Parallel computing for the finite element method

A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This paper describes how the modeling of large devices has been made possible using parallel computation, New algorithms are then proposed to implement this formulation on a cluster of workstations (10 DEC ALPHA 300X) and on a CRAY C98. Analysis of the computation efficiency is performed using simple problems. The electromagnetic scattering of a plane wave by a perfect electric conducting airplane is finally given as example

Drichlet forms for Poisson measures and L\'evy processes : the lent particle method

We present a new approach to absolute continuity of laws of Poisson functionals. The theoretical framework is that of local Dirichlet forms as a tool to study probability spaces. The method gives rise to a new explicit calculus that we show first on some simple examples : it consists in adding a particle and taking it back after computing the gradient. Then we apply it to SDE's driven by Poisson measure

Impact on floating membranes

When impacted by a rigid object, a thin elastic membrane with negligible bending rigidity floating on a liquid pool deforms. Two axisymmetric waves radiating from the impact point propagate. In the first place, a longitudinal wave front -- associated with in-plane deformation of the membrane and traveling at constant speed -- separates an outward stress free domain with a stretched but flat domain. Then, in the stretched domain a dispersive transverse wave travels at a wave speed that depends on the local stretching rate. We study the dynamics of this fluid-body system and we show that the wave dynamics is similar to the capillary waves that propagate at a liquid-gas interface but with a surface tension coefficient that depends on impact speed. We emphasize the role of the stretching in the membrane in the wave dynamics but also in the development of a buckling instability that give rise to radial wrinkles

Parsing Expression Grammars Made Practical

Parsing Expression Grammars (PEGs) define languages by specifying recursive-descent parser that recognises them. The PEG formalism exhibits desirable properties, such as closure under composition, built-in disambiguation, unification of syntactic and lexical concerns, and closely matching programmer intuition. Unfortunately, state of the art PEG parsers struggle with left-recursive grammar rules, which are not supported by the original definition of the formalism and can lead to infinite recursion under naive implementations. Likewise, support for associativity and explicit precedence is spotty. To remedy these issues, we introduce Autumn, a general purpose PEG library that supports left-recursion, left and right associativity and precedence rules, and does so efficiently. Furthermore, we identify infix and postfix operators as a major source of inefficiency in left-recursive PEG parsers and show how to tackle this problem. We also explore the extensibility of the PEG paradigm by showing how one can easily introduce new parsing operators and how our parser accommodates custom memoization and error handling strategies. We compare our parser to both state of the art and battle-tested PEG and CFG parsers, such as Rats!, Parboiled and ANTLR.Comment: "Proceedings of the International Conference on Software Language Engineering (SLE 2015)" - 167-172 (ISBN : 978-1-4503-3686-4

The skeleton of the UIPT, seen from infinity

We prove that geodesic rays in the Uniform Infinite Planar Triangulation (UIPT) coalesce in a strong sense using the skeleton decomposition of random triangulations discovered by Krikun. This implies the existence of a unique horofunction measuring distances from infinity in the UIPT. We then use this horofunction to define the skeleton "seen from infinity" of the UIPT and relate it to a simple Galton--Watson tree conditioned to survive, giving a new and particularly simple construction of the UIPT. Scaling limits of perimeters and volumes of horohulls within this new decomposition are also derived, as well as a new proof of the $2$-point function formula for random triangulations in the scaling limit due to Ambj{\o}rn and Watabiki.Comment: 34 pages, 14 figure

Energy image density property and the lent particle method for Poisson measures

We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the {\it energy image density} property for Dirichlet forms and on what we call {\it the lent particle method} which consists in adding a particle and taking it back after some calculation.Comment: 29

Contribution of studies of sub-seismic fracture populations to paleo-hydrological reconstructions (Bighorn Basin, USA)

This work reports on the reconstruction of the paleo-hydrological history of the Bighorn Basin (Wyoming, USA) and illustrates the advantages and drawbacks of using sub-seismic diffuse fracture populations (i.e., micrometric to metric joints and veins forming heterogeneous networks), rather than fault zones, to characterize paleo-fluid systems at both fold and basin scales. Because sub-seismic fractures reliably record the successive steps of deformation of folded rocks, the analysis of the geochemical signatures of fluids that precipitated in these fractures reveals the paleo-fluid history not only during, but also before and after, folding. The present study also points out the need for considering pre-existing fluid systems and basin-scale fluid migrations to reliably constrain the evolution of fluid systems in individual folds