Johansson, Fredrik

We review the Preparata-Sarwate algorithm, a simple $O(n^{3.5})$ method for computing the characteristic polynomial, determinant and adjugate of an $n \times n$ matrix using only ring operations together with exact divisions by small integers. The algorithm is a baby-step giant-step version of the more well-known Faddeev-Leverrier algorithm. We mak...

Poëtte, Gaël

In this paper, we build wellposed intrusive generalised Polynomial Chaos (gPC) based reduced models for uncertain photonics. We solve the reduced models with a Monte-Carlo (MC) scheme. Care is taken to highlight under which condition a reduced model (gPC based or not) is wellposed. The analysis is carried out thanks to an analogy between the constr...

Poëtte, Gaël Brun, Emeric

In this paper, we are interested in taking into account uncertainties for k eff computations in neu-tronics. More generally, the material of this paper can be applied to propagate uncertainties in eigenvalue/eigenvector computations for the linear Boltzmann equation. In [1, 2], an intrusive MC solver for the gPC based reduced model of the instation...

RICHARD, Benoît Le Pivert, Xavier Bourien, Yves-Marie

Battery Energy Storage Systems (BESS) are more and more competitive due to their increasing performances and decreasing costs. Although certain battery storage technologies may be mature and reliable from a technological perspective, with further cost reductions expected, the economic concern of battery systems is still a major barrier to be overco...

Mezzarobba, Marc

We develop a toolbox for the error analysis of linear recurrences with constant or polynomial coefficients, based on generating series, Cauchy's method of majorants, and simple results from analytic combinatorics. We illustrate the power of the approach by several nontrivial application examples. Among these examples are a new worst-case analysis o...

Marchal, Loris Marette, Thibault Pichon, Grégoire Vivien, Frédéric

Sparse direct solvers using Block Low-Rank compression have been proven efficient to solve problems arising in many real-life applications. Improving those solvers is crucial for being able to 1) solve larger problems and 2) speed up computations. A main characteristic of a sparse direct solver using low-rank compression is when compression is perf...

Bürgisser, Peter Cucker, Felipe Lairez, Pierre

We design a probabilistic algorithm that, on input ε>0 and a polynomial system F given by black-box evaluation functions, outputs an approximate zero of F, in the sense of Smale, with probability at least 1-ε. When applying this algorithm to u·F, where u is uniformly random in the product of unitary groups, the algorithm performs poly(n,δ) L(F) ( Γ...

El Mousaoui, Abdelghani Argoul, Pierre El Rhabi, Mohammed Hakim, Abdelilah

In this paper we are interested in a dynamic description of the collective pedestrian motion based on the kinetic model of Bathnagar-Gross-Krook (BGK). In this model a pedestrians trend towards a state of equilibrium in a certain relaxation time is modeled. An approximation of the Maxwellian function that represents this equilibrium state is determ...

Akimoto, Youhei Auger, Anne Glasmachers, Tobias Morinaga, Daiki

Evolution strategies (ESs) are zero-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are generated. Among different variants, CMA-ES is nowadays recognized as one of the state-of-the-art zero-order optim...

EL IDI, Mohamed Moussa KARKRI, Moustapha

In this paper, a numerical study is conducted on the melting and solidification process of metal foam/paraffin wax with cyclic heating and cooling. A mathematical model based on the Brinkman-Frochheimer extended Darcy equation and the local thermal non-equilibrium model (LTNE) is proposed. The paraffin phase change is modeled by enthalpy-porosity m...