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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 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 detailSpace-Time Shear-Slip Mesh Update Method for Fluid-Structure Interaction Problems
Schippke, Henning; Zilian, Andreas UL

Presentation (2013)

Many practical problems in engineering consist of a structure surrounded by a fluid. These are all from the theoretical point of view fluid-structure interaction problems, in which the movement of the ... [more ▼]

Many practical problems in engineering consist of a structure surrounded by a fluid. These are all from the theoretical point of view fluid-structure interaction problems, in which the movement of the structure influences the flow field of the fluid and vice versa. In this contribution the structure is described in a total Lagrangian representation based on velocities and the 2nd Piola-Kirchhoff stress state as primal variables in a hybrid-mixed formulation, while the fluid is modelled via the incompressible Navier-Stokes equations with velocities and pressure as unknowns. The governing equations of fluid and structural dynamics are uniformly discretised using space-time finite elements [1]. The discretised model equations of the fluid are stabilised using a SUPG/PSPG approach. Shape and test functions are continuous within the space-time slabs, while across the space- time slabs the shape and test functions are continuous only in space, but discontinuous in time yielding a time-discontinuous Galerkin approach. The space-time discretisation of the coupled system with velocities and pressure as remaining unknowns lays the basis for a mathematically profound analysis due to its methodical uniformity. During the mesh generation of the fluid-structure problem a fitting mesh at the conjoint interface of fluid and structure is generated ensuring natively the geometric continuity. In the discretised flow domain, which model equations are formulated in the Eulerian framework, a mesh-moving scheme needs to be applied to avoid severe mesh distortions. In case of large but regular structural displacements a discontinuous mesh-moving scheme like the Shear-Slip Mesh Update Method (SSMUM) is applicable [2]. In order to increase robustness and conservation behaviour of the classical SSMUM a modification based on the space-time discretisation of the problem described above is investigated. In the Space- Time SSMUM (ST-SSMUM) the alteration of the spatial connectivity takes place continuously in the space-time domain. By avoiding sudden changes in the spatial connectivity between two adjacent space-time slabs any difficulty in evaluating the jump term is circumvented. The properties of the introduced ST-SSMUM is shown by a computation of the flow field of a rotating impeller, which can be interpreted as a simplified water turbine or blood pump. [less ▲]

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See detailSpare parts planning and control for maintenance operations
Arts, Joachim UL

in Civil-Comp Proceedings (2014), 104

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See detailA Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems
Pan, Wei UL; Yuan, Ye; Goncalves, Jorge UL et al

in IEEE Transaction on Automatic Control (2016), 61(1), 182-187

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated ... [more ▼]

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear functional forms and their associated parameters from a limited number of time-series data points. For this, we cast this identification problem as a sparse linear regression problem and take a Bayesian viewpoint to solve it. As such, this approach typically leads to nonconvex optimisations. We propose a convexification procedure relying on an efficient iterative re-weighted ℓ1-minimisation algorithm that uses general sparsity inducing priors on the parameters of the system and marginal likelihood maximisation. Using this approach, we also show how convex constraints on the parameters can be easily added to our proposed iterative re-weighted ℓ1-minimisation algorithm. In the supplementary material \cite{appendix}, we illustrate the effectiveness of the proposed identification method on two classical systems in biology and physics, namely, a genetic repressilator network and a large scale network of interconnected Kuramoto oscillators. [less ▲]

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See detailSpatial play effects in a tangible game with an f-formation of multiple players
Jungmann, Manuela UL; Cox, Richard; Fitzpatrick, Geraldine

in Proceedings of the Fifteenth Australasian User Interface Conference (2014, January), 150

Drawing on Kendon's F-formation framework of social interaction, we analysed the game-space activity of collocated players engaged in a tangible multiplayer game. Game input from groups of 3 players ... [more ▼]

Drawing on Kendon's F-formation framework of social interaction, we analysed the game-space activity of collocated players engaged in a tangible multiplayer game. Game input from groups of 3 players interacting competitively in a natural spatial arrangement via balance-boards requiring whole-body movements was logged and analysed quantitatively. The spatial analysis of a range of players' activities in game-space revealed synergistic effects combining perceptual-motor factors with game-strategy behaviour which were reflected in preferred game-board playing regions. The findings illustrate the importance for HCI designers of considering interactions between human spatial behaviour, physical space and virtual game-space as games become increasingly embodied and social. [less ▲]

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See detailStable 3D extended finite elements with higher order enrichment for accurate non planar fracture
Agathos, Konstantinos UL; Chatzi, Eleni; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics & Engineering (2016), 306

An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area ... [more ▼]

An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area around the crack front, while also improving the conditioning of the resulting system matrices. This is achieved by fusing a novel form of enrichment with existing blending techniques. Further, the adoption of higher order terms of theWilliams expansion is also considered and the effects in the accuracy and conditioning of the method are studied. Moreover, some problems regarding the evaluation of stress intensity factors (SIFs) and element partitioning are dealt with. The accuracy and convergence properties of the method as well as the conditioning of the resulting stiffness matrices are investigated through the use of appropriate benchmark problems. It is shown that the proposed approach provides increased accuracy while requiring, for all cases considered, a reduced number of iterations for the solution of the resulting systems of equations. The positive impact of geometrical enrichment is further demonstrated in the accuracy of the computed SIFs where, for the examined cases, an improvement of up to 40% is achieved. [less ▲]

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See detailStable 3D extended finite elements with higher order enrichment for accurate non planar fracture
Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane UL

in Computer Methods in Applied Mechanics & Engineering (2015)

We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to ... [more ▼]

We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to contain the increase in conditioning number characteristic of enriched finite element formulations: the number of iterations to convergence of the conjugate gradient solver scales similarly to and converges faster than the topologically-enriched version of the standard XFEM. This has two advantages: (1) the residual can be driven to zero to machine precision for at least 50% fewer iterations than the standard version of XFEM; (2) additional enrichment functions can be added without significant deterioration of the conditioning. Numerical examples also show that our new approach is up to 40% more accurate in terms of stress intensity factors, than the standard XFEM. [less ▲]

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See detailStable 3D XFEM/vector-level sets for non-planar 3D crack propagation and comparison of enrichment schemes
Agathos, Konstantinos UL; Ventura, Giulio; Chatzi, Eleni et al

in International Journal for Numerical Methods in Engineering (2017)

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting ... [more ▼]

We present a three-dimensional (3D) vector level set method coupled to a recently developed stable extended finite element method (XFEM). We further investigate a new enrichment approach for XFEM adopting discontinuous linear enrichment functions in place of the asymptotic near-tip functions. Through the vector level set method, level set values for propagating cracks are obtained via simple geometrical operations, eliminating the need for solution of differential evolution equations. The first XFEM variant ensures optimal convergence rates by means of geometrical enrichment, i.e., the use of enriched elements in a fixed volume around the crack front, without giving rise to conditioning problems. The linear enrichment approach significantly simplifies implementation and reduces the computational cost associated with numerical integration. The two dicretization schemes are tested for different benchmark problems, and their combination to the vector level set method is verified for non-planar crack propagation problems. [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 detailThe stable GFEM. Convergence, accuracy and Diffpack implementation
Alves Paladim, Daniel; Natarajan, Sundarajan; Bordas, Stéphane UL et al

Presentation (2015, May 12)

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See detailA staggered cell-centered finite element method for compressible and nearly-incompressible linear elasticity on general meshes
Ong, Thanh Hai; Hoang, Thi Thao Phuong; Bordas, Stéphane UL et al

in SIAM Journal on Numerical Analysis (2015), 53(4), 2051-2073

We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its ... [more ▼]

We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its triangular submesh, the scheme can be constructed from a general mesh in which the displacement is approximated by piecewise linear (P1) functions on the dual submesh and, in the case of nearly incompressible problems, the pressure is approximated by piecewise constant (P0) functions on the dual mesh. The scheme is cell centered in the sense that the solution can be computed by cell unknowns of the primal mesh (for the displacement) and of the dual mesh (for the pressure). The method is presented within a rigorous theoretical framework to show stability and convergence. In particular, for the nearly incompressible case, stability is proved by using the macroelement technique. Numerical results show that the method, compared with other methods, is effective in terms of accuracy and computational cost. [less ▲]

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See detailStatic and fatigue strength of a novel anatomically contoured implant compared to five current open-wedge high tibial osteotomy plates
Diffo Kaze, Arnaud UL; Maas, Stefan UL; Belsey, James et al

in Journal of Experimental Orthopaedics (2017), 4(39),

Abstract Background The purpose of the present study was to compare the mechanical static and fatigue strength of the size 2 osteotomy plate “Activmotion” with the following five other common implants for ... [more ▼]

Abstract Background The purpose of the present study was to compare the mechanical static and fatigue strength of the size 2 osteotomy plate “Activmotion” with the following five other common implants for the treatment of medial knee joint osteoarthritis: the TomoFix small stature, the TomoFix standard, the Contour Lock, the iBalance and the second generation PEEKPower. Methods Six fourth-generation tibial bone composites underwent a medial open-wedge high tibial osteotomy (HTO), according to standard techniques, using size 2 Activmotion osteotomy plates. All bone-implant constructs were subjected to static compression load to failure and load-controlled cyclic fatigue failure testing, according to a previously defined testing protocol. The mechanical stability was investigated by considering different criteria and parameters: maximum forces, the maximum number of loading cycles, stiffness, the permanent plastic deformation of the specimens during the cyclic fatigue tests, and the maximum displacement range in the hysteresis loops of the cyclic loading responses. Results In each test, all bone-implant constructs with the size 2 Activmotion plate failed with a fracture of the lateral cortex, like with the other five previously tested implants. For the static compression tests the failure occurred in each tested implant above the physiological loading of slow walking (> 2400 N). The load at failure for the Activmotion group was the highest (8200 N). In terms of maximum load and number of cycles performed prior to failure, the size 2 Activmotion plate showed higher results than all the other tested implants except the ContourLock plate. The iBalance implant offered the highest stiffness (3.1 kN/mm) for static loading on the lateral side, while the size 2 Activmotion showed the highest stiffness (4.8 kN/mm) in cyclic loading. Conclusions Overall, regarding all of the analysed strength parameters, the size 2 Activmotion plate provided equivalent or higher mechanical stability compared to the previously tested implant. Implants with a metaphyseal slope adapted to the tibia anatomy, and positioned more anteriorly on the proximal medial side of the tibia, should provide good mechanical stability. [less ▲]

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See detailStatistical extraction of process zones and representative subspaces in fracture of random composites
Kerfriden, P.; Schmidt, K. M.; Rabczuk, T. et al

in International Journal for Multiscale Computational Engineering (2013), 11(3), 253-287

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly ... [more ▼]

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on precomputed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localized phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced-order model. © 2013 by Begell House, Inc. [less ▲]

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See detailA Step Beyond to Overcome Design Fixation: A Design-by-Analogy Approach
Moreno Grandas, Diana Paola UL; Yang, Maria C.; Hernandez, Alberto A. et al

in Gero, John; Hanna, Sean (Eds.) Design Computing and Cognition’14 (2014, June)

Design fixation is a phenomenon that negatively impacts design outcomes, especially when it occurs during the ideation stage of a design process. This study expands our understanding of design fixation by ... [more ▼]

Design fixation is a phenomenon that negatively impacts design outcomes, especially when it occurs during the ideation stage of a design process. This study expands our understanding of design fixation by presenting a review of de-fixation approaches, as well as metrics employed to understand and account for design fixation. The study then explores the relevant ideation approach of Design-by-Analogy (DbA) to overcome design fixation, with a fixation experiment of 73 knowledge-domain experts. The study provides a design fixation framework and constitutes a genuine contribution to effectively identify approaches to mitigate design fixation in a wide range of design problems. [less ▲]

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See detailA stochastic Galerkin cell-based smoothed finite element method (SGCS-FEM)
Mathew, Tittu; Beex, Lars UL; Bordas, Stéphane UL et al

in International Journal of Computational Methods (in press)

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the ... [more ▼]

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the corresponding stochastic results are represented by Karhunen-Lo eve expansion and polynomial chaos expansion, respectively. The Young's Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of static displacements and free vibration frequencies. The feasibility and eff ectiveness of the proposed SGCS-FEM method in terms of accuracy and lower requirement on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework is computationally less demanding without compromising accuracy. [less ▲]

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See detailThe stochastic maintenance location routing allocation problem for rolling stock
Tönissen, Denise; Arts, Joachim UL

in International Journal of Production Economics (2020), 230

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See detailStochastic Model Predictive Control for Eco-Driving Assistance Systems in Electric Vehicles
Sajadi Alamdari, Seyed Amin UL

Doctoral thesis (2018)

Electric vehicles are expected to become one of the key elements of future sustainable transportation systems. The first generation of electric cars are already commercially available but still, suffer ... [more ▼]

Electric vehicles are expected to become one of the key elements of future sustainable transportation systems. The first generation of electric cars are already commercially available but still, suffer from problems and constraints that have to be solved before a mass market might be created. Key aspects that will play an important role in modern electric vehicles are range extension, energy efficiency, safety, comfort as well as communication. An overall solution approach to integrating all these aspects is the development of advanced driver assistance systems to make electric vehicles more intelligent. Driver assistance systems are based on the integration of suitable sensors and actuators as well as electronic devices and software-enabled control functionality to automatically support the human driver. Driver assistance for electric vehicles will differ from the already used systems in fuel-powered cars such as electronic stability programs, adaptive cruise control etc. in a way that they must support energy efficiency while the system itself must also have a low power consumption. In this work, an eco-driving functionality as the first step towards those new driver assistance systems for electric vehicles will be investigated. Using information about the internal state of the car, navigation information as well as advanced information about the environment coming from sensors and network connections, an algorithm will be developed that will adapt the speed of the vehicle automatically to minimize energy consumption. From an algorithmic point of view, a stochastic model predictive control approach will be applied and adapted to the special constraints of the problem. Finally, the solution will be tested in simulations as well as in first experiments with a commercial electric vehicle in the SnT Automation & Robotics Research Group (SnT ARG). [less ▲]

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