References of "Kerfriden, Pierre"
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See detailSpace-time reduced basis approximation and goal-oriented a posteriori error estimation for wave equation
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL

in Theory and Application of Model Order Reduction (2013, December)

We study numerically the linear second order wave equation with an output quantity of interest which is a linear functional of the field variable using reduced basis approximation methods in the space ... [more ▼]

We study numerically the linear second order wave equation with an output quantity of interest which is a linear functional of the field variable using reduced basis approximation methods in the space-time domain. The essential new ingredient is the a posteriori error estimation of the output quantity of interest. The technique, which is based on the well-known dual-weighted residual (DWR) method is deployed within a reduced basis approximation context. First, we introduce the reduced basis recipe - Galerkin projection onto a space spanned by the reduced basis functions which are constructed from the solutions of the governing PDE at several selected points in the parameter space. Second, in order to construct these basis functions we propose a new “goal-oriented” Proper Orthogonal Decomposition (POD)-Greedy sampling procedure, which is based on these new a posteriori error estimations. Finally, this a posteriori error estimation is also used to evaluate approximately the quality of many output computations in the online stage within the reduced basis procedure. [less ▲]

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See detailA multiscale partitioned reduced order model applied to damage simulation
Goury, Olivier; Kerfriden, Pierre; Bordas, Stéphane UL

Scientific Conference (2013, July)

Simulating fracture in realistic engineering components is computationally expensive. In the context of early-stage design, or reverse engineering, such simulations might need to be performed for a large ... [more ▼]

Simulating fracture in realistic engineering components is computationally expensive. In the context of early-stage design, or reverse engineering, such simulations might need to be performed for a large range of material and geometric parameters, which makes the solution to the parametric problem of fracture unaffordable. Model order reduction, such as the proper orthogonal decomposition (POD), is one way to reduce significantly the computational time by reducing the number of spatial unknowns. The solution is searched for in a reduced space spanned by a few well-chosen basis vectors only. In the context of solid mechanics involving structural softening, the strong topological changes in the zone where damage localises are extremely sensitive to variations of the parameters, which requires reduced spaces of prohibitively large dimensions in order to approximate the solution with a sufficiently high degree of accuracy. Introduced in [1], partitioned model order reduction is an alternative to global model order reduction that essentially divides up the problem into smaller regions. Each region can then be tackled using a reduced model of appropriate size, if at all, depending on the local material non-linearities in the region. In the context of multiscale homogenization, simulations of representative volume elements (RVE) have to be performed to obtain the material properties in the different elements of a coarse mesh. When considering a nonlinear material, those multiple RVE simulations can be com- putationally very expensive. They however only differ by the history of boundary conditions applied. This contribution proposes to apply partitioned model order reduction to those RVEs with reduced bases parametrized by the boundary conditions. REFERENCES [1] P. Kerfriden, O. Goury, T. Rabczuk, S. Bordas, A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 256:169–188, 2013. [less ▲]

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See detailA goal-oriented reduced basis method for the wave equation in inverse analysis
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL

in International Conference on Computational Mechanics CM13 Proceedings (2013, March)

In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with a ne parameter dependence. The essential new ingredient is the dual (or adjoint ... [more ▼]

In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with a ne parameter dependence. The essential new ingredient is the dual (or adjoint) problem and the use of its solution in a sampling procedure to pick up “goal-orientedly” parameter samples. First, we introduce the reduced-basis recipe — Galerkin projection onto a space YN spanned by the reduced basis functions which are constructed from the solutions of the governing partial di erential equation at several selected points in parameter space. Second, we propose a new “goal-oriented” Proper Orthogonal Decomposition (POD)–Greedy sampling procedure to construct these associated ba-sis functions. Third, based on the assumption of a ne parameter dependence, we use the o ine-online computational procedures developed earlier to split the computational procedure into o ine and online stages. We verify the proposed computational procedure by applying it to a three-dimensional simulation dental implant problem. The good numeri-cal results show that our proposed procedure performs better than the standard POD–Greedy procedure in terms of the accuracy of output functionals. [less ▲]

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See detailStable extended finite element method: Convergence, Accuracy, Properties and Diffpack implementation
Paladim, Daniel; Natarajan, Sundarajan; Bordas, Stéphane UL et al

in International Conference on Extended Finite Element Methods - XFEM 2013, September 11 – 13, 2013, Lyon, France (2013)

Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally ... [more ▼]

Problems involving singularities and moving boundaries, especially when they involve discontinuities, create difficulties for the finite element method. On another, albeit related, front, two diametrally opposed approaches are attempting to simplify the CAD to Analysis pipeline: isogeometric methods on the one hand [1] aim at coupling the geometry and field approximations, whilst implicit boundary definition-based methods attempt to decouple them [3,4,5]. We examine in this paper one instance of the latter approach, and rely on partition of unity enrichment of the field variable to capture discontinuities along material interface or domain boundaries. We study in particular the stable generalized finite element method of Babuˇka and Banerjee [6] for higher order approximations in two and three dimensions and propose a generic implementation within the C++ library Diffpack from inuTech GmbH [7]. In a companion paper, the implementation of enrichment within Diffpack is presented in more detail. We will present results obtained with our 3D implementation of partition of unity enrichment within Diffpack. This implementation represents the interfaces through level-sets and palliates blending problems using various approaches. We study here the stabilisation approach proposed in [6] in more detail and pay particular attention to the global convergence rate of the approach and to the stability and the local flux converence close to the interfaces. [less ▲]

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See detailSpace-time goal-oriented reduced basis approximation for linear wave equation
Hoang, Khac Chi; Kerfriden, Pierre; Bordas, Stéphane UL

Report (2013)

In this paper, we study numerically the linear damped second-order hyperbolic partial differen-tial equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE ... [more ▼]

In this paper, we study numerically the linear damped second-order hyperbolic partial differen-tial equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The main contribution of this paper is the “goal-oriented” proper orthogonal decomposition (POD)–Greedy sampling procedure within the RB approximation context. First, we introduce the RB recipe: Galerkin projection onto a space YN spanned by solutions of the governing PDE at N selected points in parameter space. This set of N parameter points is constructed by the standard POD–Greedy sampling procedure already developed. Second, based on the affine parameter dependence, we make use of the offline-online computational procedures: in the offline stage, we generate the RB space; in the online stage, given a new parameter value, we calculate rapidly and accurately the space-time RB output of interest and its associated asymptotic error. The proposed goal-oriented POD–Greedy sampling procedure can now be implemented and will look for the parameter points such that it minimizes this (asymptotic) output error rather than the solution error (or, error indicator which is the dual norm of residual) as in the standard POD–Greedy procedure. Numerical results show that the new goal-oriented POD–Greedy sampling procedure improves significantly the accuracy of the space-time output computation in comparison with the standard POD–Greedy one. The method is thus ideally suited for repeated, rapid and reliable evaluation of input-output relationships within the space-time setting. [less ▲]

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See detailDealing with interfaces in partitioned model order reduction for application to nonlinear problems
Goury, Olivier; Kerfriden, Pierre; Bordas, Stéphane UL

Scientific Conference (2013)

We propose a reduced order modelling technique based on a partitioning of the domain of study in the context of para- metric nonlinear problems. A formulation of the reduction of the displacement and of ... [more ▼]

We propose a reduced order modelling technique based on a partitioning of the domain of study in the context of para- metric nonlinear problems. A formulation of the reduction of the displacement and of the interface tractions linking subdomains to each others will be performed in a FETI context. [less ▲]

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See detailALGEBRAIC COARSE-GRAINING METHODS IN FRACTURE MECHANICS: TACKLING LOCAL LACK OF CORRELATION USING DOMAIN DECOMPOSITION
Goury, Olivier; Kerfriden, Pierre; Rabczuk, Timon et al

Scientific Conference (2012, March)

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires ... [more ▼]

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires the use of a system approximation method to speed-up the assembly of the non-linear opreators. We show that the method efficiently computes a solution faster than a full order model for a given accuracy. The speed-up increases with the problem size. [less ▲]

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See detailPractical error bounds in energy norm based on a recovered displacement field
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailAccurate error estimate in energy norm using a nearly-equilibrated kinematically-admissible displacement recovery technique
Nadal, E.; González-Estrada, O. A.; Ródenas, J. J. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailError estimation of recovered solutions in FE analysis. Higher order h-adaptive refinement strategies
Ródenas, J. J.; Nadal, E.; González-Estrada, O. A. et al

in Pimienta, P M (Ed.) 10th World Congress on Computational Mechanics (WCCM 2012) (2012)

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See detailError estimation in quantities of interest for XFEM using recovery techniques
González-Estrada, O. A.; Nadal, E.; Ródenas, J. J. et al

in Yang, Z J (Ed.) 20th UK National Conference of the Association for Computational Mechanics in Engineering (ACME) (2012)

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See detailRationalised computational time in fracture simulation: adaptive model reduction and domain decomposition
Goury, Olivier; Kerfriden, Pierre; Margetts, Lee et al

Scientific Conference (2011, June)

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See detailEnhanced recovery techniques for accurate evaluation of error estimates in FE aproximations
González-Estrada, O. A.; Ródenas, J. J.; Bordas, Stéphane UL et al

in Laghrouche, O; El Kacimi, A; Woodwaed, P (Eds.) et al 19th UK National Conference of the Association for Computational Mechanics in Engineering (2011)

When modelling critical structures, it is crucial to rationally assess the outcome of numerical simu- lations. Specifically, error estimation strategies are key tools in critical decision-based processes ... [more ▼]

When modelling critical structures, it is crucial to rationally assess the outcome of numerical simu- lations. Specifically, error estimation strategies are key tools in critical decision-based processes. The development of design tools that enhance performance of the final product and give reliability on the calculations is essential in todays industrial environment, which increasingly seeks to reduce develop- ment times for new products while improving the quality. During the last years there has been an increasing interest on the use of error estimates which help to measure and control the error committed in standard or enriched finite element approximations. The error can be defined in terms of energy norm or in quantities relevant for design purposes (such as the mean stress value in a particular area, displacements, the stress intensity factor for fracture problems). In this work, we discuss the use of different a posteriori recovery techniques to evaluate error estimates for different finite element (FE) approximations. These techniques are based on equilibrated supercon- vergent patch recovery or equilibrated moving least squares procedures and can be used in smooth or singular problems. Numerical results show the capabilities of the proposed techniques to provide good error estimates. [less ▲]

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See detailAccurate evaluation of stress intensity factors using error estimation in quantities of interest based on equilibrated recovery
González-Estrada, O. A.; Ródenas, J. J.; Bordas, Stéphane UL et al

in Oliver, J; Jirasek, M; Allix, O (Eds.) et al Computational Modeling of Fracture and Failure of Materials and Structures. Proceedings of CFRAC 2011 (2011)

During the last years the use of error estimators which measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an ... [more ▼]

During the last years the use of error estimators which measure the error in a quantity of interest defined by the analyst, instead of the energy norm, have become increasingly popular as they provide an error indicator for goal oriented adaptivity procedures. In this paper we propose an a posteriori recovery-based error estimation procedure which considers the stress intensity factor K typical of singular problems as the quantity of interest in finite element (FE) approximations. In general, error estimators in quantities of interest have been based on residual techniques and, although recovery techniques have been often preferred when considering the error in energy norm due to their robustness and simplicity, so far, there is no available procedure which considers an equilibrated recovery technique that can be used in standard FE frameworks. In [1] a standard SPR recovery technique is used to obtain an error measure of the J-integral, which is closely related to the value of the SIF. However, it does not consider any equilibrium constraints or the singularity near the crack tip, thus the obtained recovered stress field is not well suited for this kind of problems. The technique proposed herein relies on the enhanced superconvergent patch recovery technique presented in [2] to evaluate highly accurate recovered stress fields of the primal and dual problems, which are then used to obtain a sharp error estimate. The primal problem is simply the problem under analysis. To formulate the dual problem we consider the linear interaction integral representing K to obtain the applied loads of the dual FE approximation to solve. The high accuracy of the recovered stress fields for both the primal and dual solutions is obtained by decomposing the raw stress field obtained from the finite element approximations into singular and smooth parts, and enforcing the fulfilment of boundary and internal equilibrium equations. The results indicate an accurate estimation of the error in K for benchmark problems with exact solution. [less ▲]

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See detailEstimación precisa del error en magnitudes de interés mediante técnicas de recovery con equilibrio local
Nadal, E.; Ródenas, J. J.; González-Estrada, O. A. et al

in Congress on Numerical Methods in Engineering (2011)

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See detailAccurate evaluation of K in XFEM using error estimation in quantities of interest based on equilibrated recovery
González-Estrada, O. A.; Ródenas, J. J.; Nadal, E. et al

in Bordas, Stéphane; Kerfriden, P (Eds.) 2nd International Conference on the Extended Finite Element Method (2011)

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See detailAn Algorithm to compute damage from load in composites
Dunant, Cyrille F.; Bordas, Stéphane UL; Kerfriden, Pierre et al

in Frontiers of Architecture and Civil Engineering in China (2011), 5(2), 180-193

We present a new method to model fracture of concrete based on energy minimisation. The concrete is considered on the mesoscale as composite consisting of cement paste, aggregates and micro pores. In this ... [more ▼]

We present a new method to model fracture of concrete based on energy minimisation. The concrete is considered on the mesoscale as composite consisting of cement paste, aggregates and micro pores. In this first step, the alkali-silica reaction is taken into account through damage mechanics though the process is more complex involving thermo-hygro-chemo-mechanical reaction. We use a non-local damage model that ensures the well-posedness of the boundary value problem (BVP). In contrast to existing methods, the interactions between degrees of freedom evolve with the damage evolutions. Numerical results are compared to analytical and experimental results and show good agreement. [less ▲]

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See detailAlleviating the Mesh Burden in Computational Solid Mechanics
Bordas, Stéphane UL; Rabczuk, Timon; Ródenas, Juan-Jo et al

in Proceedings of ECT2010 (2010, December 12)

The goal of this chapter is to review recent avenues of investigation to alleviate meshing difficulties in computational mechanics and give a few exemplar applications. Keywords: meshing; enrichment ... [more ▼]

The goal of this chapter is to review recent avenues of investigation to alleviate meshing difficulties in computational mechanics and give a few exemplar applications. Keywords: meshing; enrichment; meshfree methods; extended finite element methods; isogeometric analysis; advanced remeshing techniques. [less ▲]

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