Publications de Assyr Abdulle | EPFL Graph Search

An Elliptic Local Problem With Exponential Decay Of The Resonance Error For Numerical Homogenization

Assyr Abdulle, Edoardo Paganoni, Doghonay Arjmand

Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in the model. These ...

SIAM PUBLICATIONS2023

Drift Estimation of Multiscale Diffusions Based on Filtered Data

Assyr Abdulle, Giacomo Garegnani, Andrea Zanoni, Grigorios A. Pavliotis

We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift coeffic ...

2023

Optimal explicit stabilized postprocessed τ-leap method for the simulation of chemical kinetics

Assyr Abdulle, Giacomo Rosilho De Souza

The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chains) and a computational challenge (multiple scales, large dynamical systems, time step restrictions). In this ...

Academic Press Inc Elsevier Science2023

Explicit Stabilized Multirate Method For Stiff Stochastic Differential Equations

Assyr Abdulle, Giacomo Rosilho De Souza

Stabilized explicit methods are particularly efficient, for large systems of stiff stochastic differential equations (SDEs) due to their extended stability domain. However, they lose their efficiency when a severe stiffness is induced by very few "fast" de ...

SIAM PUBLICATIONS2022

Explicit Stabilized Multirate Method For Stiff Differential Equations

Assyr Abdulle, Giacomo Rosilho De Souza

Stabilized Runge???Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized Runge???Kutta me ...

AMER MATHEMATICAL SOC2022

Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions

Assyr Abdulle, Andrea Zanoni

We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of the hom ...

SPRINGER2022

A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

Assyr Abdulle, Giacomo Rosilho De Souza

We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subdomains ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

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

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

Assyr Abdulle, Edoardo Paganoni, Doghonay Arjmand

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a m ...

WORLD SCIENTIFIC PUBL CO PTE LTD2021

A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems

Assyr Abdulle, Giacomo Garegnani

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows to introduce a pr ...

ELSEVIER SCIENCE SA2021

Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Assyr Abdulle, Giacomo Garegnani

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...

2020

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations for wave propagation in periodic media for arbitrary timescales O(epsilon-alpha), where epsilon MUCH LESS-THAN1 is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of ...

SPRINGER2020

Ensemble Kalman Filter For Multiscale Inverse Problems

Assyr Abdulle, Giacomo Garegnani, Andrea Zanoni

We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and allows us to reco ...

SIAM PUBLICATIONS2020

A Bayesian numerical homogenization method for elliptic multiscale inverse problems

Assyr Abdulle, Andrea Di Blasio

A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly oscillatory tens ...

2020

Numerical Homogenization And Model Order Reduction For Multiscale Inverse Problems

Assyr Abdulle, Andrea Di Blasio

A new numerical method based on numerical homogenization and model order reduction is introduced for the solution of multiscale inverse problems. We consider a class of elliptic problems with highly oscillatory tensors that varies on a microscopic scale. W ...

SIAM PUBLICATIONS2019

Numerical methods for wave propagation in heterogenenous media

Assyr Abdulle

2019

Approximation of high order homogenized wave equations for long time wave propagation

Timothée Noé Pouchon, Assyr Abdulle

EMS publishing house2019

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

Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems

Assyr Abdulle, Edoardo Paganoni, Doghonay Arjmand

EMS publishing house2019

Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems

Assyr Abdulle, Edoardo Paganoni, Doghonay Arjmand

This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients sufer from the so-called resonance error, originating from a mismatch between the tr ...

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER2019