Past

We report on two joint works with Jeremy Quastel and Alejandro Ramirez, on an

interacting particle system which can be viewed as a combustion mechanism or a

chemical reaction.

We consider a model of the reaction $X+Y\to 2X$ on the integer lattice in

which $Y$ particles do not move while $X$ particles move as independent

continuous time, simple symmetric random walks. $Y$ particles are transformed

instantaneously to $X$ particles upon contact.

We start with a fixed number $a\ge 1$ of $Y$ particles at each site to the

right of the origin, and define a class of configurations of the $X$ particles

to the left of the origin having a finite $l^1$ norm with a specified

exponential weight. Starting from any configuration of $X$ particles to the left

of the origin within such a class, we prove a central limit theorem for the

position of the rightmost visited site of the $X$ particles.

We consider the parallel solution of sparse linear systems of equations in a limited memory environment. A preliminary out-of core version of a sparse multifrontal code called MUMPS (MUltifrontal Massively Parallel Solver) has been developed as part of a collaboration between CERFACS, ENSEEIHT and INRIA (ENS-Lyon and Bordeaux).

We first briefly describe the current status of the out-of-core factorization phase. We then assume that the factors have been written on the hard disk during the factorization phase and we discuss the design of an efficient solution phase.Two different approaches are presented to read data from the disk, with a discussion on the advantages and the drawbacks of each one.

Our work differs and extends the work of Rothberg and Schreiber (1999) and of Rotkin and Toledo (2004) because firstly we consider a parallel out-of-core context, and secondly we also study the performance of the solve phase.

This is work on collaboration with E. Agullo, I.S Duff, A. Guermouche, J.-Y. L'Excellent, T. Slavova

OWL Meeting

We consider Burgers type nonlinear SPDEs with L

We follow Arnold's approach of Euler equation as a geodesic on the group of

diffeomorphisms. We construct a geometrical Brownian motion on this group in the

case of the two dimensional torus, and prove the global existence of a

stochastic perturbation of Euler equation (joint work with F. Flandoli and P.

Malliavin).

Other diffusions allow us to obtain the deterministic Navier-Stokes equation

as a solution of a variational problem (joint work with F. Cipriano).

A strict adherence to threshold pivoting in the direct solution of symmetric indefinite problems can result in substantially more work and storage than forecast by an sparse analysis of the symmetric problem. One way of avoiding this is to use static pivoting where the data structures and pivoting sequence generated by the analysis are respected and pivots that would otherwise be very small are replaced by a user defined quantity. This can give a stable factorization but of a perturbed matrix.

The conventional way of solving the sparse linear system is then to use iterative refinement (IR) but there are cases where this fails to converge. We will discuss the use of more robust iterative methods, namely GMRES and its variant FGMRES and their backward stability when the preconditioning is performed by HSL_M57 with a static pivot option.

Several examples under Matlab will be presented.

In St Anne's College