Publications

2019

Journal Articles

Numerical Homogenization And Model Order Reduction For Multiscale Inverse Problems

A. Abdulle; A. Di Blasio 

Multiscale Modeling & Simulation. 2019-01-01. Vol. 17, num. 1, p. 399-433. DOI : 10.1137/16M1091320.

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

A. Abdulle; D. Arjmand; E. Paganoni 

2019. 

Temporal upscaling in micromagnetism via heterogeneous multiscale methods

D. Arjmand; S. Engblom; G. Kreiss 

Journal Of Computational And Applied Mathematics. 2019-01-01. Vol. 345, p. 99-113. DOI : 10.1016/j.cam.2018.05.059.

Theses

Penalization and Bayesian numerical methods for multiscale inverse problems

A. Di Blasio / A. Abdulle (Dir.)  

Lausanne: EPFL, 2019. DOI : 10.5075/epfl-thesis-9360.

Working Papers

MATHICSE Technical Report : Eective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales

T. N. Pouchon; A. Abdulle 

2019-05-28

MATHICSE Technical Report : Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems

A. Abdulle; D. Arjmand; E. Paganoni 

2019-03-30

MATHICSE Technical Report: Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations

A. Abdulle; G. A. Pavliotis; G. Vilmart 

2019-03-07

2018

Journal Articles

An Equation-Free Approach For Second Order Multiscale Hyperbolic Problems In Non-Divergence Form

D. Arjmand; G. Kreiss 

Communications In Mathematical Sciences. 2018-01-01. Vol. 16, num. 8, p. 2317-2343.

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

A. Abdulle; I. Almuslimani; G. Vilmart 

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION. 2018. Vol. 6, num. 2, p. 937-964. DOI : 10.1137/17M1145859.

Finite element heterogeneous multiscale method for elastic waves in heterogeneous media

A. Abdulle; M. Grote; O. Jecker 

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. 2018. Vol. 335, p. 1-23. DOI : 10.1016/j.cma.2018.01.038.

Atomistic-continuum multiscale modelling of magnetisation dynamics at non-zero temperature

D. Arjmand; M. Poluektov; G. Kreiss 

ADVANCES IN COMPUTATIONAL MATHEMATICS. 2018. Vol. 44, num. 4, p. 1119-1151. DOI : 10.1007/s10444-017-9575-3.

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

A. Abdulle; G. Rosilho De Souza 

2018. 

A Bayesian numerical homogenization method for elliptic multiscale inverse problems

A. Abdulle; A. Di Blasio 

publication. 2018. 

Effective Models for Long Time Wave Propagation in Locally Periodic Media

A. Abdulle; T. N. Pouchon 

SIAM Journal on Numerical Analysis. 2018. Vol. 56, num. 5, p. 2701-2730. DOI : 10.1137/17M113678X.

2017

Journal Articles

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

A. Abdulle; G. Garegnani 

publication. 2017. 

FE-HMM for elastic waves in heterogeneous media

A. Abdulle; M. J. Grote; O. Jecker 

publication. 2017. 

Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

A. Abdulle; I. Almuslimani; G. Vilmart 

publication. 2017. 

Spectral methods for multiscale stochastic differential equations

A. Abdulle; G. A. Pavliotis; U. Vaes 

SIAM/ASA Journal on Uncertainty Quantification. 2017. Vol. 5, num. 1, p. 720-761. DOI : 10.1137/16M1094117.

An optimization-based numerical method for diffusion problems with sign-changing coefficients

A. Abdulle; M. E. Huber; S. Lemaire 

C. R. Acad. Sci. Paris, Série I. 2017. Vol. 355, num. 4, p. 472-478. DOI : 10.1016/j.crma.2017.02.010.

A three-scale offline–online numerical method for fluid flow in porous media

A. Abdulle; O. Budác; A. Imboden 

Journal of Computational Physics. 2017. Vol. 337, p. 175-202. DOI : 10.1016/j.jcp.2017.02.006.

On heterogeneous coupling of multiscale methods for problems with and without scale separation

A. Abdulle; O. C. Jecker 

Research in the mathematical Sciences. 2017.  p. 4-28. DOI : 10.1186/s40687-017-0118-9.

Multiscale methods for wave problems in heterogenous media

A. Abdulle; P. Henning 

Handbook of Numerical Analysis. 2017. Vol. 18, p. 545-576.

Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows

A. Abdulle; M. E. Huber 

Numerische Mathematik. 2017. Vol. 136, num. 3, p. 603-649. DOI : 10.1007/s00211-016-0854-6.

A discontinuous Galerkin reduced basis numerical homogenization method for fluid flow in porous media

A. Abdulle; O. Budác 

Siam Journal on Scientific Computing. 2017. Vol. 39, num. 1, p. A83-A113. DOI : 10.1137/15M1050690.

Localized orthogonal decomposition method for the wave equation with a continuum of scales

A. Abdulle; P. Henning 

Mathematics of Computation. 2017. Vol. 86, p. 549-587. DOI : 10.1090/mcom/3114.

Theses

Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media

T. N. Pouchon / A. Abdulle (Dir.)  

Lausanne: EPFL, 2017. DOI : 10.5075/epfl-thesis-7881.

Optimization based methods for highly heterogeneous multiscale problems and multiscale methods for elastic waves

O. C. Jecker / A. Abdulle (Dir.)  

Lausanne: EPFL, 2017. DOI : 10.5075/epfl-thesis-7467.

2016

Journal Articles

An Optimization Based Coupling Method For Multiscale Problems

A. Abdulle; O. C. Jecker; A. Shapeev 

Multiscale Modeling & Simulation. 2016. Vol. 14, num. 4, p. 1377-1416. DOI : 10.1137/15M105389X.

Finite Element Heterogeneous Multiscale Method For Nonlinear Monotone Parabolic Homogenization Problems

A. Abdulle; M. E. Huber 

Esaim-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique. 2016. Vol. 50, num. 6, p. 1659-1697. DOI : 10.1051/m2an/2016003.

Numerical homogenization and model order reduction for multiscale inverse problems

A. Abdulle; A. Di Blasio 

publication. 2016. 

Multiscale model reduction methods for flow in heterogeneous porous media

A. Abdulle; O. Budác 

publication. 2016. 

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

A. Abdulle; T. N. Pouchon 

Mathematical Models and Methods in Applied Sciences. 2016. Vol. 26, num. 14, p. 2651-2684. DOI : 10.1142/S0218202516500627.

A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media

A. Abdulle; O. Budác 

Computer Methods in Applied Mechanics and Engineering. 2016. Vol. 307, p. 1-31. DOI : 10.1016/j.cma.2016.03.016.

A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time

A. Abdulle; T. N. Pouchon 

SIAM Journal on Numerical Analysis. 2016. Vol. 54, num. 3, p. 1507-1534. DOI : 10.1137/15M1025633.

Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization

A. Abdulle; M. E. Huber 

Numerical Methods for Partial Differential Equations. 2016. Vol. 32, num. 3, p. 955-969. DOI : 10.1002/num.22037.

Conference Papers

Numerical methods for wave equation in heterogenous media

A. Abdulle 

2016. Oberwolfach Workshop, Oberwolfach, March 20-26, 2016.

Numerical experiments for multiscale problems in linear elasticity

A. Abdulle; O. C. Jecker 

2016. Numerical Mathematics and Advanced Applications ‐ ENUMATH 2015, Ankara,

Theses

Multiscale methods for Stokes flow in heterogeneous media

O. Budáč / A. Abdulle (Dir.)  

Lausanne: EPFL, 2016. DOI : 10.5075/epfl-thesis-7135.

Book Chapters

Numerical homogenization methods for parabolic monotone problems

A. Abdulle 

Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations; 2016. p. 1-38.

2015

Journal Articles

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

A. Abdulle; O. Budác 

Comptes Rendus Mathematique. 2015. Vol. 353, num. 7, p. 641-645. DOI : 10.1016/j.crma.2015.03.019.

The role of numerical integration in numerical homogenization

A. Abdulle 

ESAIM: Proceedings. 2015. Vol. 50, p. 1-20.

A reduced basis localized orthogonal decomposition

A. Abdulle; P. Henning 

Journal of Computational Physics. 2015. Vol. 295, p. 379-401. DOI : 10.1016/j.jcp.2015.04.016.

Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems

A. Abdulle; M. E. Huber; G. Vilmart 

Multiscale Modeling and Simulation. 2015. Vol. 13, num. 3, p. 916-952. DOI : 10.1137/140975504.

An optimization-based multiscale coupling method

A. Abdulle; O. C. Jecker 

Communication in Mathematical Sciences. 2015. Vol. 13, num. 6, p. 1639-1648. DOI : 10.4310/CMS.2015.v13.n6.a13.

Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics

A. Abdulle; G. Vilmart; K. C. Zygalakis 

SIAM Journal on Numerical Analysis. 2015. Vol. 53, num. 1, p. 1-16. DOI : 10.1137/140962644.

An adaptive finite element heterogeneous multiscale method for Stokes flow in porous media

A. Abdulle; O. Budác 

Multiscale Modeling and Simulation. 2015. Vol. 13, num. 1, p. 256-290. DOI : 10.1137/130950136.

Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

A. Abdulle; Y. Bai; G. Vilmart 

Discrete and Continuous Dynamical Systems. 2015. Vol. 8, num. 1, p. 91-118. DOI : 10.3934/dcdss.2015.8.91.

Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales

A. Abdulle; Y. Bai 

IMA, Journal of Numerical Analysis. 2015. Vol. 35, num. 1, p. 133-160. DOI : 10.1093/imanum/drt066.

Conference Papers

Reduced basis heterogeneous multiscale methods

A. Abdulle 

2015. Euromech Colloquium 559 - Multi-scale computational methods for bridging scales in materials and structures, Eindhoven, The Netherlands, February 23-25, 2015.

Reduced basis techniques for multiscale methods

A. Abdulle 

2015. Oberwolfach Workshop, Oberwolfach, January 11-17, 2015.

Multiscale adaptive method for Stokes fow in heterogenenous media

A. Abdulle; O. Budác 

2015. Enumath 2013, EPFL, Lausanne, Switzerland, August 26-30,2013.

Reduced basis numerical homogenization method for the multiscale wave equation

A. Abdulle; Y. Bai; T. N. Pouchon 

2015. Enumath 2013, EPFL,Lausanne, Switzerland, August 26-30,2013. p. 397-405.

Improved stabilized multilevel Monte Carlo method for stiff stochastic differential equations

A. Abdulle; A. Blumenthal 

2015. Enumath 2013, EPFL, Lausanne, Switzerland, August 26-30,2013.

Theses

Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes

A. Blumenthal / A. Abdulle (Dir.)  

Lausanne: EPFL, 2015. DOI : 10.5075/epfl-thesis-6771.

Numerical homogenization methods for advection-diffusion and nonlinear monotone problems with multiple scales

M. E. Huber / A. Abdulle (Dir.)  

Lausanne: EPFL, 2015. DOI : 10.5075/epfl-thesis-6769.

Book Chapters

Numerical homogenization

A. Abdulle 

Encyclopedia of Applied and Computational Mathematics; Berlin: Springer, 2015. p. 1066-1074.

Explicit stabilized Runge-Kutta methods

A. Abdulle 

Encyclopedia of Applied and Computational Mathematics; Berlin: Springer, 2015. p. 460-468.

Conference Proceedings

Numerical Mathematics and Advanced Applications - ENUMATH 2013

A. Abdulle; S. Deparis; D. Kressner; F. Nobile; M. Picasso 

2015. 

2014

Journal Articles

Two-Level Discretization Techniques For Ground State Computations Of Bose-Einstein Condensates

P. Henning; A. Malqvist; D. Peterseim 

Siam Journal On Numerical Analysis. 2014. Vol. 52, num. 4, p. 1525-1550. DOI : 10.1137/130921520.

Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems

A. Abdulle; M. E. Huber 

publication. 2014. 

Reduced order modelling numerical homogenization

A. Abdulle; Y. Bai 

Philosophical Transactions of the Royal Society A. 2014. Vol. 372, num. 2021 20130388. DOI : 10.1098/rsta.2013.0388.

Finite element heterogeneous multiscale method for the wave equation: long-time effects

A. Abdulle; M. J. Grote; C. Stohrer 

Multiscale Modeling and Simulation. 2014. Vol. 12, num. 3, p. 1230-1257. DOI : 10.1137/13094195X.

High order numerical approximation of the invariant measure of ergodic SDEs

A. Abdulle; G. Vilmart; K. C. Zygalakis 

Siam Journal on Numerical Analysis. 2014. Vol. 52, num. 4, p. 1600-1622. DOI : 10.1137/130935616.

An online-offline homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems

A. Abdulle; Y. Bai; G. Vilmart 

International Journal for Numerical Methods in Engineering. 2014. Vol. 99, num. 7, p. 469-486. DOI : 10.1002/nme.4682.

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

A. Abdulle; M. E. Huber 

Numerische Mathematik. 2014. Vol. 126, num. 4, p. 589-633. DOI : 10.1007/s00211-013-0578-9.

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

A. Abdulle; G. Vilmart 

Mathematics of Computation. 2014. Vol. 83, num. 286, p. 513-536. DOI : 10.1090/S0025-5718-2013-02758-5.

Conference Papers

Numerical techniques for differential equations with multiple scales in space or time

A. Abdulle 

2014. Oberwolfach Workshop, Oberwolfach, p. 48-50.

Numerical methods for multiscale parabolic and hyperbolic problems

A. Abdulle 

2014. Oberwolfach Workshop, Oberwolfach, p. 1631-1633.

2013

Journal Articles

FE heterogeneous multiscale method for long time wave propagation

A. Abdulle; M. J. Grote; C. Stohrer 

Comptes Rendus Mathématique (Académie des Sciences). 2013. Vol. 351, p. 495-499. DOI : 10.1016/j.crma.2013.06.002.

Stabilized multilevel Monte Carlo method for stiff stochastic differential equations

A. Abdulle; A. Blumenthal 

Journal of Computational Physics. 2013. Vol. 251, p. 445-460. DOI : 10.1016/j.jcp.2013.05.039.

Weak second order explicit stabilized methods for stiff stochastic differential equations

A. Abdulle; G. Vilmart; K. Zygalakis 

SIAM Journal on Scientific Computing. 2013. Vol. 35, num. 4, p. A1792-A1814. DOI : 10.1137/12088954X.

Adaptive reduced basis finite element heterogeneous multiscale method

A. Abdulle; Y. Bai 

Computer Methods in Applied Mechanics and Engineering. 2013. Vol. 257, p. 201-220. DOI : 10.1016/j.cma.2013.01.002.

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

A. Abdulle; G. Vilmart; K. Zygalakis 

BIT Numerical Mathematics. 2013. Vol. 53, num. 4, p. 827-840. DOI : 10.1007/s10543-013-0430-8.

Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs

A. Abdulle; A. Barth; C. Schwab 

SIAM Multiscale Modeling & Simulation. 2013. Vol. 11, num. 4, p. 1033-1070. DOI : 10.1137/120894725.

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

A. Abdulle; G. Vilmart 

Journal of Computational Physics. 2013. Vol. 242, p. 869-888. DOI : 10.1016/j.jcp.2013.02.009.

A priori and a posteriori $W^{1,\infty}$ error analysis of a QC method for complex lattices

A. Abdulle; P. Lin; A. Shapeev 

SIAM, Journal on Numerical Analysis. 2013. Vol. 51, num. 4, p. 2357-2379. DOI : 10.1137/120894300.

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

A. Abdulle; A. Nonnenmacher 

Numerical Methods for Partial Differential Equations. 2013. Vol. 29, num. 5, p. 1629-1656. DOI : 10.1002/num.21769.

Conference Papers

Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems

A. Abdulle 

2013. Oberwolfach Workshop onInterplay of Theory and Numerics for Deterministic and Stochastic Homogenization, Oberwolfach, March 17-23, 2013. p. 807-809. DOI : 10.4171/OWR/2013/14.

Finite element heterogeneous multiscale method for the wave equation: dispersive effects

A. Abdulle; M. J. Grote; C. M. Stohrer 

2013. 11th International Conference on the Mathematical and Numerical Aspects of Waves.

Theses

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

Y. Bai / A. Abdulle (Dir.)  

Lausanne: EPFL, 2013. DOI : 10.5075/epfl-thesis-5922.

2012

Journal Articles

Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems

A. Abdulle; Y. Bai 

Journal of Computational Physics. 2012. Vol. 231, num. 21, p. 7014-7036. DOI : 10.1016/j.jcp.2012.02.019.

Numerical methods for multilattices

A. Abdulle; P. Lin; A. Shapeev 

SIAM, Multiscale Modeleling Simulation. 2012. Vol. 10, num. 3, p. 696-726. DOI : 10.1137/110841163.

High weak order methods for stochastic equations based on modified equations

A. Abdulle; D. Cohen; G. Vilmart; K. Zygalakis 

SIAM Journal of Scientific Computing. 2012. Vol. 34, num. 3, p. 1800-1823. DOI : 10.1137/110846609.

The heterogeneous multiscale method

A. Abdulle; W. E.; B. Engquist; E. Vanden-Eijnden 

Acta Numerica. 2012. Vol. 21, p. 1-87. DOI : 10.1017/S0962492912000025.

Explicit methods for stiff stochastic differential equations

A. Abdulle 

Lecture Notes in Computational Science and Engineering, Springer. 2012. Vol. 82, p. 1-22. DOI : 10.1007/978-3-642-21943-6_1.

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

Y. Hu; A. Abdulle; T. Li 

Communications in Computational Physics. 2012. Vol. 12, p. 981-1005. DOI : 10.4208/cicp.190411.301111a.

Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales

A. Abdulle 

Mathematics of Computation. 2012. Vol. 81, num. 278, p. 687-713. DOI : 10.1090/S0025-5718-2011-02527-5.

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

A. Abdulle; G. Vilmart 

Mathematical Models & Methods in Applied Sciences. 2012. Vol. 22, num. 6, p. 1250002/1-1250002/40. DOI : 10.1142/S0218202512500029.

Numerical methods for stochastic partial differential equations with multiple scales

A. Abdulle; G. A. Pavliotis 

Journal of Computational Physics. 2012. Vol. 231, p. 2482-2497. DOI : 10.1016/j.jcp.2011.11.039.

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

A. Abdulle; G. Vilmart 

Numerische Mathematik. 2012. Vol. 121, num. 3, p. 397-431. DOI : 10.1007/s00211-011-0438-4.

Conference Papers

Explicit stabilized integration of stiff determinisitic or stochastic problems

A. Abdulle 

2012. AIP Conference Proceedings, vol. 1479, p.11-15. p. 11-15. DOI : 10.1063/1.4756050.

Student Projects

An Implicit Finite Element Method for the Landau-Lifshitz-Gilbert Equation with Exchange and Magnetostriction

J. Rochat 

2012.

2011

Journal Articles

A priori and a posteriori error analysis for numerical homogenization: a unified framework

A. Abdulle 

Series in Contemporary Applied Mathematics, CAM. 2011. Vol. 16, p. 280-305.

Finite element heterogeneous multiscale method for the wave equation

A. Abdulle; M. J. Grote 

SIAM, Multiscale Modeling & Simulation. 2011. Vol. 9, p. 766-792. DOI : 10.1137/100800488.

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

A. Abdulle; G. Vilmart 

Comptes Rendus Mathématique, (Académie des Sciences). 2011. Vol. 349, p. 1041-1046. DOI : 10.1016/j.crma.2011.09.005.

Adaptive finite element heterogeneous multiscale method for homogenization problems

A. Abdulle; A. Nonnenmacher 

Computer Methods in Applied Mechanics and Engineering. 2011. Vol. 200, num. 37-40, p. 2710-2726. DOI : 10.1016/j.cma.2010.06.012.

Conference Papers

Finite element heterogeneous multiscale method for transient wave propagation

A. Abdulle; M. J. Grote; C. Stohrer 

2011. 10th International Conference on the Mathematical and Numerical Aspects of Waves, The Pacific Institute for the Mathematical Sciences, 2011.

On the efficiency of numerical homogenization methods

A. Abdulle 

2011. Oberwolfach Workshop on Geometric Numerical Integration, Oberwolfach, March 20-26, 2011. p. 857-859. DOI : 10.4171/OWR/2011/16.

Reports

The multilevel Monte Carlo method for stochastic differential equations driven by jump-diffusion processes

A. Abdulle; A. Blumenthal; E. Buckwar 

2011

Student Projects

Splitting Methods with Modified Potentials and Application to the Damped Wave Equation

J. Rochat 

2011.