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Assyr Abdulle

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Related publications (63)

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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

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

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

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

Boosted Hybrid Method for Solving Chemical Reaction Systems with Multiple Scales in Time and Population Size

Assyr Abdulle

A new algorithm, called boosted hybrid method, is proposed for the simulation of chemical reaction systems with scale-separation in time and disparity in species population. For such stiff systems, the algorithm can automatically identify scale-separation ...

Cambridge University Press2012

Chebyshev methods with discrete noise: the tau-ROCK methods

Assyr Abdulle

Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standar ...

2010

Finite element heterogeneous multiscale method for the wave equation

Assyr Abdulle

A finite element heterogeneous multiscale method is proposed for the wave equation with highly oscillatory coefficients. It is based on a finite element discretization of an effective wave equation at the macro scale, whose a priori unknown effective coeff ...

2011

A short and versatile finite element multiscale code for homogenization problems

Assyr Abdulle, Achim Nonnenmacher

We describe a multiscale finite element (FE) solver for elliptic or parabolic problems with highly oscillating coefficients. Based on recent developments of the so-called heterogeneous multiscale method (HMM), the algorithm relies on coupled macro- and mic ...

2009

Adaptive finite element heterogeneous multiscale method for homogenization problems

Assyr Abdulle, Achim Nonnenmacher

In this paper we present an a posteriori error analysis for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. Unlike standard finite element methods, our discretization scheme relies on macro- and microfini ...

Elsevier2011

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

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

Fully discrete heterogeneous Multiscale methods and application to transport problems in microarrays

Assyr Abdulle

Physical systems encompassing a variety of strongly coupled scales pose major computational challenges in terms of analysis modeling and simulation. In this report we first discuss a multiscale modeling approach for the transport of particles such as DNA i ...

EMS2005

The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods

Assyr Abdulle, Gilles Vilmart

A finite element method with numerical quadrature is considered for the solution of a class of second-order quasilinear elliptic problems of nonmonotone type. Optimal a priori error estimates for the H-1 and the L-2 norms are derived. The uniqueness of the ...

Elsevier2011

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

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

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

Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni

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

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

Explicit methods for stiff stochastic differential equations

Assyr Abdulle

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...

Springer-Verlag Berlin2012

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

An Optimization Based Coupling Method For Multiscale Problems

Assyr Abdulle, Orane Pouchon, 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