Gilles Vilmart

Cette personne n’est plus à l’EPFL

Publications associées (12)

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Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs

Assyr Abdulle, Gilles Vilmart

Explicit stabilized integrators are an efficient alternative to implicit or semiimplicit methods to avoid the severe time-step restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper we provide a fully discrete ...

OXFORD UNIV PRESS2021

Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations

Assyr Abdulle, Gilles Vilmart, Grigorios A. Pavliotis

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 t ...

2019

Optimal Explicit Stabilized Integrator of Weak Order 1 for Stiff and Ergodic Stochastic Differential Equations

Assyr Abdulle, Gilles Vilmart

2018

Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems

Assyr Abdulle, Gilles Vilmart, Martin Ernst Huber

We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the mic ...

Siam Publications2015

PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise

Assyr Abdulle, Gilles Vilmart

A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by t ...

Elsevier2013

Weak second order explicit stabilized methods for stiff stochastic differential equations

Assyr Abdulle, Gilles Vilmart

We introduce a new family of explicit integrators for stiff Ito stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from th ...

Siam Publications2013

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

Assyr Abdulle, Gilles Vilmart

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of It stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are show ...

2013

High weak order methods for stochastic equations based on modified equations

Assyr Abdulle, Gilles Vilmart, David Cohen

Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...

Siam Publications2012

A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems

Assyr Abdulle, Gilles Vilmart

The effect of numerical quadrature in finite element methods for solving quasilinear elliptic problems of nonmonotone type is studied. Under similar assumption on the quadrature formula as for linear problems, optimal error estimates in the L^2 and the H^1 ...

Springer2012

Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: A fully discrete spacetime analysis

Assyr Abdulle, Gilles Vilmart

Numerical methods for parabolic homogenization problems combining finite element methods (FEMs) in space with Runge-Kutta methods in time are proposed. The space discretization is based on the coupling of macro and micro finite element methods following th ...

2012

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