work at congresses

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  • Unstructured hexaedral mesh generation for exteroir domains by the receding front method

     Ruiz Girones, Eloi; Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    Congresso de Métodos Numéricos em Engenharia
    p. 1-17
    Presentation's date: 2011-06-14
    Presentation of work at congresses

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  • Q-00024

     Sarrate Ramos, Jose; Diez Mejia, Pedro
    Competitive project

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  • Automatic Hexahedral meshing algorithms: From structured to unstructured meshes

     Ruiz Girones, Eloi
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
    Theses

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  • Automatic hexaedral meshing algorithms: from structured to unstructured meshes

     Ruiz Girones, Eloi
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
    Theses

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  • The receding front method applied to hexahedral mesh generation of exterior domains

     Ruiz Girones, Eloi; Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    Engineering with computers
    Vol. 28, num. 4, p. 391-408
    DOI: 10.1007/s00366-011-0233-y
    Date of publication: 2011-11-30
    Journal article

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  • Using a computational domain and a three-stage node location procedure for multi-sweeping algorithms

     Ruiz Girones, Eloi; Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    Advances in engineering software
    Vol. 42, num. 9, p. 700-713
    DOI: 10.1016/j.advengsoft.2011.05.006
    Date of publication: 2011
    Journal article

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  • Defining quality measures for high-order planar triangles and curved mesh generation

     Roca Navarro, Xevi; Gargallo Peiró, Abel; Sarrate Ramos, Jose
    International Meshing Roundtable
    p. 365-383
    DOI: 10.1007/978-3-642-24734-7_20
    Presentation's date: 2011-10-23
    Presentation of work at congresses

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    Generation of structured meshes in multiply connected surfaces using submapping  Open access

     Ruiz Girones, Eloi; Sarrate Ramos, Jose
    Advances in engineering software
    Vol. 41, num. 2, p. 379-387
    DOI: 10.1016/j.advengsoft.2009.06.009
    Date of publication: 2010-02
    Journal article

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    The submapping method is one of the most widely used techniques to generate structured quadrilateral meshes. This method splits the geometry into pieces logically equivalent to a quadrilateral. Then, it meshes each piece keeping the mesh compatibility between them by solving an integer linear problem. The main limitation of submapping algorithms is that it can only be applied to geometries in which the angle between two consecutive edges is, approximately, an integer multiple of p=2. In addition, special procedures are required in order to apply it to multiply connected domains. This article presents two original modifications to mitigate these shortcomings. Finally, it presents several numerical examples that show the applicability of the developed algorithms.

    Postprint (author’s final draft)

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    An automatic and general least-squares projection procedure for sweep meshing  Open access

     Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    Engineering with computers
    DOI: 10.1007/s00366-009-0172-z
    Date of publication: 2010-01-07
    Journal article

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    In this paper, we present a new and automatic node projection algorithm to generate hexahedral meshes in extrusion geometries. It is designed to preserve the shape of the cap surfaces in the inner layers of a sweeping mesh. The algorithm is based on least-squares approximation of affine mappings. We report that the functionals that have been traditionally used to compute the affine mapping generate four undesired effects on the inner layers of nodes. Namely, the flattening, skewing, offset scaling, and flipping of the inner layer meshes. To overcome these drawbacks we first analyze several properties of a new functional that depends on two vector parameters. Second, we introduce the concept of the pseudo-area and pseudo-normal vectors defined by a loop of nodes. In addition, we prove several geometrical properties of these vectors. Third, based on the properties of the new functional and on the definition of the pseudo-normal vector, we detail a new projection algorithm that automatically selects the functional vector parameters. The aim of this paper is to provide the implementation details to developers, although we also present the background of the algorithm. Finally, several mesh examples are discussed to assess the properties of the proposed algorithm.

  • A new least-squares approximation of affine mappings for sweep algorithms.

     Roca Navarro, Francisco Javier; Sarrate Ramos, Jose; Huerta Cerezuela, Antonio
    Engineering with computers
    Vol. 26, num. 3, p. 327-337
    DOI: 10.1007/s00366-009-0161-2
    Date of publication: 2010
    Journal article

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    Local dual contributions: representing dual surfaces for block meshing  Open access

     Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    International journal for numerical methods in engineering
    Vol. 83, num. 6, p. 709-740
    DOI: 10.1002/nme.2852
    Date of publication: 2010-08-06
    Journal article

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    In this work we present a tool based on the new concept of local dual contributions for directly representing the topology and the approximated geometry of the dual of a block mesh. This tool allows us to obtain a valid block decomposition of a given geometry without a previous discretization of its boundary. Specifically, our tool is composed of a hierarchical scheme and a set of matching rules that explicitly insert descriptions of dual surfaces and handle their intersections. That is, the proposed tool generates a dual of the block mesh with intersections of the proper multiplicity without gaps and which respects the boundary features of the domain. Finally, we present several examples that illustrate the applicability of the tool.

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    Generation of structured hexahedral meshes in volumes with holes  Open access

     Ruiz Girones, Eloi; Sarrate Ramos, Jose
    Finite elements in analysis and design
    Vol. 46, num. 10, p. 792-804
    DOI: 10.1016/j.finel.2010.04.005
    Date of publication: 2010-10
    Journal article

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    The submapping method is one of the most used techniques to generate structured hexahedral meshes. This method splits the geometry into pieces logically equivalent to an hexahedron. Then, it meshes each patch keeping the mesh compatibility between pieces by solving an integer linear problem. The quality of the final discretization is governed by the objective function that defines the linear problem. Thus, in this work we propose a new objective function that better distributes the number of intervals among the edges of the geometry. In addition, special procedures have to be developed in order to apply the submapping method to volumes with holes. This article also presents two original contributions to efficiently mesh geometries that contain holes. Finally, it presents several numerical examples that show the applicability of the developed algorithms.

  • Receding front method: a new approach applied to generate hexahedral meshes of outer domains

     Roca Navarro, Francisco Javier; Ruiz Girones, Eloi; Sarrate Ramos, Jose
    International Meshing Roundtable
    p. 1-17
    DOI: 10.1007/978-3-642-15414-0_13
    Presentation of work at congresses

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    Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high quality elements in the inner part of the domain using an inside-outside approach. On the other hand, advancing front methods generate high quality hexahedra near the boundary using an outside-inside approach. In this paper we propose the receding front method, an original approach that combines the advantages of both methodologies: we use an inside-outside mesh generation approach by means of a reversed front advance. We apply this approach to mesh outer domains. To reproduce the shape of the boundaries, we first precompute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide. Further research is under way in order to apply the proposed method to more complicated geometries.

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    Automatic generation of hexahedral meshes for volumes with non-planar surfaces using the multi-sweeping method  Open access

     Ruiz Girones, Eloi; Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    International Conference on Engineering Computational Technology
    p. 1-19
    DOI: 10.4203/ccp.94.58
    Presentation's date: 2010
    Presentation of work at congresses

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    One of the most used algorithms to generate hexahedral meshes for extrusion volumes is the multi-sweeping method. The algorithm decomposes the geometry into many-to-one sub-volumes and then meshes each sub-volume separately. However, the quality of the final mesh depends on the decomposition process. First, the location of inner nodes created during the decomposition process may induce bad quality elements. To avoid this drawback, we propose a three-stage decomposition process to locate those nodes. Second, the imprinting process is not robust when dealing with non-planar surfaces. For this reason, we introduce the new concept of the computational domain. The computational domain is a planar representation of the levels of the geometry. In this way, we improve the operations needed to perform imprints.

  • Inside-to-outside hex-meshing approach guided by level sets of distance functions

     Roca Navarro, Francisco Javier; Ruiz Girones, Eloi; Sarrate Ramos, Jose
    Hex Meshing and CFD blocking seminar
    Presentation's date: 2010
    Presentation of work at congresses

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  • MÈTODES NUMÈRICS EN CIÈNCIES APLICADES I ENGINYERIA

     Roca Navarro, Francisco Javier; Giorgiani, Giorgio; Zlotnik, Sergio; Fernandez Mendez, Sonia; Rodriguez Ferran, Antonio; Muñoz Romero, Jose Javier; Arias Vicente, Irene; de Villardi de Montlaur, Adeline; Sarrate Ramos, Jose; Diez Mejia, Pedro; Arroyo Balaguer, Marino; Sevilla Cardenas, Ruben; Parés Mariné, Núria; Casoni Rero, Eva; Ruiz Girones, Eloi; Modesto Galende, David; Millan, Raul Daniel; Abdollahi Hosnijeh, Amir; Steffens, Lindaura Maria; Discacciati, Marco; Shen, Yongxing; Rahimi Lenji, Mohammad; Tamayo Mas, Elena; Diaz Cereceda, Cristina; Prat Robles, David; Verdugo Rojano, Francesc; Zhang, Kuan; Estela Carbonell, M. Rosa; Peco Regales, Christian; Huerta Cerezuela, Antonio
    Competitive project

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    A new procedure to compute imprints in multi-sweeping algorithms  Open access

     Ruiz Girones, Eloi; Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    International Meshing Roundtable
    p. 281-299
    Presentation's date: 2009-10-26
    Presentation of work at congresses

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    One of the most widely used algorithms to generate hexahedral meshes in extrusion volumes with several source and target surfaces is the multi-sweeping method. However, the multi-sweeping method is highly dependent on the final location of the nodes created during the decomposition process. Moreover, inaccurate location of inner nodes may generate erroneous imprints of the geometry surfaces such that a final mesh could not be generated. In this work, we present a new procedure to decompose the geometry in many-to-one sweepable volumes. The decomposition is based on a least-squares approximation of affine mappings defined between the loops of nodes that bound the sweep levels. In addition, we introduce the concept of computational domain, in which every sweep level is planar. We use this planar representation for two purposes. On the one hand, we use it to perform all the imprints between surfaces. Since the computational domain is planar, the robustness of the imprinting process is increased. On the other hand, the computational domain is also used to compute the projection onto source surfaces. Finally, the location of the inner nodes created during the decomposition process is computed by averaging the locations computed projecting from target and source surfaces.

  • Descomposición automática de mallas por bloques mediante contribuciones duales locales

     Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    Congreso de Métodos Numéricos en Ingeniería
    p. 193
    Presentation's date: 2009-06-29
    Presentation of work at congresses

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  • Generación automática de mallas de hexaedros mediante many-to-many sweeping

     Roca Navarro, Francisco Javier; Sarrate Ramos, Jose
    Congreso de Métodos Numéricos en Ingeniería
    p. 196
    Presentation's date: 2009-06-29
    Presentation of work at congresses

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  • Paving the path towards automatic hexahedral mesh generation  Open access

     Roca Navarro, Francisco Javier
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
    Theses

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    Esta tesis versa sobre el desarrollo de las tecnologías para la generación de mallas de hexaedros. El proceso de generar una malla de hexaedros no es automático y su generación requiere varias horas te trabajo de un ingeniero especializado. Por lo tanto, es importante desarrollar herramientas que faciliten dicho proceso de generación. Con este fin, se presenta y desarrolla un método de proyección de mallas, una técnica de sweeping o barrido, un algoritmo para la obtención de mallas por bloques, y un entorno de generación de mallas. Las implementaciones más competitivas del método de sweeping utilizan técnicas de proyección de mallas basadas en métodos afines. Los métodos afines más habituales presentan varios problemas relacionados con la obtención de sistemas de ecuaciones normales de rango deficiente. Para solucionar dichos problemas se presenta y analiza un nuevo método afín que depende de dos parámetros vectoriales. Además, se detalla un procedimiento automático para la selección de dichos vectores. El método de proyección resultante preserva la forma de las mallas proyectadas. Esta proyección es incorporada también en una nueva herramienta de sweeping. Dicha herramienta genera capas de nodos internos que respetan la curvatura de las superficies inicial y final. La herramienta de sweeping es capaz de mallar geometrías de extrusión definidas por trayectorias curvas, secciones no constantes a lo largo del eje de sweeping, y superficies inicial y final con diferente forma y curvatura.En las últimas décadas se han propuesto varios ataques para la generación automática de mallas de hexahedros. Sin embargo, todavía no existe un algoritmo rápido y robusto que genere automáticamente mallas de hexaedros de alta calidad. Se propone un nuevo ataque para la generación de mallas por bloques mediante la representación de la geometría y la topología del dual de una malla de hexaedros. En dicho ataque, primero se genera una malla grosera de tetraedros. Después, varió polígonos planos se añaden al interior de los elementos de la malla grosera inicial. Dichos polígonos se denotan como contribuciones duales locales y representan una versión discreta del dual de una malla de hexaedros. En el último paso, la malla por bloques se obtiene como el dual de la representación del dual generada. El algoritmo de generación de mallas por bloques es aplicado a geometrías que presentan diferentes características geométricas como son superficies planas, superficies curvas, configuraciones delgadas, agujeros, y vértices con valencia mayor que tres.Las mallas se generan habitualmente con la ayuda de entornos interactivos que integran una interfaz CAD y varios algoritmos de generación de mallas. Se presenta un nuevo entorno de generación de mallas especializado en la generación de cuadriláteros y hexaedros. Este entorno proporciona la tecnología necesaria para implementar les técnicas de generación de mallas de hexaedros presentadas en esta tesis.

    This thesis deals with the development of hexahedral mesh generation technology. The process of generating hexahedral meshes is not fully automatic and it is a time consuming task. Therefore, it is important to develop tools that facilitate the generation of hexahedral meshes. To this end, a mesh projection method, a sweeping technique, a block-meshing algorithm, and an interactive mesh generation environment are presented and developed. Competitive implementations of the sweeping method use mesh projection techniques based on affine methods. Standard affine methods have several drawbacks related to the statement of rank deficient sets of normal equations. To overcome these drawbacks a new affine method that depends on two vector parameters is presented and analyzed. Moreover, an automatic procedure that selects these two vector parameters is detailed. The resulting projection procedure preserves the shape of projected meshes. Then, this procedure is incorporated in a new sweeping tool. This tool generates inner layers of nodes that preserve the curvature of the cap surfaces. The sweeping tool is able to mesh extrusion geometries defined by non-linear sweeping trajectories, non-constant cross sections along the sweep axis, non-parallel cap surfaces, and cap surfaces with different shape and curvature. In the last decades, several general-purpose approaches to generate automatically hexahedral meshes have been proposed. However, a fast and robust algorithm that automatically generates high-quality hexahedral meshes is not available. A novel approach for block meshing by representing the geometry and the topology of a hexahedral mesh is presented. The block-meshing algorithm first generates an initial coarse mesh of tetrahedral elements. Second, several planar polygons are added inside the elements of the initial coarse mesh. These polygons are referred as local dual contributions and represent a discrete version of the dual of a hexahedral mesh. Finally, the dual representation is dualized to obtain the final block mesh. The block-meshing algorithm is applied to mesh geometries that present different geometrical characteristics such as planar surfaces, curved surfaces, thin configurations, holes, and vertices with valence greater than three.Meshes are usually generated with the help of interactive environments that integrate a CAD interface and several meshing algorithms. An overview of a new mesh generation environment focused in quadrilateral and hexahedral mesh generation is presented. This environment provides the technology required to implement the hexahedral meshing techniques presented in this thesis.

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    Discretización de superficies múltiplemente conexas mediante submapping  Open access

     Ruiz Girones, Eloi; Sarrate Ramos, Jose
    Revista internacional de métodos numéricos para cálculo y diseño en ingeniería
    Vol. 24, num. 2, p. 163-181
    Date of publication: 2008-09
    Journal article

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    Una de las técnicas más utilizadas para generar mallas estructuradas de cuadriláteros es el método de submapping. Este método descompone la geometría en piezas lógicamente equivalentes a un cuadrilátero y después malla cada una de ellas por separado manteniendo la compatibilidad de la malla mediante la resolución de un problema lineal entero. El algoritmo de submapping tiene dos limitaciones principales. La primera de ellas es que sólo se puede aplicar en geometrías tales que el ángulo entre dos aristas consecutivas es, aproximadamente, un múltiplo entero de π/2. La segunda limitación es que la geometría tiene que ser simplemente conexa. Con el objetivo de mitigar estas restricciones, en este artículo se presentan dos modificaciones originales que permiten reducir el efecto de dichas limitaciones. Finalmente, se presentan diversos ejemplos numéricos que ponen de manifiesto la robustez y la aplicabilidad de los algoritmos desarrollados.

  • Automatic generation of structured hexahedral meshes for non-simply connected geometries using submapping

     Sarrate Ramos, Jose; Ruiz Gironés, Eloi
    International Conference on Engineering Computational Technology
    p. 1-13
    Presentation's date: 2008-09-02
    Presentation of work at congresses

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  • Local dual contributions on simplices: a tool for block meshing

     Roca, X.; Sarrate Ramos, Jose
    International Meshing Roundtable
    p. 513-531
    Presentation's date: 2008-10-13
    Presentation of work at congresses

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  • Modelització numérica d'estructures e infraestructures: disseny, durabilitat y estats límit.

     Sarrate Ramos, Jose; Huerta Cerezuela, Antonio
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  • Modelización numérica de flujos, solidos y estructuras para aplicaciones industriales

     de Villardi de Montlaur, Adeline; Diez Mejia, Pedro; Estela Carbonell, M. Rosa; Arias Vicente, Irene; Fernandez Mendez, Sonia; Sarrate Ramos, Jose; Vidal Segui, Yolanda; Parés Mariné, Núria; Sevilla Cardenas, Ruben; Casoni Rero, Eva
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  • Modelización numérica de estructuras e infraestructuras: diseño, durabilidad y estados limite

     Muñoz Romero, Jose Javier; Huerta Cerezuela, Antonio; Sarrate Ramos, Jose; Parés Mariné, Núria; Vidal Segui, Yolanda; Roca Navarro, Francisco Javier; Poblet Puig, Jordi; Rodriguez Ferran, Antonio
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  • Diseny Workpack per a una Casa d'Acer

     Rodriguez Ferran, Antonio; Huerta Cerezuela, Antonio; Diez Mejia, Pedro; Sarrate Ramos, Jose
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  • Automatic Generation of Structured Meshes Using Linear Programming and Transfinite Interpolation Artículo

     Ruiz, E; Sarrate Ramos, Jose
    Congresso de Métodos Numéricos em Engenharia
    p. 1-15
    Presentation of work at congresses

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  • A Graphical Modeling and Mesh Generation Environment for Simulations Based on Boundary Representation Data

     Roca Navarro, Francisco Javier; Sarrate Ramos, Jose; Ruiz-Gironés, E
    Congresso de Métodos Numéricos em Engenharia
    p. 1-20
    Presentation's date: 2007-06-13
    Presentation of work at congresses

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  • Quadrilateral mesh generation over parametric surfaces

     Sarrate Ramos, Jose; Roca Navarro, Francisco Javier
    Chilean Workshop on Numerical Analysis of Partial Differential Equations
    p. 96
    Presentation's date: 2007-01-16
    Presentation of work at congresses

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  • Developing a graphical modeling and mesh generation evironment using open sourde software

     Sarrate Ramos, Jose; Roca Navarro, Francisco Javier; Ruiz-Gironés, E
    International Conference on Adaptive Modeling and Simulation
    p. 214-217
    Presentation's date: 2007-10-22
    Presentation of work at congresses

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  • Aproximacion Mediante Mínimos Cuadrados de Proyecciones Afines para la Generacion de Hexaedros en Algoritmos de Barrido

     Sarrate Ramos, Jose; Roca Navarro, Francisco Javier
    Congresso de Métodos Numéricos em Engenharia
    p. 1-25
    Presentation's date: 2007-06-13
    Presentation of work at congresses

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  • Fomento de las acciones de innovación pedagógica en la Ingeniería Civil

     Sarrate Ramos, Jose
    International Conference on Adaptive Modeling and Simulation
    p. 5-6
    Presentation of work at congresses

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    Minimización de la distorsión de mallas formadas por cuadriláteros o hexaedros  Open access

     Sarrate Ramos, Jose; Coll, Abel
    Revista internacional de métodos numéricos para cálculo y diseño en ingeniería
    Vol. 23, num. 1, p. 55-76
    Date of publication: 2007
    Journal article

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    En este artículo se presenta un algoritmo para la minimización de la medida de la distorsión definida por Oddy para una malla formada por cuadriláteros o hexaedros. Aunque dicha medida ha sido ampliamente utilizada, su definición original presenta varias propiedades que limitan su utilización en un algoritmo de minimización. Por ejemplo, sólo es válida para cuadriláteros o hexaedros convexos y proporciona un valor infinito de la distorsión en un cuadrilátero en el que tres vértices están alineados. Con el fin de superar estas limitaciones, en este trabajo primero se deduce una interpretación geométrica de la definición original de la medida de la distorsión. Además se demuestra que dicha interpretación es válida tanto para cuadriláteros como para hexaedros. Seguidamente y basándose en dicha interpretación, se desarrolla una medida de la distorsión para cuadriláteros y hexaedros no convexos. Finalmente, se presenta un algoritmo para la minimización de la nueva medida de la distorsión de la malla basado en el método de Newton-Raphson. Es importante resaltar que ambas definiciones coinciden cerca de la solución óptima. Así mismo, se presentan varios ejemplos que confirman la eficiencia del algoritmo desarrollado.

  • Minimization of the distortion of quadrilateral and hexahedral meshes

     Sarrate Ramos, Jose; COLL, A
    Revista internacional de métodos numéricos para cálculo y diseño en ingeniería
    Vol. 23, num. 1, p. 55-76
    Date of publication: 2007-01
    Journal article

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  • Verificación y validación de modelos numéricos en medio poroso

     Diez Mejia, Pedro; Arias Vicente, Irene; Arroyo Balaguer, Marino; Sarrate Ramos, Jose
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  • Generación y adaptación de mallas

     Diez Mejia, Pedro; Sarrate Ramos, Jose
    Competitive project

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  • Ajudes per a la financiació de grups d'investigació de Catalunya. (Grup consolidat d'investigació en el marc del Plan d'Investigació e Innovació de Catalunya 2005-2008)

     Huerta Cerezuela, Antonio; Sala Lardies, Esther; Rodriguez Ferran, Antonio; Arias Vicente, Irene; Pérez Foguet, Agustí; Arroyo Balaguer, Marino; Fernandez Mendez, Sonia; Sarrate Ramos, Jose
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