Mean-square A -stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stability properties of the drift-diagonally-implicit methods previously introduced (Debrabant and Rößler, Appl. Numer. Math. 59(3-4):595-607, 2009

Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings

The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called Tulczyjew's triples. The results are also extended to the case of discrete dynamics and nonholonomic mechanics. Interesting applications to geometrical integration of Hamiltonian systems are obtained.Comment: 33 page

Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of Itô stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are shown to be mean-square A-stable for the usual complex scalar linear test problem with multiplicative noise and improve significantly the stability properties of the drift-diagonally-implicit methods previously introduced (Debrabant and Rößler, Appl. Numer. Math. 59(3–4):595–607, 2009)

Rapport annuel : tome 1 suite

In this paper, we propose a new approach for sampling from probability measures in, possibly, high-dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the invariant measure of the original system, we show that accelerated convergence to equilibrium and reduced asymptotic variance can be achieved, leading, thus, to a computationally advantageous sampling algorithm. The new perturbed Langevin dynamics is reversible with respect to the target probability measure and, consequently, does not suffer from the drawbacks of the nonreversible Langevin samplers that were introduced in C.-R. Hwang et al. (1993)[1]and studied in, e.g., T. Lelièvre et al. (2013)[2]and A.B. Duncan et al. (2016)[3], while retaining all of their advantages in terms of accelerated convergence and reduced asymptotic variance. In particular, the reversibility of the dynamics ensures that there is no oscillatory transient behaviour. The improved performance of the proposed methodology, in comparison to the standard overdamped Langevin dynamics and its nonreversible perturbation, is illustrated on an example of sampling from a two-dimensional warped Gaussian target distribution

Second weak order explicit stabilized methods for stiff stochastic differential equations

We introduce a new family of explicit integrators for stiff Itˆo stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of onestep stabilized methods with extended stability domains and do not suffer from stepsize reduction that standard explicit methods face. The family is based on the classical stabilized methods of order two for deterministic problems and its construction relies on the strategy of modified equations recently introduced for SDEs. The convergence and the stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations (SPDEs), are presented and confirm the theoretical results

Splitting methods with complex times for parabolic equations

Abstract We consider splitting methods with complex coefficients to approximate the solutions of parabolic equations. We show resorting to complex times makes it possible to construct high order composition schemes that remain applicable for non-reversible operators

Détection des atomes de fer par spectrocopie d'émission et de fluorescence induite par laser en flammes de propergols solide.

International audiencePlanar laser-induced fluorescence on atomic iron is investigated in this paper, and a measurement strategy is proposed to monitor the fluorescence of iron atoms with good sensitivity. A model is proposed to fit the experimental fluorescence spectra, and good agreement is found between simulated and experimental spectra. Emission and laser-induced fluorescence measurements are performed in the flames of ammonium perchlorate composite propellants containing iron-based catalysts. A fluorescence signal from iron atoms after excitation at 248 nm is observed for the first time in propellant flames. Images of the spatial distribution of iron atoms are recorded in the flame in which turbulent structures are generated. Iron fluorescence is detected up to 1.0 MPa, which opens the way to application in propellant combustion.L'imagerie de fluorescence induite par laser est appliquée aux atomes de fer et une stratégie pour leurs mesurer avec une bonne sensibilité est présentée dans cet article. Un modèle est développé pour calculer les spectres de fluorescence et un bon accord est trouvé entre les spectres calculés et expérimentaux. Les mesures en émission et en fluorescence induite par laser sont effectuées dans des flammes de propergols composites à base de perchlorate d'ammonium dopés avec des catalyseurs ferriques.Le signal de fluorescence induit par l'excitation laser à 248 nm des atomes de fer est observé pour la première fois dans les flammes de propergol. La répartition spatiale des atomes de fer est visualisée en flamme dont les structures turbulentes sont forcées. La fluorescence du fer est détectée jusqu'à 1,0 MPa, ce qui ouvre des perspectives de visualisation d'écoulements de gaz de combustion de propergols solides