Coupling Harmonic Functions-Finite Elements for Solving the Stream Function-Vorticity Stokes Problem

We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity form. The classical finite element method of degree one usually used does not allow the vorticity on the boundary of the domain to be computed satisfactorily when the meshes are unstructured and does not converge optimally. To better approach the vorticity along the boundary, we propose that harmonic functions obtained by integral representation be used. Numerical results are very satisfactory, and we prove that this new numerical scheme leads to an optimal convergence rate of order 1 for the natural norm of the vorticity and, under higher regularity assumptions, from 3/2 to 2 for the quadratic norm of the vorticity

Uterus transplantation:An update and the Middle East perspective

Uterus transplantation (UTx) is the only available treatment for absolute uterine factor infertility (AUFI), which is caused by either absence (congenital or after hysterectomy) or presence of a non-functioning uterus. Uterus transplantation became a clinical reality after more than 10 years of structured animal-based research. Aside from gestational surrogacy, this procedure is the only alternative for women with AUFI to attain genetic motherhood. In the Middle East, North Africa and Turkey (MENAT) region, out of a population of around 470 million, more than 100,000 women of fertile age are estimated to suffer from AUFI. Introduction of UTx as an infertility treatment in this region will certainly differ in specific countries from ethical, religious and legal standpoints depending on culture and religion. The MENAT region is the cradle of three religions and the geographic area encompasses a variety of cultures and religions with different views on assisted reproduction. In light of these issues, the aim of this article is to give an overview of the research-based development of UTx and its clinical results up until today as well as to explore how UTx would fit into current infertility treatments in the MENAT region, with its existing multifaceted religious perspectives

Integral Formulations for the EEG Problem

The forward electro-encephalography (EEG) problem involves finding a potential V from the Poisson equation (V)=f, in which f represents electrical sources in the brain, and the conductivity of the head tissues. In the piecewise constant conductivity head model, this can be accomplished by the Boundary Element Method (BEM) using a suitable integral formulation. Most previous work is based on the same integral formulation, based on a double-lay- er potential. In this article we detail several alternative possibilities. We present a dual approach which involves a single-layer potential. Finally, we propose a symmetric formulation, which combines single and double-layer potentials, and which is new to the field of EEG, although it has been applied to other problems in electromagnetism. The three methods have been evaluated numerically using a semi-realistic geometry with known analytical solution, and the symmetric method achieves a significantly higher accuracy

Etude mathematique et numerique de quelques problemes de diffraction d'ondes electromagnetiques

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : T 79571 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Etude mathematique et numerique de quelques problemes de diffraction d'ondes electromagnetiques

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : T 79571 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Coupling discontinuous Galerkin methods and retarded potentials for transient wave propagation on unbounded domains

International audienceThis work deals with the numerical simulation of wave propagation on unbounded domains with localized heterogeneities. To do so, we propose to combine a discretization based on a discontinuous Galerkin method in space and explicit finite differences in time on the regions containing heterogeneities with the retarded potential method to account the unbounded nature of the computational domain. The coupling formula enforces a discrete energy identity ensuring the stability under the usual CFL condition in the interior. Moreover, the scheme allows to use a smaller time step in the interior domain yielding to quasi-optimal discretization parameters for both methods. The aliasing phenomena introduced by the local time stepping are reduced by a post-processing by averaging in time obtaining a stable and second order consistent (in time) coupling algorithm. We compute the numerical rate of convergence of the method for an academic problem. The numerical results show the feasibility of the whole discretization procedure. © 2011 Elsevier Inc