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1 to 50 of 327 results
  • Error assessment in structural transient dynamics

     Verdugo Rojano, Francesc; Parés Mariné, Núria; Diez Mejia, Pedro
    Archives of computational methods in engineering
    Date of publication: 2014-03-01
    Journal article

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    This paper presents in a unified framework the most representative state-of-the-art techniques on a posteriori error assessment for second order hyperbolic problems, i.e., structural transient dynamics. For the sake of presentation, the error estimates are grouped in four types: recovery-based estimates, the dual weighted residual method, the constitutive relation error method and error estimates for timeline-dependent quantities of interest. All these methodologies give a comprehensive overview on the available error assessment techniques in structural dynamics, both for energy-like and goal-oriented estimates.

  • Computable exact bounds for linear outputs from stabilized solutions of the advection-diffusion-reaction equation

     Parés Mariné, Núria; Diez Mejia, Pedro; Huerta Cerezuela, Antonio
    International journal for numerical methods in engineering
    Date of publication: 2013-02-01
    Journal article

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  • Streamline upwind/Petrov¿Galerkin-based stabilization of proper generalized decompositions for high-dimensional advection¿diffusion equations

     González, David; Cueto, Elias; Chinesta, Francisco; Diez Mejia, Pedro; Huerta Cerezuela, Antonio
    International journal for numerical methods in engineering
    Date of publication: 2013-06
    Journal article

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    This work is a first attempt to address efficient stabilizations of high dimensional advection-diffusion models encountered in computational physics. When addressing multidimensional models, the use of mesh-based discretization fails because the exponential increase of the number of degrees of freedom related to a multidimensional mesh or grid, and alternative discretization strategies are needed. Separated representations involved in the so-called proper generalized decomposition method are an efficient alternative as proven in our former works; however, the issue related to efficient stabilizations of multidimensional advection-diffusion equations has never been addressed to our knowledge. Thus, this work is aimed at extending some well-experienced stabilization strategies widely used in the solution of 1D, 2D, or 3D advection-diffusion models to models defined in high-dimensional spaces, sometimes involving tens of coordinates

  • An algorithm for mesh refinement and un-refinement in fast transient dynamics

     Casadei, Folco; Diez Mejia, Pedro; Verdugo Rojano, Francesc
    International journal of computational methods
    Date of publication: 2013-08
    Journal article

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    A procedure to locally refine and un-refine an unstructured computational grid of four-node quadrilaterals (in 2D) or of eight-node hexahedra (in 3D) is presented. The chosen refinement strategy generates only elements of the same type as their parents, but also produces so-called hanging nodes along nonconforming element-to-element interfaces. Continuity of the solution across such interfaces is enforced strongly by Lagrange multipliers. The element split and un-split algorithm is entirely integer-based. It relies only upon element connectivity and makes no use of nodal coordinates or other real-number quantities. The chosen data structure and the continuous tracking of the nature of each node facilitate the treatment of natural and essential boundary conditions in adaptivity. A generalization of the concept of neighbor elements allows transport calculations in adaptive fluid calculations. The proposed procedure is tested in structure and fluid wave propagation problems in explicit transient dynamics

  • Modal-based goal-oriented error assessment for timeline-dependent quantities in transient dynamics

     Verdugo Rojano, Francesc; Parés Mariné, Núria; Diez Mejia, Pedro
    International journal for numerical methods in engineering
    Date of publication: 2013-08-24
    Journal article

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    This article presents a new approach to assess the error in specific quantities of interest in the framework of linear elastodynamics. In particular, a new type of quantities of interest (referred as timeline-dependent quantities) is proposed. These quantities are scalar time-dependent outputs of the transient solution, which are better suited to time-dependent problems than the standard scalar ones, frozen in time. The proposed methodology furnishes error estimates for both the standard scalar and the new timeline-dependent quantities of interest. The key ingredient is the modal-based approximation of the associated adjoint problems, which allows efficiently computing and storing the adjoint solution. The approximated adjoint solution is readily post-processed to produce an enhanced solution, requiring only one spatial post-process for each vibration mode and using the time-harmonic hypothesis to recover the time dependence. Thus, the proposed goal-oriented error estimate consists in injecting this enhanced adjoint solution into the residual of the direct problem. The resulting estimate is very well suited for transient dynamic simulations because the enhanced adjoint solution is computed before starting the forward time integration of the direct problem. Thus, the cost of the error estimate at each time step is very low.

    This article presents a new approach to assess the error in specific quantities of interest in the framework of linear elastodynamics. In particular, a new type of quantities of interest (referred as timeline-dependent quantities) is proposed. These quantities are scalar time-dependent outputs of the transient solution, which are better suited to time-dependent problems than the standard scalar ones, frozen in time. The proposed both the standard scalar and the new timeline-dependent quantities of interest. The key ingredient is the modal-based approximation of the associated adjoint problems, which allows efficiently computing and storing the adjoint solution. The approximated adjoint solution is readily post-processed to produce an enhanced solution, requiring only one spatial post-process for each vibration mode and using the time-harmonic hypothesis to recover the time dependence. Thus, the proposed goal-oriented error estimate consists in injecting this enhanced adjoint solution into the residual of the direct problem. The resulting estimate is very well suited for transient dynamic simulations because the enhanced adjoint solution is computed before starting the forward time integration of the direct problem. Thus, the cost of the error estimate at each time step is very low.

  • Error assessment and adaptivity for structural transient dynamics

     Verdugo Rojano, Francesc
    Defense's date: 2013-10-15
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
    Theses

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    El mètode dels elements finits és una eina valuosa per a simular fenòmens físics complexos. Tot i això, aquest mètode només proporciona aproximacions de la solució exacta del model físic considerat. Per tant, quantificar l'error comés en l'aproximació és important si la simulació numèrica s'utilitza per a prendre decisions que poden tenir importants conseqüències. Actualment, les eines que permeten avaluar aquest error són ben conegudes per a problemes estacionaris, però encara presenten importants limitacions per a problemes transitoris com la dinàmica d'estructures.L'objectiu d'aquest treball és contribuir a millorar les tècniques existents per estimar l'error en dinàmica d'estructures i proposar-ne de noves. La primera contribució és una nova metodologia per a calcular cotes de l'error en una quantitat d'interès del problema. Les cotes proposades són més precises i proporcionen una millor estima de l'error que les cotes calculades amb tècniques prèvies. La segona contribució és una una nova tècnica que proporciona aproximacions de l'error en una quantitat d'interès utilitzant càlculs eficients. La novetat principal d'aquesta proposta és aproximar la solució del problema adjunt associat a la quantitat d'interès utilitzant l'anàlisi modal. El resultat és un estimador de l'error indicat particularment per a problemes transitoris, ja que el cost de calcular l'estimador a cada pas de temps és molt baix. La tercera contribució és una tècnica que permet construir de manera adaptada tant la discretizació temporal com espacial amb l'objectiu de millorar l'eficiència de la simulació. Aquesta tècnica es basa en la informació proporcionada per l'estima de l'error amb anàlisi modal. Les aproximacions calculades utilitzant les discretitzacions adaptades són més precises que les obtingudes amb un simple refinament uniforme de la malla de càlcul. És a dir, les discretitzacions adaptades proporcionen un error en la quantitat d'interès menor que les discretizacions no adaptades per al mateix nombre d'elements espai-temps. Finalment, la quarta contribució és un nou tipus de quantitats d'interès especialment indicades per a estimar l'error en problemes transitoris. Aquest nou tipus de quantitats són funcions escalars dependents del temps que proporcionen una informació més completa sobre l'error en problemes transitoris que les quantitats d'interès estàndard. L'error en aquestes noves quantitats és estimat eficientment utilitzant la descripció modal de la solució del problema adjunt.Les contribucions d'aquest treball es troben recopilades en cinc articles que s'inclouen adjunts en el document de la tesi.

  • A stable extended FEM formulation for multi-phase problems enforcing the accuracy of the fluxes through Lagrange multipliers

     Diez Mejia, Pedro; Cottereau, Régis; Zlotnik, Sergio
    International journal for numerical methods in engineering
    Date of publication: 2013-11
    Journal article

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    When applied to diffusion problems in a multi-phase setup, the popular extended finite element method (XFEM) strategy suffers from an inaccurate representation of the local fluxes in the vicinity of the interface. The XFEM enrichment improves the global quality of the solution but it is not enforcing any local feature to the fluxes. Thus, the resulting numerical fluxes in the vicinity of the interface are not realistic, in particular when conductivity ratios between the different phases are very high. This paper introduces an additional restriction to the XFEM formulation aiming at properly reproducing the features of the local fluxes in the transition zone. This restriction is implemented through Lagrange multipliers, and the stability of the resulting mixed formulation is tested satisfactorily through the Chapelle-Bathe numerical procedure. Several examples are presented, and the solutions obtained show a spectacular improvement with respect to the standard XFEM.

  • PGD-based ¿Computational Vademecum¿ for efficient design, optimization and control

     Chinesta, Francisco; Leygue, Adrien; Bordeu, F.; Cueto Prendes, Elias; González, David; Alfaro, Icíar; Ammar, Amine; Huerta Cerezuela, Antonio; Diez Mejia, Pedro
    IACM expressions: Bulletin for the international association for computational mechanics
    Date of publication: 2013
    Journal article

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    D espite the impressive progresses attained by simulation capabilities and techniques, some challenging problems remain today intractable. These prob- lems, that are common to many branches of science and engineering, are of differ- ent nature. Among them, we can cite those related to high-dimensional models, on which mesh-based approaches fail due to the exponential increase of degrees of freedom. Other challenging scenarios concern problems requiring many direct solutions (optimization, inverse identifica- tion, uncertainty quantification ! ) or those needing very fast solutions (real time simulation, simulation based control ! ).

  • Non intrusive stochastic simulations using a goal oriented adaptive strategy

     Florentin, Eric; Diez Mejia, Pedro
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2013-06-04
    Presentation of work at congresses

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  • Goal-oriented error control for dynamical and evolutionary systems: assessing time-line dependent quantities of interest

     Diez Mejia, Pedro; Verdugo Rojano, Francesc; Parés Mariné, Núria
    International Conference on Computational Methods for Coupled Problems in Science and Engineering
    Presentation's date: 2013-06-17
    Presentation of work at congresses

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  • Error assessment for timeline-dependent quantities of interest in transient elastodynamics

     Verdugo Rojano, Francesc; Parés Mariné, Núria; Diez Mejia, Pedro
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2013-06-04
    Presentation of work at congresses

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    This work presents a new approach to assess the error in speci c quantities of interest in the framework of linear elastodynamics. In particular, a new type of quantities of interest (referred as timeline-dependent quantities) is proposed. These quantities are scalar time-dependent outputs of the transient solution which are better suited to time-dependent problems than the standard scalar ones available in the literature. The proposed methodology furnishes error estimates for both the standard scalar and the new timeline-dependent quantities of interest. The key ingredient is the modal-based approximation of the associated adjoint problems which allows e ciently computing and storing the adjoint solution.

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    Computable bounds of functional outputs in linear visco-elastodynamics  Open access

     Verdugo Rojano, Francesc; Diez Mejia, Pedro
    Computer methods in applied mechanics and engineering
    Date of publication: 2012
    Journal article

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    This work presents a new technique yielding computable bounds of quantities of interest in the framework of linear visco-elastodynamics. A novel expression for the error representation is introduced, alternative to the previous ones using the Cauchy-Schwarz inequality. The proposed formulation utilizes symmetrized forms of the error equations to derive error bounds in terms of energy error measures. The practical implementation of the method is based on constructing admissible elds for both the original problem and the adjoint problem associated with the quantity of interest. Here, the ux-free technique is considered to compute the admissible stress elds. The proposed methodology yields estimates with better quality than the ones based on the Cauchy-Schwarz inequality. In the studied examples the bound gaps obtained are approximately halved, that is the estimated intervals of con dence are reduced.

  • Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems

     Florentin, Eric; Diez Mejia, Pedro
    Computer methods in applied mechanics and engineering
    Date of publication: 2012
    Journal article

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  • Enforcing interface flux continuity in enhanced XFEM: stability analysis

     Diez Mejia, Pedro; Zlotnik, Sergio; Cottereau, Régis
    Oberwolfach reports
    Date of publication: 2012
    Journal article

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  • Numerical Approach For Modeling Steel Fiber Reinforced Concrete  Open access

     Pros Parés, Alba
    Defense's date: 2012-02-06
    Universitat Politècnica de Catalunya
    Theses

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    One alternative to overcome the main drawbacks of plain concrete in tension (its brittleness and weakness) is Steel Fiber Reinforced Concrete (SFRC), a technique introduced in the 70's, which consists of adding steel fibers into the concrete matrix. Due to the presence of the steel fibers into the concrete matrix, the residual strength and the energy dissipation of the material increase. Moreover, once a crack appears in the concrete, the steel fibers sew this fissure. The shape, the length and the slenderness of the fibers influence on the SFRC behavior. Moreover, the distribution and the orientation of the fibers into the concrete domain must be taken into account for characterizing the material. In order to characterize the behavior of SFRC, a numerical tool is needed. The aim is to simulate the most standard and common tests (direct and indirect tension tests, flexural test, double punch tes,¿) and more complex setups. This thesis proposes a numerical tool for modeling SFRC avoiding homogenized models (not accurate enough) and conformal meshes (too expensive). Therefore, the numerical tool accounts for the actual geometry of the fibers, discretized as 1D bars nonconformal with the concrete bulk mesh (2D or 3D domains). The two materials, corresponding to the concrete bulk and the fiber cloud, are defined independently, but coupled by imposing displacement compatibility. This compatibility is enforced following the ideas of the Immersed Boundary methods. Two different models are considered for modeling the concrete bulk (a continuous one and a discontinuous one). The parametric study of each model is done for only plain concrete, before the addition of the steel fibers. A phenomenological mesomodel is defined for modeling steel fibers, on the basis of the analytical expressions describing the pullout tests. This phenomenological mesomodel not only describes the behavior of the steel fibers, but also accounts for the concrete-fiber interaction behavior. For each fiber, its constitutive equation is defined depending on its shape (straight or hooked) and the angle between the fiber and the normal direction of the failure pattern. Both 2D and 3D examples are reproduced with the proposed numerical tool. The obtained results illustrate the presence of the steel fibers into the concrete matrix. The shape of the fiber influences of the SFRC behavior: the residual strength is higher for hooked fibers than for straight ones. Moreover, increasing the quantity of fibers means increasing the residual strength of the material. The obtained numerical results are compared to the experimental ones (under the same hypothesis). Therefore, the proposed numerical approach of SFRC is validated experimentally.

  • Desarrollo y análisis del métod PGD para procesos de conformado termoplástico

     Diez Mejia, Pedro; Parés Mariné, Núria; Modesto Galende, David; Zlotnik, Sergio; Verdugo Rojano, Francesc; Huerta Cerezuela, Antonio
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  • Desarrollo y análisis del método PGD para procesos de conformado termoplástico

     Huerta Cerezuela, Antonio; Diez Mejia, Pedro; Parés Mariné, Núria; Modesto Galende, David; Zlotnik, Sergio; Verdugo Rojano, Francesc
    Participation in a competitive project

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  • Numerical tool for modeling steel fiber reinforced concrete

     Molins Borrell, Climent; Pros Parés, Alba; Diez Mejia, Pedro
    RILEM International Symposium on Fibre Reinforced Concrete
    Presentation's date: 2012-09-20
    Presentation of work at congresses

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    Steel Fiber Reinforced Concrete (SFRC) allows overcoming brittleness and weakness in tension, the main drawbacks of plain concrete. The goal of the present presentation is to present an ad-hoc numerical strategy to account for the contribution of the fibers in the simulation of the mechanical response of SFRC. In the model presented, the individual fibers immersed in the concrete bulk are accounted for in their actual location and orientation. The selected approach is based on the ideas introduced in the Immersed Boundary (IB) methods. These methods were developed to account for 1D (or 2D) solids immersed in 2D (or 3D) fluids. Here, the concrete bulk is playing the role of the fluid and the cloud of steel fibers is acting as the immerse boundary (that is a 1D structure in a 2D or 3D continuous). Thus, the philosophy of the IB methodology is used to couple the behavior of the two systems, the concrete bulk and the fiber cloud, precluding the need of matching finite element meshes. In the proposed approach, the meshes of the concrete bulk and fiber cloud are independent and the models are coupled imposing displacement compatibility and equilibrium of the two systems. The concrete bulk is modeled using any nonlinear model. The constitutive model for the fibers is designed to account for the complex interaction between fibers and concrete. The fiber models are based on previous investigations describing the concrete-fiber interaction and its dependence on the factors identified to be relevant: shape of the fiber (straight or hooked) and angle between the fiber and the crack plane. 3D examples with fibers distributed and oriented randomly are reproduced using the proposed approach.

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    Computable bounds of linear functional outputs in linear visco- elastodynamics  Open access

     Verdugo Rojano, Francesc; Diez Mejia, Pedro
    European Congress on Computational Methods in Applied Sciences and Engineering
    Presentation's date: 2012-09-12
    Presentation of work at congresses

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    This work presents a new technique yielding computable bounds of quantities of interest in the framework of linear visco-elastodynamics. A novel expression for the error representation is introduced, alternative to the previous ones using the Cauchy-Schwarz inequality. The proposed formulation utilizes symmetrized forms of the error equations to derive error bounds in terms of energy error measures. The practical implementation of the method is based on constructing admissible fields for both the original problem and the adjoint problem associated with the quantity of interest. Here, the flux-free technique is considered to compute the admissible stress fields. The proposed methodology yields estimates with better quality than the ones based on the Cauchy-Schwarz inequality. In the studied examples the bound gaps obtained are approximately halved, that is the estimated intervals of confidence are reduced.

  • Enforcing interface flux continuity in enhanced XFEM: stability analysis

     Diez Mejia, Pedro; Zlotnik, Sergio; Cottereau, Régis
    Oberwolfach Reports
    Presentation's date: 2012-02-14
    Presentation of work at congresses

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    XFEM is found to be an efficient approach for solving multiphase problems.

  • Goal-oriented error assessment for structural dynamics

     Diez Mejia, Pedro; Verdugo Rojano, Francesc
    World Congress on Computational Mechanics
    Presentation's date: 2012-07-09
    Presentation of work at congresses

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  • Assessment of the error and adaptivity for wave problems

     Steffens, Lindaura; Diez Mejia, Pedro; Parés Mariné, Núria; Kranjc Alves, M.
    World Congress on Computational Mechanics
    Presentation's date: 2012-07-10
    Presentation of work at congresses

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  • A stable XFEM formulation for multi-phase problems enforcing the accuracy of the fluxes

     Zlotnik, Sergio; Diez Mejia, Pedro; Cottereau, Régis
    European Congress on Computational Methods in Applied Sciences and Engineering
    Presentation's date: 2012-09-12
    Presentation of work at congresses

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  • Enforcing interface ux continuity in enhanced XFEM: stability analysis

     Diez Mejia, Pedro; Zlotnik, Sergio; Cottereau, Régis
    European Community on Computational Methods in Applied Sciences Young Investigators Conference
    Presentation's date: 2012-04-26
    Presentation of work at congresses

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  • Being aware of accuracy. How many digits you should trust in your numerical results?

     Diez Mejia, Pedro
    IACM expressions: Bulletin for the international association for computational mechanics
    Date of publication: 2011-12
    Journal article

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    Numerical modeling of the double punch test for plain concrete  Open access

     Pros Parés, Alba; Diez Mejia, Pedro; Molins Borrell, Climent
    International journal of solids and structures
    Date of publication: 2011-04
    Journal article

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    Double punch test is used to indirectly assess the tensile strength of plain concrete, ft. For this normalized test, the tensile strength is obtained as a function of the failure load, P, which is expressed as f_t = F(P). Different authors have proposed different expressions for the relation F(·), yielding scattered values of f_t. None of these alternatives is universally recognized as being more suitable than the others. In fact, these expressions are mainly based on elastic models considering the maximum tensile stress under the load P and ft is obtained as an output of the linear model. A numerical simulation allows using models in which f_t is an input of the material model and the corresponding failure load P is obtained associated with each value of f_t. In the present work, double punch test is simulated numerically considering two alternatives for modeling plain concrete accounting for damage and cracking: (a) the nonlocal Mazars damage model and (b) an heuristic crack model including joint elements in an a priori defined crack pattern. Numerical results are validated with experimental data and compared with the analytical expressions available in the literature.

  • Modeling steel fiber reinforced concrete: numerical immersed boundary approach and a phenomenological mesomodel for concrete-fiber interaction

     Pros Parés, Alba; Diez Mejia, Pedro; Molins Borrell, Climent
    International journal for numerical methods in engineering
    Date of publication: 2011-11-30
    Journal article

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  • Goal-oriented h-adaptivity for the Helmholtz equation: error estimates, local indicators and refinement strategies

     Steffens, Lindaura; Parés Mariné, Núria; Diez Mejia, Pedro
    Computational Mechanics
    Date of publication: 2011-01-14
    Journal article

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  • Numerical modeling of erosion using an improvement of the extended finite element method

     Cottereau, Régis; Diez Mejia, Pedro
    European journal of environmental and civil engineering
    Date of publication: 2011
    Journal article

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  • Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation

     Steffens, Lindaura Maria; Parés Mariné, Núria; Diez Mejia, Pedro
    International journal for numerical methods in engineering
    Date of publication: 2011-06-10
    Journal article

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  • Q-00024

     Sarrate Ramos, Jose; Diez Mejia, Pedro
    Participation in a competitive project

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  • Implementation of adaptivity in 2D cell centred finite volumes in EUROPLEXUS

     Casadei, Folco; Valsamos, G.; Diez Mejia, Pedro; Verdugo Rojano, Francesc
    Date: 2011
    Report

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  • Implementation of adaptivity in 3D cell centred finite volumes in EUROPLEXUS

     Casadei, Folco; Diez Mejia, Pedro; Verdugo Rojano, Francesc
    Date: 2011-12
    Report

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  • Simulación numérica del hormigón reforzado con fibras de acero

     Pros Parés, Alba; Diez Mejia, Pedro; Molins Borrell, Climent
    Congreso de la Asociación Científico-Técnica del Hormigón Estructural
    Presentation's date: 2011-10-27
    Presentation of work at congresses

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    El Hormigón Reforzado con Fibras de Acero (HRFA) es una técnica que consiste en añadir fibras de acero en el hormigón. La forma, las dimensiones, la esbeltez, la orientación y la distribución de las fibras caracterizan el comportamiento del material. Para caracterizar y estudiar el HRFA, se han empleado distintos ensayos: de tracción directa e indirecta y de flexotracción. En esta ponencia se presenta un modelo simplificado para simular el acoplamiento fibra-hormigón mediante el cual es posible tener en cuenta el efecto real de cada una de las fibras individuales. Así, es posible obtener la respuesta resistente teniendo en cuenta el número real de fibras, su orientación y posición. Para poder tener en cuenta la interacción fibra-hormigón, las ecuaciones constitutivas de las fibras se basan en expresiones analíticas dependiendo del ángulo entre cada fibra y la fisura en el hormigón. El hormigón se modeliza considerando un modelo no lineal.

  • Natural quantities of interest in linear elastodynamics for goal oriented error estimation and adaptivity

     Diez Mejia, Pedro; Casadei, Folco; Verdugo Rojano, Francesc
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2011
    Presentation of work at congresses

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  • How bad XFEM behaves at estimating fluxes close to the interface and how to improve that behaviour

     Cottereau, Régis; Diez Mejia, Pedro
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2011
    Presentation of work at congresses

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  • Testing adaptivity in 2D cell centred finite volumes with the CDEM combustion model in EUROPLEXUS

     Casadei, Folco; Diez Mejia, Pedro; Verdugo Rojano, Francesc
    Date: 2011-12
    Report

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  • Meshless methods in dual analysis: theoretical and implementation issues

     Ivannikov, Vladimir; Tiago, C.; Moitinho de Almeida Pereira, José Paulo; Diez Mejia, Pedro
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2011-06-06
    Presentation of work at congresses

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  • How bad XFEM behaves at estimating fluxes close to the interface and how to improve that behavior

     Cottereau, Régis; Diez Mejia, Pedro
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2011-06-06
    Presentation of work at congresses

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  • Numerical simulation of steel fiber reinforced concrete: including fibers into plain concrete

     Pros Parés, Alba; Diez Mejia, Pedro; Molins Borrell, Climent
    Congreso en Métodos Numéricos em Engenharia
    Presentation's date: 2011-06-15
    Presentation of work at congresses

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  • Goal-oriented error estimates and adaptivity for wave propagation problems

     Diez Mejia, Pedro; Parés Mariné, Núria; Steffens, Lindaura; Alves, M.K.
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2011-06-06
    Presentation of work at congresses

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  • Discrete meso-modeling of steel fiber reinforced concrete: simulation of flexural behavior

     Pros Parés, Alba; Diez Mejia, Pedro; Molins Borrell, Climent
    International Conference on Computational Plasticity
    Presentation's date: 2011-09-08
    Presentation of work at congresses

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  • Numerical modeling for steel fiber reinforced concrete: flexural behavior

     Pros Parés, Alba; Diez Mejia, Pedro; Molins Borrell, Climent
    International Conference on Computational Modeling of Fracture and Failure of Materials and Structures
    Presentation's date: 2011-06-07
    Presentation of work at congresses

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  • XFEM+: una modificación de XFEM para mejorar la precisión de los flujos locales en problemas de difusión con conductividades muy distintas

     Cordero, Felipe; Diez Mejia, Pedro
    Revista internacional de métodos numéricos para cálculo y diseño en ingeniería
    Date of publication: 2010
    Journal article

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    SUPG-based stabilization using a separated representations approach  Open access

     González, D.; Debeugny, L.; Cueto, E.; Chinesta, F.; Diez Mejia, Pedro; Huerta Cerezuela, Antonio
    International journal of material forming
    Date of publication: 2010-04
    Journal article

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    We have developed a new method for the construction of Streamline Upwind Petrov Galerkin (SUPG) stabilization techniques for the resolution of convection-diffusion equations based on the use of separated representations inside the Proper Generalized Decompositions (PGD) framework. The use of SUPG schemes produces a consistent stabilization adding a parameter to all the terms of the equation (not only the convective one). SUPG obtains an exact solution for problems in 1D, nevertheless, a generalization does not exist for elements of high order or for any system of convection-diffusion equations. We introduce in this paper a method that achieves stabilization in the context of Proper Generalzied Decomposition (PGD). This class of approximations use a representation of the solution by means of the sum of a finite number of terms of separable functions. Thus it is possible to use the technique of separation of variables in the context of problems of convection-diffusion that will lead to a sequence of problems in 1D where the parameter of stabilization is well known.

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    A flux-free a posteriori error estimator for the incompressible Stokes problem using a mixed FE formulation  Open access

     Larsson, Fredrik; Diez Mejia, Pedro; Huerta Cerezuela, Antonio
    Computer methods in applied mechanics and engineering
    Date of publication: 2010-08-01
    Journal article

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    In this contribution, we present an a posteriori error estimator for the incompressible Stokes problem valid for a conventional mixed FE formulation. Due to the saddle-point property of the problem, conventional error estimators developed for pure minimization problems cannot be utilized straight-forwardly. The new estimator is built up by two key ingredients. At first, a computed error approximation, exactly fulfilling the continuity equation for the error, is obtained via local Dirichlet problems. Secondly, we adopt the approach of solving local equilibrated flux-free problems in order to bound the remaining, incompressible, error. In this manner, guaranteed upper and lower bounds, of the velocity “energy norm” of the error as well as goaloriented (linear) output functionals, with respect to a reference (overkill) mesh are obtained. In particular, it should be noted that this approach requires no computation of hybrid fluxes. Furthermore, the estimator is applicable to mixed FE formulations using continuous pressure approximations, such as the Mini and Taylor– Hood class of elements. In conclusion, a few simple numerical examples are presented, illustrating the accuracy of the error bounds.

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    Strict error bounds for linear and nonlinear solid mechanics problems using a patch-based flux-free method  Open access

     Cottereau, Regis; Chamoin, Ludovic; Diez Mejia, Pedro
    Mecanique and industries
    Date of publication: 2010-12
    Journal article

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    We discuss, in this paper, a common ux-free method for the computation of strict error bounds for linear and nonlinear Finite Element computations. In the linear case, the error bounds are on the energy norm of the error, while, in the nonlinear case, the concept of error in constitutive relation is used. In both cases, the error bounds are strict in the sense that they re- fer to the exact solution of the continuous equations, rather than to some FE computation over a refined mesh. For both linear and nonlinear solid mechanics, this method is based on the computation of a statically admissible stress field, which is performed as a series of local problems on patches of elements. There is no requirement to solve a previous problem of ux equilibration globally, as happens with other methods.

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    Accurate recovery-based upper error bounds for the extended finite element framework  Open access

     Ródenas García, Juan José; González Estrada, O. A.; Diez Mejia, Pedro; Fuenmayor, F. J.
    Computer methods in applied mechanics and engineering
    Date of publication: 2010-08-01
    Journal article

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    This paper introduces a recovery-type error estimator yielding upper bounds of the error in energy norm for linear elastic fracture mechanics problems solved using the extended finite element method (XFEM). The paper can be considered as an extension and enhancement of a previous work in which the upper bounds of the error were developed in a FEM framework. The upper bound property requires the recovered solution to be equilibrated and continuous. The proposed technique consists of using a recovery technique, especially adapted to the XFEM framework that yields equilibrium at a local level (patch by patch). Then a postprocess based on the partition of unity concept is used to obtain continuity. The result is a very accurate but only nearly-statically admissible recovered stress field, with small equilibrium defaults introduced by the postprocess. Sharp upper bounds are obtained using a new methodology accounting for the equilibrium defaults, as demonstrated by the numerical tests.

  • Modeling, with a unified level-set representation, of the expansion of a hollow in the ground under different physical phenomena

     Cottereau, Regis; Diez Mejia, Pedro; Huerta Cerezuela, Antonio
    Computational Mechanics
    Date of publication: 2010
    Journal article

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  • Assembling sparse matrices in MATLAB

     Zlotnik, Sergio; Diez Mejia, Pedro
    Communications in numerical methods in engineering
    Date of publication: 2010
    Journal article

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