output
20052025
most citedDegenerate parabolic stochastic partial differential equations: Quasilinear case

90 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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14 papers · 1 filter

math.NA2025

High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods

Eugen Bronasco, Adrien Busnot Laurent, Baptiste Huguet

We present a new class of numerical methods for solving stochastic differential equations with additive noise on general Riemannian manifolds with high weak order of accuracy. In o…

math.NA2024★ 1 cited

Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations

Eugen Bronasco, Adrien Laurent

While backward error analysis does not generalise straightforwardly to the strong and weak approximation of stochastic differential equations, it extends for the sampling of ergodi…

math.NA2024

Control theory and splitting methods

Karine Beauchard, Adrien Busnot Laurent, Frédéric Marbach

Our goal is to highlight some deep connections between numerical splitting methods and control theory. We consider evolution equations of the form , wher…

math.NA2023★ 5 cited

The universal equivariance properties of exotic aromatic B-series

Adrien Laurent, Hans Munthe-Kaas

The exotic aromatic Butcher series were originally introduced for the calculation of order conditions for the high order numerical integration of ergodic stochastic differential eq…

math.NA2023★ 8 cited

The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators

Adrien Laurent, Robert I. McLachlan, Hans Z. Munthe-Kaas +1

Aromatic B-series were introduced as an extension of standard Butcher-series for the study of volume-preserving integrators. It was proven with their help that the only volume-pres…

math.NA2022★ 3 cited

Conservative stabilized Runge-Kutta methods for the Vlasov-Fokker-Planck equation

Ibrahim Almuslimani, Nicolas Crouseilles

In this work, we aim at constructing numerical schemes, that are as efficient as possible in terms of cost and conservation of invariants, for the Vlasov--Fokker--Planck system cou…

math.NA2019★ 24 cited

Exponential methods for solving hyperbolic problems with application to kinetic equations

Nicolas Crouseilles, Lukas Einkemmer, Josselin Massot

The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as th…

math.NA2017★ 15 cited

Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs

Adrien Laurent, Gilles Vilmart

We introduce a new algebraic framework based on a modification (called exotic) of aromatic Butcher-series for the systematic study of the accuracy of numerical integrators for the…

math.NA2017★ 3 cited

Nonlinear Geometric Optics Based Multiscale Stochastic Galerkin Methods for Highly Oscillatory Transport Equations with Random Inputs

Nicolas Crouseilles, Shi Jin, Mohammed Lemou +1

We develop generalized polynomial chaos (gPC) based stochastic Galerkin (SG) methods for a class of highly oscillatory transport equations that arise in semiclassical modeling of n…

math.NA2013★ 5 cited

Weak backward error analysis for Langevin process

Marie Kopec

We consider numerical approximations of stochastic Langevin equations by implicit methods. We show a weak backward error analysis result in the sense that the generator associated…

math.NA2013★ 2 cited

Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties

Philippe Chartier, Norbert J. Mauser, Florian Méhats +1

In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory differential equations.…

math.NA2013

Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme

Charles-Edouard Bréhier, Erwan Faou

We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We s…

math.NA2012

Fast weak-KAM integrators for separable Hamiltonian systems

Anne Bouillard, Erwan Faou, Maxime Zavidovique

We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to…

math.NA2011

Optimized high-order splitting methods for some classes of parabolic equations

Sergio Blanes, Fernando Casas, Philippe Chartier +1

We are concerned with the numerical solution obtained by splitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real…