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Assyr Abdulle

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Publications associées (65)

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Assyr Abdulle, Giacomo Rosilho De Souza

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

EDP SCIENCES S A2019

Effective equations of arbitrary order for wave propagation in periodic media

Timothée Noé Pouchon, Assyr Abdulle

2019

Finite element heterogeneous multiscale method for elastic waves in heterogeneous media

Assyr Abdulle

2018

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

Assyr Abdulle, Gilles Vilmart

2018

Effective Models for Long Time Wave Propagation in Locally Periodic Media

Timothée Noé Pouchon, Assyr Abdulle

2018

Spectral methods for multiscale stochastic differential equations

Assyr Abdulle, Grigorios A. Pavliotis

This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free method, which rely o ...

2017

Numerical experiments for multiscale problems in linear elasticity

Orane Pouchon, Assyr Abdulle

This paper gives numerical experiments for the Finite Element Heterogeneous Multiscale Method applied to problems in linear elasticity, which has been analyzed in [A. Abdulle, Math. Models Methods Appl. Sci. 16, 2006]. The main results for the FE-HMM a pri ...

Springer2016

An Optimization Based Coupling Method For Multiscale Problems

Orane Pouchon, Assyr Abdulle, Alexander Shapeev

A new multiscale coupling method is proposed for elliptic problems with highly oscillatory coefficients with a continuum of scales in a subset of the computational domain and scale separation in complementary regions of the computational domain. A disconti ...

Society for Industrial and Applied Mathematics2016

Finite Element Heterogeneous Multiscale Method For Nonlinear Monotone Parabolic Homogenization Problems

Assyr Abdulle, Martin Ernst Huber

We propose a multiscale method based on a finite element heterogeneous multiscale method (in space) and the implicit Euler integrator (in time) to solve nonlinear monotone parabolic problems with multiple scales due to spatial heterogeneities varying rapid ...

Edp Sciences S A2016

Multiscale model reduction methods for flow in heterogeneous porous media

Assyr Abdulle, Ondrej Budác

In this paper we provide a general framework for model reduction methods applied to fluid flow in porous media. Using reduced basis and numerical homogenization techniques we show that the complexity of the numerical approximation of Stokes flow in heterog ...

Springer2016

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain Omega subset of R-d is proposed and analyzed. For a wave equation with highly oscillatory ...

World Scientific Publ Co Pte Ltd2016

Explicit stabilized Runge-Kutta methods

Assyr Abdulle

Springer2015

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

A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries

Assyr Abdulle, Ondrej Budác

We present a Petrov-Galerkin reduced basis (RB) approximation for the parameterized Stokes equation. Our method, which relies on a reduced solution space and a parameter-dependent test space, is shown to be stable (in the sense of Babuska) and algebraicall ...

Elsevier2015

Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales

Assyr Abdulle, Martin Ernst Huber

A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advectiondiffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advectio ...

Springer2014

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

Adaptive reduced basis finite element heterogeneous multiscale method

Assyr Abdulle, Yun Bai

An adaptive reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) is proposed for elliptic problems with multiple scales. The multiscale method is based on the RB-FE-HMM introduced in [A. Abdulle, Y. Bai, Reduced basis finite element het ...

Elsevier2013

Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs

Assyr Abdulle

In this paper Monte Carlo finite element approximations for elliptic homogenization problems with random coefficients, which oscillate on n is an element of N a priori known, separated microscopic length scales, are considered. The convergence of multileve ...

2013

A posteriori error estimate in quantities of interest for the finite element heterogeneous multiscale method

Assyr Abdulle, Achim Nonnenmacher

We present an "a posteriori" error analysis in quantities of interest for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. The multiscale method is based on a macro-to-micro formulation, where the macrosco ...

Wiley-Blackwell2013

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