114 research outputs found
An enriched finite element model with q-refinement for radiative boundary layers in glass cooling
Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P1 approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework. A class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls. Using an industrial electromagnetic spectrum, the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h -version finite element method. Furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries. The time integration choice is essential to implement a q -refinement procedure introduced in the current study. The enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment. The performance of the proposed method is analysed for glass annealing in two enclosures where the simplified P1 approximation solution with the partition of unity method, the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical Rosseland model
Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain
This paper proposes a partition of unity enrichment scheme for the solution of the electromagnetic wave equation in the time domain. A discretization scheme in time is implemented to render implicit solutions of systems of equations possible. The scheme allows for calculation of the field values at different time steps in an iterative fashion. The spatial grid is partitioned into a finite number of elements with intrinsic shape functions to form the bases of solution. Furthermore, each finite element degree of freedom is expanded into a sum of a slowly varying term and a combination of highly oscillatory functions. The combination consists of plane waves propagating in multiple directions, with a fixed frequency. This significantly reduces the number of degrees of freedom required to discretize the unknown field, without compromising on the accuracy or allowed tolerance in the errors, as compared to that of other enriched FEM approaches. Also, this considerably reduces the computational costs in terms of memory and processing time. Parametric studies, presented herein, confirm the robustness and efficiency of the proposed method and the advantages compared to another enrichment method
Path following for a target point attached to a unicycle type vehicle
In this article, we address the control problem of unicycle path following,
using a rigidly attached target point. The initial path following problem has
been transformed into a reference trajectory following problem, using saturated
control laws and a geometric characterization hypothesis, which links the
curvature of the path to be followed with the target point. The proposed
controller allows global stabilization without restrictions on initial
conditions. The effectiveness of this controller is illustrated through
simulations
Mixed enrichment for the finite element method in heterogeneous media
Problems of multiple scales of interest or of locally nonsmooth solutions may often involve heterogeneous media. These problems are usually very demanding in terms of computations with the conventional finite element method. On the other hand, different enriched finite element methods such as the partition of unity, which proved to be very successful in treating similar problems, are developed and studied for homogeneous media. In this work, we present a new idea to extend the partition of unity finite element method to treat heterogeneous materials. The idea is studied in applications to wave scattering and heat transfer problems where significant advantages are noted over the standard finite element method. Although presented within the partition of unity context, the same enrichment idea can also be extended to other enriched methods to deal with heterogeneous materials
Medical image information representation: Gabor Filter solution for the Big Data
International audienceIn the health field, several thousand images are generated every day in medical imaging establishments. The volume of information involved is still far from being fully controlled. On the other hand, the development of machine learning tools today opens the way to a new generation of image analysis in this context of "BigData". Moreover, our approach is part of this research dynamic. In order to test the robustness of our algorithm and its degree of adaptation to BigData, we tested, in a first phase of analysis, our algorithm on an image-database containing 320 mammograms. The precision obtained is estimated at 75% for a recall of 33%. In a second analysis phase, we performed the test on an image database containing 1000 medical images. The precision obtained is estimated at nearly 70% for a recall of 33%. Although the precision obtained in this first step is far from perfect, our processing algorithm remains promising and shows a good adaptation to the management of "Digdat
On stability of discretizations of the Helmholtz equation (extended version)
We review the stability properties of several discretizations of the
Helmholtz equation at large wavenumbers. For a model problem in a polygon, a
complete -explicit stability (including -explicit stability of the
continuous problem) and convergence theory for high order finite element
methods is developed. In particular, quasi-optimality is shown for a fixed
number of degrees of freedom per wavelength if the mesh size and the
approximation order are selected such that is sufficiently small and
, and, additionally, appropriate mesh refinement is used near
the vertices. We also review the stability properties of two classes of
numerical schemes that use piecewise solutions of the homogeneous Helmholtz
equation, namely, Least Squares methods and Discontinuous Galerkin (DG)
methods. The latter includes the Ultra Weak Variational Formulation
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