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1 to 50 of 633 results
  • Parametric solutions involving geometry: a step towards efficient shape optimization

     Ammar, Amine; Huerta Cerezuela, Antonio; Chinesta, Francisco; Cueto Prendes, Elias; Leygue, Adrien
    Computer methods in applied mechanics and engineering
    Date of publication: 2014-01
    Journal article

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    Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions. © 2013 Elsevier B.V.

  • Dimensionless analysis of HSDM and application to simulation of breakthrough curves of highly adsorbent porous media

     Perez Foguet, Agusti; Casoni Rero, Eva; Huerta Cerezuela, Antonio
    Journal of environmental engineering (ASCE)
    Date of publication: 2013-05
    Journal article

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    The homogeneous surface diffusion model (HSDM) is widely used for adsorption modeling of aqueous solutions. The Biot number is usually used to characterize model behavior. However, some limitations of this characterization have been reported recently, and the Stanton number has been proposed as a complement to be considered. In this work, a detailed dimensionless analysis of HSDM is presented and limit behaviors of the model are characterized, confirming but extending previous results. An accurate and efficient numerical solver is used for these purposes. The intraparticle diffusion equation is reduced to a system of two ordinary differential equations, the transport-reaction equation is discretized by using a discontinuous Galerkin method, and the overall system evolution is integrated with a time-marching scheme. This approach facilitates the simulation of HSDM with a wide range of dimensionless numbers and with a correct treatment of shocks, which appear with nonlinear adsorption isotherms and with large Biot numbers and small surface diffusivity modulus. The approach is applied to simulate the breakthrough curves of granular ferric hydroxide. Published experimental data is adequately simulated.

  • Efficiency of high-order elements for continuous and disconrinuous Galerkin

     Angeloski, Aleksandar; Roca Navarro, Xevi; Peraire Guitart, Jaume; Huerta Cerezuela, Antonio
    Congreso de Métodos Numéricos en Ingeniería
    Presentation's date: 2013-06-26
    Presentation of work at congresses

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  • Advanced harmonic techniques for solving the transient heat equation

     Aguado, José Vicente; Huerta Cerezuela, Antonio; Chinesta, Francisco; Cueto Prendes, Elias; Leygue, Adrien
    Congreso de Métodos Numéricos en Ingeniería
    Presentation's date: 2013-06-26
    Presentation of work at congresses

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  • Deim-based PGD for parametric nonlinear model order reduction

     Aguado, José V.; Chinesta, Francisco; Leygue, Adrien; Cueto Prendes, Elias; Huerta Cerezuela, Antonio
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2013-06-04
    Presentation of work at congresses

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  • Decomposition techniques in computational limit analysis

     Muñoz Romero, Jose Javier; Rabiei, Syednima; Huerta Cerezuela, Antonio
    International Conference on Computational Plasticity Fundamentals and Applications
    Presentation's date: 2013-09-03
    Presentation of work at congresses

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    Numerical techniques for the computation of strict bounds in limit analyses have been developed for more than thirty years. The efficiency of these techniques have been substantially improved in the last ten years, and have been successfully applied to academic problems, foundations and excavations. We here extend the theoretical background to problems with anchors, interface conditions, and joints. Those extensions are relevant for the analysis of retaining and anchored walls, which we study in this work. The analysis of three-dimensional domains remains as yet very scarce. From the computational standpoint, the memory requirements and CPU time are exceedingly prohibitive when mesh adaptivity is employed. For this reason, we also present here the application of decomposition techniques to the optimisation problem of limit analysis. We discuss the performance of different methodologies adopted in the literature for general optimisation problems, such as primal and dual decomposition, and suggest some strategies that are suitable for the parallelisation of large three-dimensional problems. The proposed decomposition techniques are tested against representative problems.

  • Stability of anchored sheet wall in cohesive-frictional soils by FE limit analysis

     Muñoz Romero, Jose Javier; Lyamin, Andrei; Huerta Cerezuela, Antonio
    International journal for numerical and analytical methods in geomechanics
    Date of publication: 2013-06-03
    Journal article

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    This study extends the limit analysis techniques used for the computation of strict bounds of the load factors in solids to stability problems with interfaces, anchors and joints. The cases considered include the pull-out capacity of multibelled anchors and the stability of retaining walls for multiple conditions at the anchor/soil and wall/soil interfaces. Three types of wall supports are examined: free standing wall, simply supported wall and anchored wall. The results obtained are compared against available experimental and numerical data. The conclusion drawn confirms the validity of numerical limit analysis for the computation of accurate bounds on limit loads and capturing failure modes of structures with multiple inclusions of complex interface and support conditions.

  • PGD-Based computational vademecum for efficient design, optimization and control

     Chinesta, Francisco; Leygue, Adrien; Bordeu, Felipe; Aguado, José Vicente; Cueto, Elias; González, David; Alfaro, Icíar; Ammar, Amine; Huerta Cerezuela, Antonio
    Archives of computational methods in engineering
    Date of publication: 2013
    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

  • 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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  • On the natural stabilization of convection dominated problems using high order Bubnov¿Galerkin finite elements

     Cai, Quanji; Kollmannsberger, Stefan; Sala Lardies, Esther; Huerta Cerezuela, Antonio; Rank, Ernst
    Computers & mathematics with applications
    Date of publication: 2013-10-15
    Journal article

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  • 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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  • Efficiency of high-order elements for continuous and discontinuous Galerkin methods

     Huerta Cerezuela, Antonio; Angeloski, Aleksandar; Roca Navarro, Xevi; Peraire Guitart, Jaume
    International journal for numerical methods in engineering
    Date of publication: 2013
    Journal article

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  • High-order continuous and discontinuous Galerkin methods for wave problems

     Giorgiani, Giorgio; Modesto Galende, David; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    International journal for numerical methods in fluids
    Date of publication: 2013-12-10
    Journal article

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    Three Galerkin methods-continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin-are compared in terms of performance and computational efficiency in 2-D scattering problems for low and high-order polynomial approximations. The total number of DOFs and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for continuous Galerkin and hybridizable discontinuous Galerkin, when high-order elements are adopted, both of them clearly outperforming compact discontinuous Galerkin.

  • Hybridizable discontinuous Galerkin p-adaptivity for wave propagation problems

     Giorgiani, Giorgio; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    International journal for numerical methods in fluids
    Date of publication: 2013
    Journal article

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  • 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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  • Adaptive hybrid discontinuous methods for fluid and wave problems  Open access

     Giorgiani, Giorgio
    Defense's date: 2013-04-02
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
    Theses

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    This PhD thesis proposes a p-adaptive technique for the Hybridizable Discontinuous Galerkin method (HDG). The HDG method is a novel discontinuous Galerkin method (DG) with interesting characteristics. While retaining all the advantages of the common DG methods, such as the inherent stabilization and the local conservation properties, HDG allows to reduce the coupled degrees of freedom of the problem to those of an approximation of the solution de¿ned only on the faces of the mesh. Moreover, the convergence properties of the HDG solution allow to perform an element-by-element postprocess resulting in a superconvergent solution. Due to the discontinuous character of the approximation in HDG, p-variable computations are easily implemented. In this work the superconvergent postprocess is used to de¿ne a reliable and computationally cheap error estimator, that is used to drive an automatic adaptive process. The polynomial degree in each element is automatically adjusted aiming at obtaining a uniform error distribution below a user de¿ned tolerance. Since no topological modi¿cation of the discretization is involved, fast adaptations of the mesh are obtained. First, the p-adaptive HDG is applied to the solution of wave problems. In particular, the Mild Slope equation is used to model the problem of sea wave propagation is coastal areas and harbors. The HDG method is compared with the continuous Galerkin (CG) ¿nite element method, which is nowadays the common method used in the engineering practice for this kind of applications. Numerical experiments reveal that the e¿ciency of HDG is close to CG for uniform degree computations, clearly outperforming other DG methods such as the Compact Discontinuous Galerkin method. When p-adaptivity is considered, an important saving in computational cost is shown. Then, the methodology is applied to the solution of the incompressible Navier-Stokes equations for the simulation of laminar ¿ows. Both steady state and transient applications are considered. Various numerical experiments are presented, in 2D and 3D, including academic examples and more challenging applications of engineering interest. Despite the simplicity and low cost of the error estimator, high e¿ciency is exhibited for analytical examples. Moreover, even though the adaptive technique is based on an error estimate for just the velocity ¿eld, high accuracy is attained for all variables, with sharp resolution of the key features of the ¿ow and accurate evaluation of the ¿uid-dynamic forces. In particular, high degrees are automatically located along boundary layers, reducing the need for highly distorted elements in the computational mesh. Numerical tests show an important reduction in computational cost, compared to uniform degree computations, for both steady and unsteady computations.

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    Hybridizable discontinuous Galerkin p-adaptivity for wave problems  Open access

     Giorgiani, Giorgio; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    European Community on Computational Methods in Applied Sciences Young Investigators Conference
    Presentation's date: 2012-04-24
    Presentation of work at congresses

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    A p-adaptive Hybridizable Discontinuous Galerkin (HDG) method is presented for the solution of wave problems. The HDG method allows to drastically reduce the coupled degrees of freedom of the computation seeking for an approximation of the solution that is defined only on the edges of the mesh. The particular choice of the numerical fluxes driven by the hybridization technique allows to obtain an optimally converging solution not only for the primal unknown but also for its derivative. This characteristic allows to perform a post-process of the solution that provides a super-convergent solution. The discontinuous character of the solution provides an optimal framework for a p-adaptive technique. The post-processed solution of the HDG method is used to construct a cheap and reliable error estimator that drives an element by element modification of the approximation degree. The proposed p-adaptive HDG method is compared with high-order CG computation with static condensation of the interior nodes. A challenging problem is considered for the comparison: a non-homogeneous scattering problem in an open domain.

  • Are high-order and hybridizable discontinuous Galerkin methods competitive?

     Huerta Cerezuela, Antonio; Angeloski, Aleksandar; Roca Navarro, Xevi; Peraire Guitart, Jaume
    Oberwolfach Reports
    Presentation's date: 2012-02-14
    Presentation of work at congresses

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    The talk covered several issues motivated by a practical engineering wave propagation problem: real-time evaluation of wave agitation in harbors. The first part, presented the application of a reduced order model in the framework of a Helmholtz equation with non-constant coefficients in an unbounded domain. This problem requires large numbers of degrees of freedom (ndof) because relatively high frequencies with small (compared with the domain size) geometric features must be considered.

  • Efficiency and accuracy of high-order computations and reduced order modelling in coastal engineering wave propagation problems

     Modesto Galende, David; Giorgiani, Giorgio; Zlotnik, Sergio; Huerta Cerezuela, Antonio
    European Community on Computational Methods in Applied Sciences Young Investigators Conference
    Presentation's date: 2012-04-24
    Presentation of work at congresses

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    Several numerical issues have to be considered when solving wave propagation problems, between which there are the artificial boundary conditions, the small geometrical features that can be influential or the variable coefficients. Apart from them, two issues are mainly addressed and discussed. Firstly, low order elements need very high wave resolution for capturing the solution in the area of interest, leading to extremely dense meshes. High-order finite elements are proposed to be an efficient and accurate solution for solving the problem. Secondly, the very large number of test cases. When designing harbour models, a huge number of incident waves, in term of wavelengths and directions, have to be studied. The excessive computational cost to carry out all the possible direct problems prevents the whole data evaluation, inducing the lost of important information. Reduced order models may be an alternative if they are computable, efficient and accurate. The applicability of Proper Generalized Decomposition (PGD) is exploited. Unlike previous PGD contributions, which deal with elliptic problems, the present work is focused on a more challenging scenario for the separable representation due to the loss of the elliptic behaviour. The proposed PGD involves a separable representation of the unknown reflected wave in space, wave number and angle of incidence. Such decomposition appears to be really interesting for practical purpose, where goal-oriented results are critical for a wide range of frequencies and incident waves. Moreover, when accuracy and efficiency are of concern, the number of terms in the reduced model are determined by means of an error estimation based on the dual formulation of the problem.

  • Hybridizable discontinuous Galerkin p-adaptivity for fluid problems

     Giorgiani, Giorgio; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    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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    Optimally convergent high-order X-FEM for problems with voids and inclusions  Open access

     Sala Lardies, Esther; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    European Congress on Computational Methods in Applied Sciences and Engineering
    Presentation's date: 2012-09-13
    Presentation of work at congresses

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    Solution of multiphase problems shows discontinuities across the material interfaces, which are usually weak. Using the eXtended Finite Element Method (X-FEM), these problems can be solved even for meshes that do not match the geometry. The basic idea is to enrich the interpolation space by means of a ridge function that is able to reproduce the discontinuity inside the elements. This approach yields excellent results for linear elements, but fails to be optimal if high-order interpolations are used. In this work, we propose a formulation that ensures optimal convergence rates for bimaterial problems. The key idea is to enrich the interpolation using a Heaviside function that allows the solution to represent polynomials on both sides of the interface and, provided the interface is accurately approximated, it yields optimal convergence rates. Although the interpolation is discontinuous, the desired continuity of the solution is imposed modifying the weak form. Moreover, in order to ensure optimal convergence, an accurate description of the interface (which also defines an integration rule for the elements cut by the interface) is needed. Here, we comment on different options that have been successfully used to integrate high-order X-FEM elements, and describe a general algorithm based on approximating the interface by piecewise polynomials of the same degree that the interpolation functions.

  • Are High-order and Hybridizable Discontinuous Galerkin methods competitive?

     Huerta Cerezuela, Antonio; Angeloski, Aleksandar; Roca Navarro, Xevi; Peraire Guitart, Jaume
    Oberwolfach reports
    Date of publication: 2012
    Journal article

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  • A note on upper bound formulations in limit analysis

     Muñoz Romero, Jose Javier; Huerta Cerezuela, Antonio; Bonet, Javier; Peraire, Jaume
    International journal for numerical methods in engineering
    Date of publication: 2012-08-24
    Journal article

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    In this paper we study some recent formulations for the computation of upper bounds in limit analysis. We show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound, nor does it provide a velocity field that satisfies the normality rule everywhere. We show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power. We derive a formulation that furnishes a strict upper bound of the load factor, which in fact coincides with a formulation reported in the literature. From the analysis of these formulations we propose a post-process which consists in computing exactly the dissipation power for the optimum upper bound velocity field. This post-process may further reduce the strict upper bound of the load factor in particular situations. Finally, we also determine the quadratures that must be used in the elemental and edge gap contributions so that they are always positive and their addition equals the global bound gap.

  • Interactive simulation on a smart Phone

     Cueto, E.; Huerta Cerezuela, Antonio; Chinesta, Francisco
    Benchmark
    Date of publication: 2012-01
    Journal article

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    Traditionally, Simulationbased Engineering Sciences (SBES) made use of static data inputs to perform the simulations. Namely parameters of the model, boundary conditions, etc. were traditionally obtained by experimentation and could not be modified during the course of the simulation. More recently, large efforts have been invested in developing dynamic datadriven application systems (DDDAS): systems in which measurements and simulations are continuously influencing each other in a symbiotic manner. It should be understood that measurements should be incorporated in real time to the simulations, while simulations could eventually control the way in which measurements are done.

  • Estimation of crack opening from a two-dimensional continuum-based finite element computation

     Dufour, F.; Legrain, Dominique; Pijaudier Cabot, Gilles; Huerta Cerezuela, Antonio
    International journal for numerical and analytical methods in geomechanics
    Date of publication: 2012-11
    Journal article

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  • Proper generalized decomposition based dynamic data-driven control of thermal processes

     Ghnatios, Ch.; Masson, F.; Huerta Cerezuela, Antonio; Leygue, Adrien; Cueto, E.; Chinesta, Francisco
    Computer methods in applied mechanics and engineering
    Date of publication: 2012
    Journal article

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  • One-dimensional shock-capturing for high-order discontinuous Galerkin methods

     Casoni Rero, Eva; Peraire Guitart, Jaume; Huerta Cerezuela, Antonio
    International journal for numerical methods in fluids
    Date of publication: 2012-02
    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.

  • Point-set Manifold Processing for Computational Mechanics: thin shells, reduced order modeling, cell motility and molecular conformations  Open access

     Millan, Raul Daniel
    Defense's date: 2012-11-12
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
    Theses

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    In many applications, one would like to perform calculations on smooth manifolds of dimension d embedded in a high-dimensional space of dimension D. Often, a continuous description of such manifold is not known, and instead it is sampled by a set of scattered points in high dimensions. This poses a serious challenge. In this thesis, we approximate the point-set manifold as an overlapping set of smooth parametric descriptions, whose geometric structure is revealed by statistical learning methods, and then parametrized by meshfree methods. This approach avoids any global parameterization, and hence is applicable to manifolds of any genus and complex geometry. It combines four ingredients: (1) partitioning of the point set into subregions of trivial topology, (2) the automatic detection of the local geometric structure of the manifold by nonlinear dimensionality reduction techniques, (3) the local parameterization of the manifold using smooth meshfree (here local maximum-entropy) approximants, and (4) patching together the local representations by means of a partition of unity. In this thesis we show the generality, flexibility, and accuracy of the method in four different problems. First, we exercise it in the context of Kirchhoff-Love thin shells, (d=2, D=3). We test our methodology against classical linear and non linear benchmarks in thin-shell analysis, and highlight its ability to handle point-set surfaces of complex topology and geometry. We then tackle problems of much higher dimensionality. We perform reduced order modeling in the context of finite deformation elastodynamics, considering a nonlinear reduced configuration space, in contrast with classical linear approaches based on Principal Component Analysis (d=2, D=10000's). We further quantitatively unveil the geometric structure of the motility strategy of a family of micro-organisms called Euglenids from experimental videos (d=1, D~30000's). Finally, in the context of enhanced sampling in molecular dynamics, we automatically construct collective variables for the molecular conformational dynamics (d=1...6, D~30,1000's).

  • 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
    Participation in a competitive project

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  • Proper Generalized Decomposition based dynamic data-driven control of material forming processes

     Ghnatios, Ch.; Masson, F.; Huerta Cerezuela, Antonio; Leygue, Adrien; Cueto, E.; Chinesta, Francisco
    Computer methods in applied mechanics and engineering
    Date of publication: 2012
    Journal article

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    High-order implicit time integration for unsteady incompressible flows  Open access

     de Villardi de Montlaur, Adeline; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    International journal for numerical methods in fluids
    Date of publication: 2012-10-20
    Journal article

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    The spatial discretization of unsteady incompressible Navier–Stokes equations is stated as a system of differential algebraic equations, corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Asymptotic stability of Runge–Kutta and Rosenbrock methods applied to the solution of the resulting index-2 differential algebraic equations system is analyzed. A critical comparison of Rosenbrock, semi-implicit, and fully implicit Runge–Kutta methods is performed in terms of order of convergence and stability. Numerical examples, considering a discontinuous Galerkin formulation with piecewise solenoidal approximation, demonstrate the applicability of the approaches and compare their performance with classical methods for incompressible flows.

  • A proper generalized decomposition for the parametrized wave problem

     Modesto Galende, David; Zlotnik, Sergio; Huerta Cerezuela, Antonio
    International Conference on Adaptive Modeling and Simulation
    Presentation's date: 2011-06-07
    Presentation of work at congresses

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  • Métodos Runge-Kutta implícitos de alto orden para flujos incompresibles

     de Villardi de Montlaur, Adeline; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    Revista internacional de métodos numéricos para cálculo y diseño en ingeniería
    Date of publication: 2011
    Journal article

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  • A simple shock-capturing technique for high-order discontinuous Galerkin methods

     Casoni Rero, Eva; Peraire Guitart, Jaume; Huerta Cerezuela, Antonio
    International journal for numerical methods in fluids
    Date of publication: 2011-11-11
    Journal article

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  • 3D NURBS-enhanced finite element method (NEFEM)

     Sevilla Cardenas, Ruben; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    International journal for numerical methods in engineering
    Date of publication: 2011-10-14
    Journal article

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    This paper presents the extension of the recently proposed NURBS-enhanced finite element method (NEFEM) to 3D domains. NEFEM is able to exactly represent the geometry of the computational domain by means of its CAD boundary representation with non-uniform rational B-splines (NURBS) surfaces. Specific strategies for interpolation and numerical integration are presented for those elements affected by the NURBS boundary representation. For elements not intersecting the boundary, a standard finite element rationale is used, preserving the efficiency of the classical FEM. In 3D NEFEM special attention must be paid to geometric issues that are easily treated in the 2D implementation. Several numerical examples show the performance and benefits of NEFEM compared with standard isoparametric or cartesian finite elements. NEFEM is a powerful strategy to efficiently treat curved boundaries and it avoids excessive mesh refinement to capture small geometric features.

  • Stabilized finite element methods for convection-diffusion-reaction, helmholtz and stokes problems  Open access

     Nadukandi, Prashanth
    Defense's date: 2011-05-13
    Department of Strength of Materials and Structural Engineering, Universitat Politècnica de Catalunya
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    We present three new stabilized finite element (FE) based Petrov-Galerkin methods for the convection-diffusionreaction (CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of a consistency recovery procedure for some stabilization methods belonging to the Petrov- Galerkin framework. It was ound that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov-Galerkin (HRPG) method for the CDR problem. The structure of the method in 1 D is identical to the consistent approximate upwind (CAU) Petrov-Galerkin method [doi: 10.1016/0045-7825(88)90108-9] except for the definitions of he stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [doi: 10.1 016/S0045-7825(97)00119-9] by an appropriate definition of the characteristic length. The prefix high-resolution is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in non-regular re9jmes. The design procedure in 1 D embarks on the problem of circumventing the Gibbs phenomenon observed in L projections. Next, we study the conditions on the stabilization parameters to ircumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi dimensional extension of the HRPG method using multi-linear block finite elements is also presented. Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method (FEM) and the classical central finite difference method. In 1 D this scheme is identical to the alpha-interpolation method [doi: 10.1 016/0771 -050X(82)90002-X] and in 2D choosing the value 0.5 for both the parameters, we recover he generalized fourth-order compact Pade approximation [doi: 10.1 006/jcph.1995.1134, doi: 10.1016/S0045- 7825(98)00023-1] (therein using the parameter V = 2). We follow [doi: 10.1 016/0045-7825(95)00890-X] for the analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [doi: 10.1016/0045-7825(95)00890-X]. Generic expressions for the parameters are given that guarantees a dispersion accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an expression for the parameter is given that minimizes the maximum relative phase error in 2D. A Petrov-Galerkin ormulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the error in the L2 norm, the H1 semi-norm and the I ~ Euclidean norm is done and the pollution effect is found to be small.

    Presentamos tres nuevos metodos estabilizados de tipo Petrov- Galerkin basado en elementos finitos (FE) para los problemas de convecci6n-difusi6n- reacci6n (CDR), de Helmholtz y de Stokes, respectivamente. El trabajo comienza con un analisis a priori de un metodo de recuperaci6n de la consistencia de algunos metodos de estabilizaci6n que pertenecen al marco de Petrov-Galerkin. Hallamos que el uso de algunas de las practicas estandar (por ejemplo, la eoria de Matriz-M) para el diserio de metodos numericos esencialmente no oscilatorios no es apropiado cuando utilizamos los metodos de recu eraci6n de la consistencia. Por 10 tanto, con res ecto a la estabilizaci6n de conveccion, no preferimos tales metodos de recuperacion . A continuacion, presentamos el diser'io de un metodo de Petrov-Galerkin de alta-resolucion (HRPG) para el problema CDR. La estructura del metodo en 10 es identico al metodo CAU [doi: 10.1016/0045-7825(88)90108-9] excepto en la definicion de los parametros de estabilizacion. Esta estructura tambien se puede obtener a traves de la formulacion del calculo finito (FIC) [doi: 10.1 016/S0045- 7825(97)00119-9] usando una definicion adecuada de la longitud caracteristica. El prefijo de "alta-resolucion" se utiliza aqui en el sentido popularizado por Harten, es decir, tener una solucion con una precision de segundo orden en los regimenes suaves y ser esencialmente no oscilatoria en los regimenes no regulares. El diser'io en 10 se embarca en el problema de eludir el fenomeno de Gibbs observado en las proyecciones de tipo L2. A continuacion, estudiamos las condiciones de los parametros de estabilizacion para evitar las oscilaciones globales debido al ermino convectivo. Combinamos los dos resultados (una conjetura) para tratar el problema COR, cuya solucion numerica sufre de oscilaciones numericas del tipo global, Gibbs y dispersiva. Tambien presentamos una extension multidimensional del metodo HRPG utilizando los elementos finitos multi-lineales. fa. continuacion, proponemos un esquema compacto de orden superior (que incluye dos parametros) en mallas estructuradas para la ecuacion de Helmholtz. Haciendo igual ambos parametros, se recupera la interpolacion lineal del metodo de elementos finitos (FEM) de tipo Galerkin y el clasico metodo de diferencias finitas centradas. En 10 este esquema es identico al metodo AIM [doi: 10.1 016/0771 -050X(82)90002-X] y en 20 eligiendo el valor de 0,5 para ambos parametros, se recupera el esquema compacto de cuarto orden de Pade generalizada en [doi: 10.1 006/jcph.1 995.1134, doi: 10.1 016/S0045-7825(98)00023-1] (con el parametro V = 2). Seguimos [doi: 10.1 016/0045-7825(95)00890-X] para el analisis de este esquema y comparamos su rendimiento en las mallas uniformes con el de "FEM cuasi-estabilizado" (QSFEM) [doi: 10.1016/0045-7825 (95) 00890-X]. Presentamos expresiones genericas de los para metros que garantiza una precision dispersiva de sexto orden si ambos parametros son distintos y de cuarto orden en caso de ser iguales. En este ultimo caso, presentamos la expresion del parametro que minimiza el error maxima de fase relativa en 20. Tambien proponemos una formulacion de tipo Petrov-Galerkin ~ue recupera los esquemas antes mencionados en mallas estructuradas. Presentamos estudios de convergencia del error en la norma de tipo L2, la semi-norma de tipo H1 y la norma Euclidiana tipo I~ y mostramos que la perdida de estabilidad del operador de Helmholtz ("pollution effect") es incluso pequer'ia para grandes numeros de onda. Por ultimo, presentamos una coleccion de metodos FE estabilizado para el problema de Stokes desarrollados a raves del metodo FIC de primer orden y de segundo orden. Mostramos que varios metodos FE de estabilizacion existentes y conocidos como el metodo de penalizacion, el metodo de Galerkin de minimos cuadrados (GLS) [doi: 10.1016/0045-7825(86)90025-3], el metodo PGP (estabilizado a traves de la proyeccion del gradiente de presion) [doi: 10.1 016/S0045-7825(96)01154-1] Y el metodo OSS (estabilizado a traves de las sub-escalas ortogonales) [doi: 10.1016/S0045-7825(00)00254-1] se recuperan del marco general de FIC. Oesarrollamos una nueva familia de metodos FE, en adelante denominado como PLS (estabilizado a traves del Laplaciano de presion) con las formas no lineales y consistentes de los parametros de estabilizacion. Una caracteristica distintiva de la familia de los metodos PLS es que son no lineales y basados en el residuo, es decir, los terminos de estabilizacion dependera de los residuos discretos del momento y/o las ecuaciones de incompresibilidad. Oiscutimos las ventajas y desventajas de estas tecnicas de estabilizaci6n y presentamos varios ejemplos de aplicacion

  • SHOCK CAPTURING FOR DISCONTINUOUS GALERKIN METHODS  Open access

     Casoni Rero, Eva
    Defense's date: 2011-10-14
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
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    Aquesta tesi doctoral proposa formulacions de Galerkin Discontinu (DG) d’alt ordre per la captura de shocks, obtenint alhora solucions altament precises per problemes de flux compressible. En les últimes dècades, la investigació en els mètodes de DG ha estat en constant creixement. L'èxit dels mètodes DG en problemes hiperbòlics ha conduit el seu desenvolupament en lleis de conservació no lineals i problemes de convecció dominant. Entre els avantatges dels mètodes DG, destaquen la seva estabilitat inherent i les propietats locals de conservació. D'altra banda, els mètodes DG estan especialment dissenyats per l’ús aproximacions d'ordre superior. De fet, en els últims anys s'ha demostrat que la resolució de problemes de convecció dominant ja no es restringeix només a elements d'ordre inferior. De fet, es necessiten models numèrics d'alta precisió per aconseguir prediccions altament fiables dins la dinàmica de fluids computacional (CFD). En aquest context es presenten i discuteixen dos tècniques de captura de shocks. En primer lloc, es presenta una tècnica novedosa i senzilla basada en la introducció d'una nova base de funcions de forma. Aquesta base té la capacitat de canviar a nivell local entre una interpolació contínua o discontínua, depenent de la suavitat de la funció que es vol aproximar. En presència de xocs, les discontinuïtats introduïdes dins l’element permeten incloure l'estabilització necessària gràcies a l’ús dels fluxos numèrics, i alhora exploten les propietats intrínsiques del mètodes DG. En conseqüència, es poden utilitzar malles grolleres amb elements d’ordre superior. Amb aquestes discretitzacions i, utilitzant el mètode proposats, els xocs queden continguts a l’interior de l’element i per tant, és possible evitar l’ús de tècniques de refinament adaptatiu de la malla, alhora que es manté la localitat i compacitat dels esquemes DG. En segon lloc, es proposa una tècnica clàssica i, aparentment simple: la introducció de la viscositat artificial. Primerament es realitza un estudi detallat per al cas unidimensional. S’obté una viscositat d’alta precisió que escala segons el valor hk amb 1 ≤ k ≤ p i essent h la mida de l’element. En conseqüència, s’obté un xoc amb amplitud del mateix ordre. Seguidament, l'estudi de la viscositat unidimensional obtenida s'extén al cas multidimensional per a malles triangulars. L'extensió es basa en la projecció de la viscositat unidimensional en unes determinades direccions espacials dins l’element. Es demostra de manera consistent que la viscositat introduïda és, com a molt, del mateix ordre que la resolució donada per la discretització espacial, és a dir, h/p. El mètode és especialment eficient per aproximacions de Galerkin discontinu d’alt ordre, per exemple p≥ 3. Les dues metodologies es validen mitjançant una àmplia selecció d’exemples numèrics. En alguns exemples, els mètodes proposats permeten una reducció en el nombre de graus de llibertat necessaris per capturar xocs acuradament de fins i tot un ordre de magnitud, en comparació amb mètodes estàndar de refinament adaptatiu amb aproximacions de baix ordre.

    This thesis proposes shock-capturing methods for high-order Discontinuous Galerkin (DG) formulations providing highly accurate solutions for compressible flows. In the last decades, research in DG methods has been very active. The success of DG in hyperbolic problems has driven many studies for nonlinear conservation laws and convection-dominated problems. Among all the advantages of DG, their inherent stability and local conservation properties are relevant. Moreover, DG methods are naturally suited for high-order approximations. Actually, in recent years it has been shown that convection-dominated problems are no longer restricted to low-order elements. In fact, highly accurate numerical models for High-Fidelity predictions in CFD are necessary. Under this rationale, two shock-capturing techniques are presented and discussed. First, a novel and simple technique based on on the introduction of a new basis of shape functions is presented. It has the ability to change locally between a continuous or discontinuous interpolation depending on the smoothness of the approximated function. In the presence of shocks, the new discontinuities inside an element introduce the required stabilization thanks to the numerical fluxes, thus exploiting DG inherent properties. Large high-order elements can therefore be used and shocks are captured within a single element, avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme. Second, a classical and, apparently simple, technique is advocated: the introduction of artificial viscosity. First, a one-dimensional study is perfomed. Viscosity of the order O(hk) with 1≤ k≤ p is obtained, hence inducing a shock width of the same order. Second, the study extends the accurate one-dimensional viscosity to triangular multidimensional meshes. The extension is based on the projection of the one-dimensional viscosity into some characteristic spatial directions within the elements. It is consistently shown that the introduced viscosity scales, at most, withthe DG resolutions length scales, h/p. The method is especially reliable for highorder DG approximations, say p≥3. A wide range of different numerical tests validate both methodologies. In some examples the proposed methods allow to reduce by an order of magnitude the number of degrees of freedom necessary to accurately capture the shocks, compared to standard low order h-adaptive approaches.

  • Automatic Hexahedral meshing algorithms: From structured to unstructured meshes

     Ruiz Girones, Eloi
    Defense's date: 2011-02-28
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
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  • Developments in maximum entropy approximants and application to phase field models

     Rosolen, Adrian Martin
    Defense's date: 2011-07-11
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
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  • VIRTUAL CONTROL METHODS FOR COUPLING HETEROGENEOUS PROBLEMS

     Discacciati, Marco; Huerta Cerezuela, Antonio
    Participation in a competitive project

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  • Comparison of high-order curved finite elements

     Sevilla Cardenas, Ruben; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    International journal for numerical methods in engineering
    Date of publication: 2011-02-02
    Journal article

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    Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation of the domain and the consistency of the approximation. The influence of the number of integration points on the accuracy of the computation is also studied. Two-dimensional numerical examples, solved with continuous and discontinuous Galerkin formulations, are used to test and compare all these methodologies. In every example shown, the recently proposed NURBS-enhanced finite element method (NEFEM) provides the maximum accuracy for a given spatial discretization, at least one order of magnitude more accurate than classical isoparametric finite element method (FEM). Moreover, NEFEM outperforms Cartesian FEM and p-FEM, stressing the importance of the geometrical model as well as the relevance of a consistent approximation in finite element simulations.

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    NURBS-Enhanced Finite Element Method (NEFEM)  Open access

     Sevilla Cardenas, Ruben; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    Archives of computational methods in engineering
    Date of publication: 2011-11
    Journal article

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    The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.

  • SUPG-based stabilization using proper generalized decomposition

     González, D.; Cueto, E.; Debeugny, L.; Chinesta, Francisco; Diez Mejia, Pedro; Huerta Cerezuela, Antonio
    International Conference on Engineering Computational Technology
    Presentation's date: 2010
    Presentation of work at congresses

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    High-Order discontinuous Galerkin methods for incompressible flows  Open access

     de Villardi de Montlaur, Adeline; Fernandez Mendez, Sonia; Huerta Cerezuela, Antonio
    European Conference on Computational Fluid Dynamics
    Presentation's date: 2010-06-15
    Presentation of work at congresses

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    The spatial discretization of the unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Runge-Kutta methods applied to the solution of the resulting index-2 DAE system are analyzed, allowing a critical comparison in terms of accuracy of semi-implicit and fully implicit Runge-Kutta methods. Numerical examples, considering a discontinuous Galerkin Interior Penalty Method with piecewise solenoidal approximations, demonstrate the applicability of the approach, and compare its performance with classical methods for incompressible flows.

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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.

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

     Roca Navarro, Francisco Javier; Sarrate Ramos, Jose; Huerta Cerezuela, Antonio
    Engineering with computers
    Date of publication: 2010
    Journal article

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  • 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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    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.