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See detailAn a posteriori error estimator for the spectral fractional power of the Laplacian
Bulle, Raphaël UL; Barrera, Olga; Bordas, Stéphane UL et al

E-print/Working paper (2022)

We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes ... [more ▼]

We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi–discretization scheme using a rational approximation which allows to reformulate the fractional problem into a family of non–fractional parametric problems. The estimator involves applying the implicit Bank–Weiser error estimation strategy to each parametric non–fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement strategy. [less ▲]

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See detailHierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
Bulle, Raphaël UL; Hale, Jack UL; Lozinski, Alexei et al

E-print/Working paper (2021)

In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of ... [more ▼]

In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of the finite element mesh. Despite the promise of Bank-Weiser type estimators, namely locality, computational efficiency, and asymptotic sharpness, they have seen little use in practical computational problems. The focus of this contribution is to describe a novel implementation of hierarchical estimators of the Bank-Weiser type in a modern high-level finite element software with automatic code generation capabilities. We show how to use the estimator to drive (goal-oriented) adaptive mesh refinement and to mixed approximations of the nearly-incompressible elasticity problems. We provide comparisons with various other used estimators. An open-source implementation based on the FEniCS Project finite element software is provided as supplementary material. [less ▲]

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See detailProjected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes
van Jaarsveld, Willem; Arts, Joachim UL

E-print/Working paper (2021)

Detailed reference viewed: 68 (7 UL)
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See detailAll in one stroke? Intervention Spaces for Dark Patterns
Rossi, Arianna UL; Bongard, Kerstin UL

E-print/Working paper (2021)

This position paper draws from the complexity of dark patterns to develop arguments for differentiated interventions. We propose a matrix of interventions with a \textit{measure axis} (from user-directed ... [more ▼]

This position paper draws from the complexity of dark patterns to develop arguments for differentiated interventions. We propose a matrix of interventions with a \textit{measure axis} (from user-directed to environment-directed) and a \textit{scope axis} (from general to specific). We furthermore discuss a set of interventions situated in different fields of the intervention spaces. The discussions at the 2021 CHI workshop "What can CHI do about dark patterns?" should help hone the matrix structure and fill its fields with specific intervention proposals. [less ▲]

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See detailA hybrid MGA-MSGD ANN training approach for approximate solution of linear elliptic PDEs
Dehghani, Hamidreza UL; Zilian, Andreas UL

E-print/Working paper (2020)

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems ... [more ▼]

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs via ANNs (Artificial Neural Networks). This presented approach allows the selection of a number of locations of interest at which the state variables are expected to fulfil the governing equations associated with a physical problem. Unlike classical PDE approximation methods such as finite differences or the finite element method, there is no need to establish and reconstruct the physical field quantity throughout the computational domain in order to predict the mechanical response at specific locations of interest. The basic idea of MGA-MSGD is the manipulation of the learnable parameters’ components responsible for the error explosion so that we can train the network with relatively larger learning rates which avoids trapping in local minima. The proposed training approach is less sensitive to the learning rate value, training points density and distribution, and the random initial parameters. The distance function to minimise is where we introduce the PDEs including any physical laws and conditions (so-called, Physics Informed ANN). The Genetic algorithm is modified to be suitable for this type of ANN in which a Coarse-level Stochastic Gradient Descent (CSGD) is exploited to make the decision of the offspring qualification. Employing the presented approach, a considerable improvement in both accuracy and efficiency, compared with standard training algorithms such classical SGD and Adam optimiser, is observed. The local displacement accuracy is studied and ensured by introducing the results of Finite Element Method (FEM) at sufficiently fine mesh as the reference displacements. A slightly more complex problem is solved ensuring the feasibility of the methodology [less ▲]

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See detailOn the Composition and Limitations of Publicly Available COVID-19 X-Ray Imaging Datasets
Garcia Santa Cruz, Beatriz UL; Sölter, Jan UL; Bossa, Matias Nicolas UL et al

E-print/Working paper (2020)

 Machine learning based methods for diagnosis and progression prediction of COVID-19 from imaging data have gained significant attention in the last months, in particular by the use of deep learning ... [more ▼]

 Machine learning based methods for diagnosis and progression prediction of COVID-19 from imaging data have gained significant attention in the last months, in particular by the use of deep learning models. In this context hundreds of models where proposed with the majority of them trained on public datasets. Data scarcity, mismatch between training and target population, group imbalance, and lack of documentation are important sources of bias, hindering the applicability of these models to real-world clinical practice. Considering that datasets are an essential part of model building and evaluation, a deeper understanding of the current landscape is needed. This paper presents an overview of the currently public available COVID-19 chest X-ray datasets. Each dataset is briefly described and potential strength, limitations and interactions between datasets are identified. In particular, some key properties of current datasets that could be potential sources of bias, impairing models trained on them are pointed out. These descriptions are useful for model building on those datasets, to choose the best dataset according the model goal, to take into account the specific limitations to avoid reporting overconfident benchmark results, and to discuss their impact on the generalisation capabilities in a specific clinical setting. [less ▲]

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See detailFluctuations for matrix-valued Gaussian processes
Jaramillo Gil, Arturo UL; Pardo Millan, Juan Carlos; Diaz Torres, Mario Alberto

E-print/Working paper (2020)

We consider a symmetric matrix-valued Gaussian process $Y^{(n)}=(Y^{(n)}(t);t\ge0)$ and its empirical spectral measure process $\mu^{(n)}=(\mu_{t}^{(n)};t\ge0)$. Under some mild conditions on the ... [more ▼]

We consider a symmetric matrix-valued Gaussian process $Y^{(n)}=(Y^{(n)}(t);t\ge0)$ and its empirical spectral measure process $\mu^{(n)}=(\mu_{t}^{(n)};t\ge0)$. Under some mild conditions on the covariance function of $Y^{(n)}$, we find an explicit expression for the limit distribution of $$Z_F^{(n)} := \left( \big(Z_{f_1}^{(n)}(t),\ldots,Z_{f_r}^{(n)}(t)\big) ; t\ge0\right),$$ where $F=(f_1,\dots, f_r)$, for $r\ge 1$, with each component belonging to a large class of test functions, and $$ Z_{f}^{(n)}(t) := n\int_{\R}f(x)\mu_{t}^{(n)}(\ud x)-n\E\left[\int_{\R}f(x)\mu_{t}^{(n)}(\ud x)\right].$$ More precisely, we establish the stable convergence of $Z_F^{(n)}$ and determine its limiting distribution. An upper bound for the total variation distance of the law of $Z_{f}^{(n)}(t)$ to its limiting distribution, for a test function $f$ and $t\geq0$ fixed, is also given. [less ▲]

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See detailIsogeometric analysis of thin Reissner-Mindlin plates and shells: Locking phenomena and generalized local B-bar method
Hu, Qingyuan UL; Xia, Yang; Natarajan, Sundararajan et al

E-print/Working paper (2017)

We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are ... [more ▼]

We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation is general and allows the flexible utilization of basis functions of different order as the projection bases. The present formulation is much cheaper computationally than the global $\bar{B}$ method. Through numerical examples, we show the consistency of the scheme, although the method is not Hu-Washizu variationally consistent. The numerical examples show that the proposed formulation alleviates locking and yields good accuracy for various thicknesses, even for slenderness ratios of $1 \times 10^5$, and has the ability to capture deformations of thin shells using relatively coarse meshes. From the detailed numerical study, it can be opined that the proposed method is less sensitive to locking and mesh distortion. [less ▲]

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See detailWhat makes Data Science different? A discussion involving Statistics2.0 and Computational Sciences
Ley, Christophe; Bordas, Stéphane UL

E-print/Working paper (2017)

Data Science is today one of the main buzzwords be it in business, industrial or academic settings. Machine learning, experimental design, data-driven modelling are all, undoubtedly, rising disciplines if ... [more ▼]

Data Science is today one of the main buzzwords be it in business, industrial or academic settings. Machine learning, experimental design, data-driven modelling are all, undoubtedly, rising disciplines if one goes by the soaring number of research papers and patents appearing each year. The prospect of becoming a ``Data Scientist'' appeals to many. A discussion panel organised as part of the European Data Science Conference (European Association for Data Science (EuADS)) asked the question: ``What makes Data Science different?'' In this paper we give our own, personal and multi-facetted view on this question, from an engineering and a statistics perspective. In particular, we compare Data Science to Statistics and discuss the connection between Data Science and Computational Science. [less ▲]

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See detailSustainability Research and Interactive Knowledge Generation
JUNG ép. PRELLER, Bérénice UL; Affolderbach, Julia UL; Schulz, Christian UL et al

E-print/Working paper (2014)

Based on experiences from the GreenRegio research project that investigates framework conditions for innovations in sustainable/green building, this working paper explores the potential of interactive and ... [more ▼]

Based on experiences from the GreenRegio research project that investigates framework conditions for innovations in sustainable/green building, this working paper explores the potential of interactive and collaborative methods for knowledge generation and co-production. Engagement with local practi-tioners, private industry, academics, political decision-makers and representatives of the non-profit sector early on in the research process allows researchers to gain better understanding of the re-search object and context. It also creates a platform for (mutual) knowledge exchange. Methodologi-cally, the project incorporates interactive workshops and Delphi-based feedback and validation rounds, that – over the lifespan of the project – offer a mutual learning process further inspired by in-sights and experiences across four case studies in Europe, Australia, and Canada. The exchange and learning processes provide important insights on different forms and pathways of sustainability transi-tions in the building sector to all participants involved in the project, researchers and researched alike. [less ▲]

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See detailA hybrid T-Trefftz polygonal finite element for linear elasticity
Bhattacharjee, Kalyan; Natarajan, Sundararajan; Bordas, Stéphane UL

E-print/Working paper (2014)

In this paper, we construct hybrid T-Trefftz polygonal finite elements. The displacement field within the polygon is repre- sented by the homogeneous solution to the governing differential equation, also ... [more ▼]

In this paper, we construct hybrid T-Trefftz polygonal finite elements. The displacement field within the polygon is repre- sented by the homogeneous solution to the governing differential equation, also called as the T-complete set. On the boundary of the polygon, a conforming displacement field is independently defined to enforce continuity of the displacements across the element boundary. An optimal number of T-complete functions are chosen based on the number of nodes of the polygon and degrees of freedom per node. The stiffness matrix is computed by the hybrid formulation with auxiliary displacement frame. Results from the numerical studies presented for a few benchmark problems in the context of linear elasticity shows that the proposed method yield highly accurate results. [less ▲]

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See detailOn the equivalence between the cell-based smoothed finite element method and the virtual element method
Natarajan, Sundararajan; Bordas, Stéphane UL; Ean Tat, Ooi

E-print/Working paper (2014)

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity ... [more ▼]

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEMis combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D. [less ▲]

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See detailZwei IT-Sicherheitsmethoden im Vergleich: Mehari versus BSI IT-Grundschutz
Dagorn, Nathalie; Schiltz, Jang UL

E-print/Working paper (2008)

Detailed reference viewed: 90 (3 UL)
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See detailBayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights
Rappel, Hussein UL; Beex, Lars UL; Hale, Jack UL et al

E-print/Working paper (n.d.)

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼]

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲]

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See detailLinear smoothed extended finite element method
Murugesan; Natarajan, Sundararajan; Gadyam, Palani et al

E-print/Working paper (n.d.)

The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to ... [more ▼]

The extended finite element method (XFEM) was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong or weak and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. Moreover, in the case of open surfaces and singularities, special, usually non-polynomial functions must also be integrated.A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and convergence of the numerical solution. The smoothed extended finite element method (SmXFEM) [1], for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in [1, 2] that the strain smoothing is inaccurate when non-polynomial functions are in the basis. This is due to the constant smoothing function used over the smoothing domains which destroys the effect of the singularity. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure [3] which provides better approximation to higher order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics (LEFM) are solved to compare the standard XFEM, the constant-smoothed XFEM (Sm-XFEM) and the linear-smoothed XFEM (LSm-XFEM). We observe that the convergence rates of all three methods are the same. The stress intensity factors (SIFs) computed through the proposed LSm-XFEM are however more accurate than that obtained through Sm-XFEM. To conclude, compared to the conventional XFEM, the same order of accuracy is achieved at a relatively low computational effort. [less ▲]

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See detailOn the weightwise nonlinearity of weightwise perfectly balanced functions
Gini, Agnese UL; Meaux, Pierrick UL

E-print/Working paper (n.d.)

Detailed reference viewed: 35 (6 UL)
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See detailLinear smoothed polygonal and polyhedral finite elements
Francis, Amrita; Ortiz-Bernardin, Alejandro; Bordas, Stéphane UL et al

E-print/Working paper (n.d.)

It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal ... [more ▼]

It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes to deliver improved accuracy and pass the patch test to machine precision. [less ▲]

Detailed reference viewed: 463 (10 UL)