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Results 121-140 of 474.
Guaranteed error bounds in homogenisation: an optimum stochastic approach to preserve the numerical separation of scales ; ; Bordas, Stéphane et al in International Journal for Numerical Methods in Engineering (2017), 110(2), 103132 This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion ... [more ▼] This paper proposes a new methodology to guarantee the accuracy of the homogenisation schemes that are traditionally employed to approximate the solution of PDEs with random, fast evolving diffusion coefficients. We typically consider linear elliptic diffusion problems in randomly packed particulate composites. Our work extends the pioneering work presented in [26,32] in order to bound the error in the expectation and second moment of quantities of interest, without ever solving the fine-scale, intractable stochastic problem. The most attractive feature of our approach is that the error bounds are computed without any integration of the fine-scale features. Our computations are purely macroscopic, deterministic, and remain tractable even for small scale ratios. The second contribution of the paper is an alternative derivation of modelling error bounds through the Prager-Synge hypercircle theorem. We show that this approach allows us to fully characterise and optimally tighten the interval in which predicted quantities of interest are guaranteed to lie. We interpret our optimum result as an extension of Reuss-Voigt approaches, which are classically used to estimate the homogenised diffusion coefficients of composites, to the estimation of macroscopic engineering quantities of interest. Finally, we make use of these derivations to obtain an efficient procedure for multiscale model verification and adaptation. [less ▲] Detailed reference viewed: 302 (20 UL)An implicit potential method along with a meshless technique for incompressible fluid flows for regular and irregular geometries in 2D and 3D Bourantas, Georgios ; ; et al in Engineering Analysis with Boundary Elements (2017), 77 We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state ... [more ▼] We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state, incompressible Navier-Stokes (N-S) equations in their primitive variable (u-v-w-p) formulation. The governing equations are solved in their strong form using either a collocated or a semi-staggered type meshless nodal configuration. The unknown field functions and derivatives are calculated using the Modified Moving Least Squares (MMLS) interpolation method. Both velocity-correction and pressure correction methods applied ensure the incompressibility constraint and mass conservation. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it can be applied, in a straightforward manner to: steady, unsteady, internal and external fluid flows in 2D and 3D, (ii) it equally applies to regular an irregular geometries, (iii) a distribution of points is sufficient, no numerical integration in space nor any mesh structure are required, (iv) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (v) it is quite simple and accurate, (vi) results can be obtained using collocated or semi-staggered nodal distributions, (vii) there is no need to compute the velocity potential nor the unit normal vectors and (viii) there is no need for a curvilinear system of coordinates. Simulations of fluid flow in 2D and 3D for regular and irregular geometries indicate the validity of the proposed methodology. [less ▲] Detailed reference viewed: 138 (2 UL)Computational Sciences Year 2016 Activity Report Bordas, Stéphane Report (2016) Born from a bottom-up initiative of Mathematics, Computer Science, Physics and Computational Engineering, Computational Sciences (CoSc) have contributed to create at UL a positive and symbiotic research ... [more ▼] Born from a bottom-up initiative of Mathematics, Computer Science, Physics and Computational Engineering, Computational Sciences (CoSc) have contributed to create at UL a positive and symbiotic research environment relying on a strong fundamental scientific research core. CoSc will continue to rationalize research efforts across a range of strategic innovation domains by centralizing research and development tools and building upon the existing strengths of the Luxembourgish research and socio-economic landscape. [less ▲] Detailed reference viewed: 108 (4 UL)Image to analysis pipeline: single and double balloons kyphoplasty Baroli, Davide ; Hauseux, Paul ; Hale, Jack et al Poster (2016, December 12) In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical ... [more ▼] In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical image are pre-processed using open-source software Slice3D for segmentation and 3D reconstruction operation. Then, using geometric processing the 3D surface geometry is enhanced to avoid degenerate element and trigging phenomena on vertebra and cement area. We perform a finite element analysis to evaluate the risk of subsequent vertebral fracture. Finally using Monte-Carlo technique, we assess the propagation of uncertainty of material parameter on the evaluation of this risk. Based on the developed semi-automatic pipelines, it is possible to perform a patient-specific simulation that assesses the successful of kyphoplasty operation. [less ▲] Detailed reference viewed: 231 (35 UL)Elastography under uncertainty Hale, Jack ; ; Bordas, Stéphane Poster (2016, December 12) Detailed reference viewed: 208 (11 UL)Bayesian inference for parameter identification in computational mechanics Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Poster (2016, December 12) Detailed reference viewed: 182 (10 UL)Real-time error control for surgical simulation Bui, Huu Phuoc ; Tomar, Satyendra ; et al Poster (2016, December 12) Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use ... [more ▼] Objective: To present the first real-time a posteriori error-driven adaptive finite element approach for real-time simulation and to demonstrate the method on a needle insertion problem. Methods: We use corotational elasticity and a frictional needle/tissue interaction model based on friction. The problem is solved using finite elements within SOFA. The refinement strategy relies upon a hexahedron-based finite element method, combined with a posteriori error estimation driven local $h$-refinement, for simulating soft tissue deformation. Results: We control the local and global error level in the mechanical fields (e.g. displacement or stresses) during the simulation. We show the convergence of the algorithm on academic examples, and demonstrate its practical usability on a percutaneous procedure involving needle insertion in a liver. For the latter case, we compare the force displacement curves obtained from the proposed adaptive algorithm with that obtained from a uniform refinement approach. Conclusions: Error control guarantees that a tolerable error level is not exceeded during the simulations. Local mesh refinement accelerates simulations. Significance: Our work provides a first step to discriminate between discretization error and modeling error by providing a robust quantification of discretization error during simulations. [less ▲] Detailed reference viewed: 251 (20 UL)Uncertainty quantification for soft tissue biomechanics Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane Poster (2016, December) Detailed reference viewed: 234 (20 UL)Numerical methods for fracture/cutting of heterogeneous materials Sutula, Danas ; Agathos, Konstantinos ; Ziaei Rad, Vahid et al Presentation (2016, December) Detailed reference viewed: 210 (15 UL)Shape Optimization Directly from CAD: an Isogeometric Boundary Element Approach Using T-splines ; ; Bordas, Stéphane Report (2016) Detailed reference viewed: 328 (5 UL)Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems ; ; Bordas, Stéphane E-print/Working paper (2016) We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The ... [more ▼] We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the isogeometric analysis, in particular of the related pollution error. Numerical results performed with high-order basis functions (third or fourth orders) showed no visible pollution error even for very high frequencies. This property combined with exact geometrical representation makes isogeometric analysis a very promising platform to solve high-frequency acoustic problems. [less ▲] Detailed reference viewed: 213 (16 UL)Bayesian inference for material parameter identification in elastoplasticity Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Scientific Conference (2016, September 07) Detailed reference viewed: 248 (29 UL)Stochastic FE analysis of brain deformation with different hyper-elastic models Hauseux, Paul ; Hale, Jack ; Bordas, Stéphane Scientific Conference (2016, September) Detailed reference viewed: 267 (29 UL)Multi-scale modelling of fracture Bordas, Stéphane ; ; et al Speeches/Talks (2016) We present recent models on complexity reduction for computational fracture mechanics Detailed reference viewed: 193 (7 UL)Numerical studies of magnetic particles concentration in biofluid (blood) under the influence of high gradient magnetic field in microchannel ; Bourantas, Georgios ; et al Scientific Conference (2016, July 15) Detailed reference viewed: 162 (9 UL)Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment ; ; et al in International Journal of Fracture (2016) Detailed reference viewed: 292 (21 UL)Simulating topological changes in real time for surgical assistance Bordas, Stéphane ; ; et al Speeches/Talks (2016) Detailed reference viewed: 589 (38 UL)A Bayesian approach for parameter identification in elastoplasticity Rappel, Hussein ; Beex, Lars ; Hale, Jack et al Scientific Conference (2016, June 09) Detailed reference viewed: 150 (15 UL)Phase field approach to fracture: Towards the simulation of cutting soft tissues Ziaei Rad, Vahid ; Hale, Jack ; et al Scientific Conference (2016, June 08) Detailed reference viewed: 339 (11 UL)Weakening the tight coupling between geometry and simulation in isogeometric analysis Tomar, Satyendra ; ; et al Presentation (2016, June 07) In the standard paradigm of isogeometric analysis, the geometry and the simulation spaces are tightly integrated, i.e. the same non-uniform rational B-splines (NURBS) space, which is used for the geometry ... [more ▼] In the standard paradigm of isogeometric analysis, the geometry and the simulation spaces are tightly integrated, i.e. the same non-uniform rational B-splines (NURBS) space, which is used for the geometry representation of the domain, is employed for the numerical solution of the problem over the domain. However, there are situations where this tight integration is a bane rather than a boon. Such situations arise where, e.g., (1) the geometry of the domain is simple enough to be represented by low order NURBS, whereas the unknown (exact) solution of the problem is sufficiently regular, and thus, the numerical solution can be obtained with improved accuracy by using NURBS of order higher than that required for the geometry, (2) the constraint of using the same space for the geometry and the numerical solution is particularly undesirable, such as in the shape and topology optimization, and (3) the solution of the problem has low regularity but for the curved boundary of the domain one can employ higher order NURBS. Therefore, we propose to weaken this constraint. An extensive study of patch tests on various combinations of polynomial degree, geometry type, and various cases of varying degrees and control variables between the geometry and the numerical solution will be discussed. It will be shown, with concrete reasoning, that why patch test fails in certain cases, and that those cases should be avoided in practice. Thereafter, selective numerical examples will be presented to address some of the above-mentioned situations, and it will be shown that weakening the tight coupling between geometry and simulation offers more flexibility in choosing the numerical solution spaces, and thus, improved accuracy of the numerical solution. [less ▲] Detailed reference viewed: 180 (9 UL) |
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