# 2017

## Articles de journaux

A. Abdulle and T. N. Pouchon. Effective models for long time wave propagation in locally periodic media, submitted to publication, 2017.
A. Abdulle, M. J. Grote and O. Jecker. FE-HMM for elastic waves in heterogeneous media, submitted to publication, 2017.
A. Abdulle, I. Almuslimani and G. Vilmart. Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations, submitted to publication, 2017.
A. Abdulle, G. A. Pavliotis and U. Vaes. Spectral methods for multiscale stochastic differential equations, in SIAM/ASA Journal on Uncertainty Quantification, vol. 5, num. 1, p. 720-761, 2017.
A. Abdulle, M. E. Huber and S. Lemaire. An optimization-based numerical method for diffusion problems with sign-changing coefficients, in C. R. Acad. Sci. Paris, Série I, vol. 355, num. 4, p. 472-478, 2017.
A. Abdulle, O. Budác and A. Imboden. Multiscale methods and model order reduction for flow problems in three-scale porous media, submitted to Journal of Computational Physics, vol. 337, p. 175-202, 2017.
A. Abdulle and O. C. Jecker. On heterogeneous coupling of multiscale methods for problems with and without scale separation, accepted in Research in the mathematical Sciences, 2017.
A. Abdulle and M. E. Huber. Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows, in Numerische Mathematik, vol. 136, num. 3, p. 603-649, 2017.
A. Abdulle and O. Budác. A discontinuous Galerkin reduced basis numerical homogenization method for fluid flow in porous media, in Siam Journal on Scientific Computing, vol. 39, num. 1, p. A83-A113, 2017.
A. Abdulle and P. Henning. Localized orthogonal decomposition method for the wave equation with a continuum of scales, in Mathematics of Computation, vol. 86, p. 549-587, 2017.

## Thèses

T. N. Pouchon, A. Abdulle (Dir.). Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media. EPFL, Lausanne, 2017.
O. C. Jecker, A. Abdulle (Dir.). Optimization based methods for highly heterogeneous multiscale problems and multiscale methods for elastic waves. EPFL, Lausanne, 2017.

# 2016

## Articles de journaux

A. Abdulle, O. C. Jecker and A. Shapeev. An Optimization Based Coupling Method For Multiscale Problems, in Multiscale Modeling & Simulation, vol. 14, num. 4, p. 1377-1416, 2016.
A. Abdulle and M. E. Huber. Finite Element Heterogeneous Multiscale Method For Nonlinear Monotone Parabolic Homogenization Problems, in Esaim-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, vol. 50, num. 6, p. 1659-1697, 2016.
A. Abdulle and A. Di Blasio. Numerical homogenization and model order reduction for multiscale inverse problems, submitted to publication, 2016.
A. Abdulle and P. Henning. Multiscale methods for wave problems in heterogenous media, submitted to publication, 2016.
A. Abdulle and O. Budác. Multiscale model reduction methods for flow in heterogeneous porous media, submitted to publication, 2016.
A. Abdulle and T. N. Pouchon. Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization, in Mathematical Models and Methods in Applied Sciences, vol. 26, num. 14, p. 2651-2684, 2016.
A. Abdulle. Numerical homogenization methods for parabolic monotone problems, in Springer, Lecture Notes in Computational Science and Engineering, vol. 114, p. 1-38, 2016.
A. Abdulle and O. Budác. A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media, in Computer Methods in Applied Mechanics and Engineering, vol. 307, p. 1-31, 2016.
A. Abdulle and T. N. Pouchon. A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time, in SIAM Journal on Numerical Analysis, vol. 54, num. 3, p. 1507-1534, 2016.
A. Abdulle and M. E. Huber. Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization, in Numerical Methods for Partial Differential Equations, vol. 32, num. 3, p. 955-969, 2016.

## Papiers de conférences

A. Abdulle. Numerical methods for wave equation in heterogenous media. Oberwolfach Workshop, Oberwolfach, Oberwolfach report, 2016.
A. Abdulle and O. C. Jecker. Numerical experiments for multiscale problems in linear elasticity. Numerical Mathematics and Advanced Applications ‐ ENUMATH 2015, Ankara, 2016.

## Thèses

O. Budáč, A. Abdulle (Dir.). Multiscale methods for Stokes flow in heterogeneous media. EPFL, Lausanne, 2016.
A. E. Grandchamp, J. Maddocks (Dir.). On the statistical physics of chains and rods, with application to multi-scale sequence-dependent DNA modelling. EPFL, Lausanne, 2016.
F. Tesei, F. Nobile (Dir.). Numerical Approximation of Flows in Random Porous Media. EPFL, Lausanne, 2016.

# 2015

## Articles de journaux

A. Abdulle and O. Budác. A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries, in Comptes Rendus Mathematique, vol. 353, num. 7, p. 641-645, 2015.
A. Abdulle. The role of numerical integration in numerical homogenization, in ESAIM: Proceedings, vol. 50, p. 1-20, 2015.
A. Abdulle and P. Henning. A reduced basis localized orthogonal decomposition, in Journal of Computational Physics, vol. 295, p. 379-401, 2015.
A. Abdulle, M. E. Huber and G. Vilmart. Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems, in Multiscale Modeling and Simulation, vol. 13, num. 3, p. 916-952, 2015.
A. Abdulle and O. C. Jecker. An optimization-based multiscale coupling method, in Communication in Mathematical Sciences, vol. 13, num. 6, p. 1639-1648, 2015.
A. Abdulle, G. Vilmart and K. C. Zygalakis. Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics, in SIAM Journal on Numerical Analysis, vol. 53, num. 1, p. 1-16, 2015.
A. Abdulle and O. Budác. An adaptive finite element heterogeneous multiscale method for Stokes flow in porous media, in Multiscale Modeling and Simulation, vol. 13, num. 1, p. 256-290, 2015.
A. Abdulle, Y. Bai and G. Vilmart. Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, in Discrete and Continuous Dynamical Systems, vol. 8, num. 1, p. 91-118, 2015.
A. Abdulle and Y. Bai. Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales, in IMA, Journal of Numerical Analysis, vol. 35, num. 1, p. 133-160, 2015.

## Papiers de conférences

A. Abdulle. Reduced basis heterogeneous multiscale methods. Euromech Colloquium 559 - Multi-scale computational methods for bridging scales in materials and structures, Eindhoven, The Netherlands, 2015.
A. Abdulle. Reduced basis techniques for multiscale methods. Oberwolfach Workshop, Oberwolfach, Oberwolfach Report 02/2015, 2015.
G. Migliorati. Adaptive polynomial approximation by means of random discrete least squares. ENUMATH 2013, Lausanne, Lecture Notes in Computational Science and Engineering 103, 2015.
A. Abdulle and O. Budác. Multiscale adaptive method for Stokes fow in heterogenenous media. Enumath 2013, EPFL, Lausanne, Switzerland, 2015.
A. Abdulle, Y. Bai and T. N. Pouchon. Reduced basis numerical homogenization method for the multiscale wave equation. Enumath 2013, EPFL,Lausanne, Switzerland, 2015.
A. Abdulle and A. Blumenthal. Improved stabilized multilevel Monte Carlo method for stiff stochastic differential equations. Enumath 2013, EPFL, Lausanne, Switzerland, 2015.

## Thèses

A. Blumenthal, A. Abdulle (Dir.). Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes. EPFL, Lausanne, 2015.
M. E. Huber, A. Abdulle (Dir.). Numerical homogenization methods for advection-diffusion and nonlinear monotone problems with multiple scales. EPFL, Lausanne, 2015.

## Chapitres de livres

A. Abdulle. Numerical homogenization, in Encyclopedia of Applied and Computational Mathematics, p. 1066-1074, 2015.
A. Abdulle. Explicit stabilized Runge-Kutta methods, in Encyclopedia of Applied and Computational Mathematics, p. 460-468, 2015.

## Actes de congrès

A. Abdulle, S. Deparis, D. Kressner, F. Nobile and M. Picasso (Eds.). Numerical Mathematics and Advanced Applications - ENUMATH 2013. Springer International Publishing, 978-3-319-10704-2, Lecture Notes in Computational Science and Engineering 103, 2015.

# 2014

## Articles de journaux

A. Abdulle and M. E. Huber. Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems, accepted in publication, 2014.
A. Abdulle and Y. Bai. Reduced order modelling numerical homogenization, in Philosophical Transactions of the Royal Society A, vol. 372, num. 2021 20130388, 2014.
A. Abdulle, M. J. Grote and C. Stohrer. Finite element heterogeneous multiscale method for the wave equation: long-time effects, in Multiscale Modeling and Simulation, vol. 12, num. 3, p. 1230-1257, 2014.
A. Abdulle, G. Vilmart and K. C. Zygalakis. High order numerical approximation of the invariant measure of ergodic SDEs, in Siam Journal on Numerical Analysis, vol. 52, num. 4, p. 1600-1622, 2014.
A. Abdulle, Y. Bai and G. Vilmart. An online-offline homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems, in International Journal for Numerical Methods in Engineering, vol. 99, num. 7, p. 469-486, 2014.
A. Abdulle and M. E. Huber. Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales, in Numerische Mathematik, vol. 126, num. 4, p. 589-633, 2014.
A. Abdulle and G. Vilmart. Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, in Mathematics of Computation, vol. 83, num. 286, p. 513-536, 2014.

## Papiers de conférences

A. Abdulle. Numerical techniques for differential equations with multiple scales in space or time. Oberwolfach Workshop, Oberwolfach, 2014.
A. Abdulle. Numerical methods for multiscale parabolic and hyperbolic problems. Oberwolfach Workshop, Oberwolfach, 2014.

# 2013

## Articles de journaux

A. Abdulle, M. J. Grote and C. Stohrer. FE heterogeneous multiscale method for long time wave propagation, in Comptes Rendus Mathématique (Académie des Sciences), vol. 351, p. 495-499, 2013.
A. Abdulle and A. Blumenthal. Stabilized multilevel Monte Carlo method for stiff stochastic differential equations, in Journal of Computational Physics, vol. 251, p. 445-460, 2013.
A. Abdulle, G. Vilmart and K. Zygalakis. Weak second order explicit stabilized methods for stiff stochastic differential equations, in SIAM Journal on Scientific Computing, vol. 35, num. 4, p. A1792-A1814, 2013.
A. Abdulle and Y. Bai. Adaptive reduced basis finite element heterogeneous multiscale method, in Computer Methods in Applied Mechanics and Engineering, vol. 257, p. 201-220, 2013.
A. Abdulle, G. Vilmart and K. Zygalakis. Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations, in BIT Numerical Mathematics, vol. 53, num. 4, p. 827-840, 2013.
A. Abdulle, A. Barth and C. Schwab. Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs, in SIAM Multiscale Modeling & Simulation, vol. 11, num. 4, p. 1033-1070, 2013.
A. Abdulle and G. Vilmart. PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise, in Journal of Computational Physics, vol. 242, p. 869-888, 2013.
A. Abdulle, P. Lin and A. Shapeev. A priori and a posteriori $W^{1,\infty}$ error analysis of a QC method for complex lattices, in SIAM, Journal on Numerical Analysis, vol. 51, num. 4, p. 2357-2379, 2013.
A. Abdulle and A. Nonnenmacher. A posteriori error estimate in quantities of interest for the finite element heterogeneous multiscale method, in Numerical Methods for Partial Differential Equations, vol. 29, num. 5, p. 1629-1656, 2013.

## Papiers de conférences

A. Abdulle. Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems. Oberwolfach Workshop onInterplay of Theory and Numerics for Deterministic and Stochastic Homogenization, Oberwolfach, Oberwolfach Report 2013/14, 2013.
A. Abdulle, M. J. Grote and C. M. Stohrer. Finite element heterogeneous multiscale method for the wave equation: dispersive effects. 11th International Conference on the Mathematical and Numerical Aspects of Waves, 2013.

## Thèses

Y. Bai, A. Abdulle (Dir.). Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems. EPFL, Lausanne, 2013.

# 2012

## Articles de journaux

A. Abdulle and Y. Bai. Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems, in Journal of Computational Physics, vol. 231, num. 21, p. 7014-7036, 2012.
A. Abdulle, P. Lin and A. Shapeev. Numerical methods for multilattices, in SIAM, Multiscale Modeleling Simulation, vol. 10, num. 3, p. 696-726, 2012.
A. Abdulle, D. Cohen, G. Vilmart and K. Zygalakis. High weak order methods for stochastic equations based on modified equations, in SIAM Journal of Scientific Computing, vol. 34, num. 3, p. 1800-1823, 2012.
A. Abdulle, W. E., B. Engquist and E. Vanden-Eijnden. The heterogeneous multiscale method, in Acta Numerica, vol. 21, p. 1-87, 2012.
A. Abdulle. Explicit methods for stiff stochastic differential equations, in Lecture Notes in Computational Science and Engineering, Springer, vol. 82, p. 1-22, Lecture Notes in Computational Science and Engineering, 2012.
Y. Hu, A. Abdulle and T. Li. Boosted Hybrid Method for Solving Chemical Reaction Systems with Multiple Scales in Time and Population Size, in Communications in Computational Physics, vol. 12, p. 981-1005, 2012.
A. Abdulle. Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales, in Mathematics of Computation, vol. 81, num. 278, p. 687-713, 2012.
A. Abdulle and G. Vilmart. Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: A fully discrete spacetime analysis, in Mathematical Models & Methods in Applied Sciences, vol. 22, num. 6, p. 1250002/1-1250002/40, 2012.
A. Abdulle and G. A. Pavliotis. Numerical methods for stochastic partial differential equations with multiple scales, in Journal of Computational Physics, vol. 231, p. 2482-2497, 2012.
A. Abdulle and G. Vilmart. A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems, in Numerische Mathematik, vol. 121, num. 3, p. 397-431, 2012.

## Papiers de conférences

A. Abdulle. Explicit stabilized integration of stiff determinisitic or stochastic problems. AIP Conference Proceedings, vol. 1479, p.11-15, AIP Conference Proceedings, 2012.

## Travaux d'étudiants

J. Rochat, A. Abdulle (Dir.). An Implicit Finite Element Method for the Landau-Lifshitz-Gilbert Equation with Exchange and Magnetostriction. , 2012.

# 2011

## Articles de journaux

A. Abdulle. A priori and a posteriori error analysis for numerical homogenization: a unified framework, in Series in Contemporary Applied Mathematics, CAM, vol. 16, p. 280-305, 2011.
A. Abdulle and M. J. Grote. Finite element heterogeneous multiscale method for the wave equation, in SIAM, Multiscale Modeling & Simulation, vol. 9, p. 766-792, 2011.
A. Abdulle and G. Vilmart. The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods, in Comptes Rendus Mathématique, (Académie des Sciences), vol. 349, p. 1041-1046, 2011.
A. Abdulle and A. Nonnenmacher. Adaptive finite element heterogeneous multiscale method for homogenization problems, in Computer Methods in Applied Mechanics and Engineering, vol. 200, num. 37-40, p. 2710-2726, 2011.

## Papiers de conférences

A. Abdulle, M. J. Grote and C. Stohrer. Finite element heterogeneous multiscale method for transient wave propagation. 10th International Conference on the Mathematical and Numerical Aspects of Waves, The Pacific Institute for the Mathematical Sciences, 2011.
A. Abdulle. On the efficiency of numerical homogenization methods. Oberwolfach Workshop on Geometric Numerical Integration, Oberwolfach, Oberwolfach Report 2011/16, 2011.

## Thèses

A. Nonnenmacher, A. Abdulle (Dir.). Adaptive Finite Element Methods for Multiscale Partial Differential Equations. EPFL, Lausanne, 2011.

## Rapports techniques

A. Abdulle, A. Blumenthal and E. Buckwar. The multilevel Monte Carlo method for stochastic differential equations driven by jump-diffusion processes, 2011.

## Travaux d'étudiants

J. Rochat, A. Abdulle (Dir.). Splitting Methods with Modified Potentials and Application to the Damped Wave Equation. , 2011.

# 2010

## Articles de journaux

A. Abdulle and A. Nonnenmacher. Erratum to “A short and versatile finite element multiscale code for homogenization problems” [Comput. Methods Appl. Mech. Engrg. 198 (2009) 2839–2859], in Computer Methods in Applied Mechanics and Engineering, vol. 199, num. 17-20, p. 1240, 2010.
A. Abdulle, Y. Hu and T. Li. Chebyshev methods with discrete noise: the tau-ROCK methods, in Journal of Computational Mathematics, vol. 28, num. 2, p. 195-217, 2010.
A. Abdulle and A. Nonnenmacher. A short and versatile finite element multiscale code for homogenization problems (vol 198, pg 2839, 2009), in Computer Methods In Applied Mechanics And Engineering, vol. 198, num. 37-40, p. 2839-2859, 2010.

## Rapports techniques

A. Abdulle, A. Shapeev and P. Lin. Homogenization-based analysis of quasicontinuum method for complex crystals, 2010.

# 2009

## Articles de journaux

A. Abdulle. The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs, in GAKUTO International Series Mathematical Sciences and Applications, vol. 31, p. 135-184, 2009.
A. Abdulle and A. Nonnenmacher. A short and versatile finite element multiscale code for homogenization problems, in Computer Methods in Applied Mechanics and Engineering, vol. 198, p. 2839-2859, 2009.
A. Abdulle and A. Nonnenmacher. A posteriori error analysis of the heterogeneous multiscale method for homogenization problems, in Comptes Rendus Mathematique, vol. 347, num. 17-18, p. 1081-1086, 2009.

# 2008

## Articles de journaux

A. Abdulle and S. Attinger. Effective velocity for transport in heterogeneous compressible flows with mean drift, in Physics of Fluids, vol. 20, num. 016102-12, p. 12, 2008.
A. Abdulle and T. Li. S-ROCK methods for stiff Itô SDEs, in Communications in Mathematical Sciences, vol. 6, num. 4, p. 845-868, 2008.
T. Li, A. Abdulle and W. E.. Effectiveness of implicit methods for stiff stochastic differential equations, in Communication in Computational Physics, vol. 3, num. 2, p. 295-307, 2008.
A. Abdulle and S. Cirilli. S-ROCK: Chebyshev methods for stiff stochastic differential equations, in SIAM Journal on Scientific Computing, vol. 30, num. 2, p. 997-1014, 2008.
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