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

  G. Giorgiani, D. Modesto, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Fluids (2013). Vol. 73 (10), pp. 883-903

  
  

  Abstract

  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. hree 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

  Abstract
  Three Galerkin methods-continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin-are compared in terms of performance and computational [...]

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

  A. Huerta, A. Angeloski, X. Roca, J. Peraire

  Int. J. Numer. Meth. Engng. (2013). Vol. 96 (6), pp. 529-560 (Preprint)

  
  

  Abstract

  To evaluate the computational performance of high-order elements, a comparison based on operation count is proposed instead of runtime comparisons. More specifically, linear versus high-order approximations are analyzed for implicit solver under a standard set of hypotheses for the mesh and the solution. Continuous and discontinuous Galerkin methods are considered in two-dimensional and three-dimensional domains for simplices and parallelotopes. Moreover, both element-wise and global operations arising from different Galerkin approaches are studied. The operation count estimates show, that for implicit solvers, high-order methods are more efficient than linear ones.

  Abstract
  To evaluate the computational performance of high-order elements, a comparison based on operation count is proposed instead of runtime comparisons. More specifically, linear [...]

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

  J. Muñoz, A. Lyamin, A. Huerta

  Int. J. Numer. Anal. Meth. Geomech. (2013). Vol. 37 (9), pp. 1213-1230 (Preprint)

  
  

  Abstract

  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.

  Abstract
  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 [...]

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

  A. Pérez-Foguet, E. Casoni, A. Huerta

  Journal of Environmental Engineering (ASCE) (2013). Vol. 139 (5), pp. 667-676 (Preprint)

  
  

  Abstract

  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.

  Abstract
  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. [...]

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

  F. Chinesta, A. Leygue, F. Bordeu, J. Aguado, E. Cueto, D. González, I. Ruiz, A. Ammar, A. Huerta

  Archives of Comp. Meths. Engng. (2013). Vol. 20 (1), pp. 31-59

  
  

  Abstract

  In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.

  Abstract
  In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite [...]

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• Hybridizable discontinuous Galerkin p-adaptivity for wave propagation problems

  G. Giorgiani, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Fluids (2013). Vol. 72 (12), pp. 12144-1262 (preprint)

  
  

  Abstract

  A p-adaptive hybridizable discontinuous Galerkin method for the solution of wave problems is presented in a challenging engineering problem. Moreover, its performance is compared with a high-order continuous Galerkin. The hybridization technique allows to reduce the coupled degrees of freedom to only those on the mesh element boundaries, whereas the particular choice of the numerical fluxes opens the path to a superconvergent postprocessed solution. This superconvergent postprocessed solution is used to construct a simple and inexpensive error estimator. The error estimator is employed to obtain solutions with the prescribed accuracy in the area (or areas) of interest and also drives a proposed iterative mesh adaptation procedure. The proposed method is applied to a nonhomogeneous scattering problem in an unbounded domain. This is a challenging problem because, on the one hand, for high frequencies, numerical difficulties are an important issue because of the loss of the ellipticity and the oscillatory behavior of the solution. And on the other hand, it is applied to real harbor agitation problems. That is, the mild slope equation in frequency domain (Helmholtz equation with nonconstant coefficients) is solved on real geometries with the corresponding perfectly matched layer to damp the diffracted waves. The performance of the method is studied on two practical examples. The adaptive hybridizable discontinuous Galerkin method exhibits better efficiency compared with a high-order continuous Galerkin method using static condensation of the interior nodes.

  Abstract
  A p-adaptive hybridizable discontinuous Galerkin method for the solution of wave problems is presented in a challenging engineering problem. Moreover, its performance is compared [...]

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

  F. Chinesta, A. Leygue, F. Bordeu, E. Cueto, D. González, I. Ruiz, A. Ammar, A. Huerta

  IACM expressions (2013). Vol. 33 (4), pp. 4-7

  
  

  Abstract

  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 ! ).

  Abstract
  D espite the impressive progresses attained by simulation capabilities and techniques, some challenging problems remain today intractable. These prob- lems, that are common [...]

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

  F. Dufour, G. Legrain, G. Pijaudier, A. Huerta

  Int. J. Numer. Anal. Meth. Geomech. (2012). Vol. 36 (16), pp. 1813-1830

  
  

  Abstract

  Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one dimensional approach for estimating a crack opening from a continuum based fi nite element calculation to two dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post treatment procedure. The orig inal one dimensional problem devised in Dufour et al . [4] is recovered as pro fi les of deformation orthog onal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing fi nite element deformation pro fi les and theoretical pro fi les corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the pro fi les are assumed to be equal; in the weak approach, the integrals of each pro fi le are set equal. Two dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, de fi ned as the distance between the numerical and theoretical pro fi les, are less than a few percentages. In the case of a three point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack ( > 40 m m )

  Abstract
  Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. [...]

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• High-order implicit time integration for unsteady incompressible flows

  A. Montlaur, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Fluids (2012). Vol. 70 (5), pp. 603-626

  
  

  Abstract

  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.

  Abstract
  The spatial discretization of unsteady incompressible Navier–Stokes equations is stated as a system of differential algebraic equations, corresponding to the conservation [...]

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• A note on upper bound formulations in limit analysis

  J. Muñoz, A. Huerta, J. Bonet, J. Peraire

  Int. J. Numer. Meth. Engng. (2012). Vol. 91 (8), pp. 896-908

  
  

  Abstract

  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.

  Abstract
  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 [...]

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