Toufic Abboud

Electromagnetic waves in an inhomogeneous medium

Abstract In this paper we consider the electromagnetic wave problem in an inhomogeneous medium. We first prove uniqueness of the solution using Rellich and Cauchy-Kowalewska theorems. Then we explicitly compute the Dirichlet-Neumann operator on the sphere, we reduce the equations to a problem on a truncated domain, and we give a variational formulation. This formulation reads as a compact perturbation of a coercive operator, which leads to the existence of the solution according to Fredholms alternative.

Numerical prediction of SDOF-Perforated Plate Acoustic Treatment Impedance. Part 1 : Linear domain

A new numerical prediction tool has been developed in order to improve acoustics impedance predictions for typical Nacelle SDOF with perforated-plate liners, accounting for realistic geometry and flow. This method is based on domain breakdown and Linearized Compressible Navier-Stokes equations in the holes. Numerical Results are successfully compared to analytical predictions and measurements in the linear domain without flow. Next steps are non-linear effects and the influence of grazing mean flow.

Integral method for the Stokes problem

Abstract We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity formulation. For this problem, the classical finite elements method of degree one converges only in O ( h ) for the quadratic norm of the vorticity, if the domain is convex and the solution regular. We propose to use harmonic functions obtained by a simple layer potential to approach vorticity along the boundary. Numerical results are very satisfying and we prove that this new numerical scheme leads to an error of order O (h) for the natural norm of the vorticity and under more regularity assumptions from O (h 3/2 ) to O (h 2 ) for the quadratic norm of the vorticity. To cite this article: T. Abboud et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 71–76

Hi-B o X: A generic library of fast solvers for boundary element methods

Hi-BoX is a generic library implementing state-of-the-art fast direct and iterative solvers for existing codes based on Boundary Element Method (BEM) or Method of Moments (MoM). It benefits from recent advances in numerical methods, linear algebra and High Performance Computing (HPC). This includes new advances in H-matrix and Fast Multipole Method (FMM) and their hybridization, new approaches for handling a large number of right-hand sides, and finally the use of new parallelization techniques based on a runtime system simplifying the use of modern massively parallel and heterogeneous architectures.

A new method for investigating boundary vorticity

We consider the bi-dimensional Stokes problem for incompressible fluids in the stream function-vorticity formulation. For this problem, the classical finite-element method of degree one converges with an order of only 1/2 for the quadratic norm of the error on the vorticity. We propose changing the method of approximation and adding harmonic functions to approach vorticity along the boundary. The numerical results are very satisfactory and we prove that this new numerical scheme leads to an error of order 1 for the natural norm of the vorticity and under more regularity assumptions from 3/2 to 2 for the quadratic norm of the vorticity. This article was chosen from Selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.