Publications

2020

Journal Articles

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

A. Abdulle; T. Pouchon 

Foundations Of Computational Mathematics. 2020-03-16. DOI : 10.1007/s10208-020-09456-x.

Modelling long-range interactions in multiscale simulations of ferromagnetic materials

D. Arjmand; M. Poluektov; G. Kreiss 

Advances In Computational Mathematics. 2020-01-29. Vol. 46, num. 1, p. 2. DOI : 10.1007/s10444-020-09747-5.

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

A. Abdulle; G. Garegnani 

Statistics and Computing. 2020. Vol. 30, num. 4, p. 907-932. DOI : 10.1007/s11222-020-09926-w.

A Bayesian numerical homogenization method for elliptic multiscale inverse problems

A. Abdulle; A. Di Blasio 

SIAM/ASA Journal on uncertainty Quantification. 2020. Vol. 8, num. 1, p. 414-450. DOI : 10.1137/18M1187891.

Theses

Novel corrector problems with exponential decay of the resonance error for numerical homogenization

E. Paganoni / A. Abdulle (Dir.)  

Lausanne, EPFL, 2020. 

Numerical methods for deterministic and stochastic differential equations with multiple scales and high contrasts

G. Rosilho De Souza / A. Abdulle (Dir.)  

Lausanne, EPFL, 2020. 

Working Papers

MATHICSE Technical Report : Explicit stabilized multirate method for stiff stochastic differential equations

A. Abdulle; G. Rosilho De Souza 

2020-10-29

MATHICSE Technical Report : Drift Estimation of Multiscale Diffusions Based on Filtered Data

A. Abdulle; G. Garegnani; G. A. Pavliotis; A. M. Stuart; A. Zanoni 

2020-09-28

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

A. Abdulle; D. Arjmand; E. Paganoni 

2020-07-21

MATHICSE technical Report : Stabilized explicit multirate methods for stiff differential equations

A. Abdulle; M. J. Grote; G. Rosilho De Souza 

2020-06-01

MATHICSE Technical Report : A posteriori error analysis of a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

A. Assyr; G. Rosilho De Souza 

2020-04-15

MATHICSE technical Report : A parabolic local problem with exponential decay of the resonance error for numerical homogenization

A. Assyr; D. Arjmand; E. Paganoni 

2020-04-15

MATHICSE Technical Report : An elliptic local problem with exponential decay of the resonance error for numerical homogenization

A. Abdulle; D. Arjmand; E. Paganoni 

2020

2019

Journal Articles

A Hybrid High-Order Method for Highly Oscillatory Elliptic Problems

M. Cicuttin; A. Ern; S. Lemaire 

Computational Methods In Applied Mathematics. 2019-10-01. Vol. 19, num. 4, p. 723-748. DOI : 10.1515/cmam-2018-0013.

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

A. Abdulle; G. Rosilho De Souza 

Esaim-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique. 2019-07-09. Vol. 53, num. 4, p. 1269-1303.

Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations

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

Comptes Rendus Mathematique. 2019-04-01. Vol. 357, num. 4, p. 349-354. DOI : 10.1016/j.crma.2019.04.008.

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 

Comptes Rendus Mathematique. 2019. Vol. 357, num. 6, p. 545-551. DOI : 10.1016/j.crma.2019.05.011.

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.

Conference Papers

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

D. Arjmand; A. Abdulle; E. Paganoni 

2019-07-28.  p. 2138-2140.

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

T. N. Pouchon; A. Abdulle 

2019-07-28.  p. 2167-2170.

Numerical methods for wave propagation in heterogenenous media

A. Abdulle 

2019. 14th International Conference on the Mathematical and Numerical Aspects of Waves.

Effective equations of arbitrary order for wave propagation in periodic media

T. N. Pouchon; A. Abdulle 

2019. 14th International Conference on the Mathematical and Numerical Aspects of Waves, Wien, Austria, August 28-30, 2019.

Theses

Penalization and Bayesian numerical methods for multiscale inverse problems

A. Di Blasio / A. Abdulle (Dir.)  

Lausanne, EPFL, 2019. 

Working Papers

MATHICSE Technical Report : Ensemble Kalman filter for multiscale inverse problems

A. Abdulle; G. Garegnani; A. Zanoni 

2019-08-15

MATHICSE Technical Report : Effective 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. DOI : 10.4310/CMS.2018.v16.n8.a11.

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.

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.

Working Papers

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

A. Abdulle; G. Garegnani 

2018-09-05

MATHICSE Technical Report : A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

A. Abdulle; G. Rosilho De Souza 

2018-08-21

MATHICSE Technical Report : A Bayesian numerical homogenization method for elliptic multiscale inverse problems

A. Abdulle; A. Di Blasio 

2018-05-29

2017

Journal Articles

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. 

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

O. C. Jecker / A. Abdulle (Dir.)  

Lausanne, EPFL, 2017. 

Working Papers

MATHICSE Technical Report : FE-HMM for elastic waves in heterogeneous media

A. Abdulle; M. J. Grote; O. Jecker 

2017-11-21

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

A. Abdulle; I. Almuslimani; G. Vilmart 

2017-11-17

MATHICSE Technical Report : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations

A. Abdulle; I. Almuslimani; G. Vilmart 

2017-09-08

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

A. Abdulle; T. N. Pouchon 

2017-07-18

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.

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

Multiscale model reduction methods for flow in heterogeneous porous media

A. Abdulle; O. Budác 

2016. Numerical Mathematics and Advanced Applications ENUMATH 2015, Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, September 14 to 18, 2015. DOI : 10.1007/978-3-319-39929-4_32.

Numerical methods for wave equation in heterogenous media

A. Abdulle 

2016. Oberwolfach Workshop, Oberwolfach, March 20-26, 2016. p. 875-878. DOI : 10.4171/OWR/2016/18.

Numerical experiments for multiscale problems in linear elasticity

A. Abdulle; O. C. Jecker 

2016. Numerical Mathematics and Advanced Applications ‐ ENUMATH 2015, Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational m. p. 123-131. DOI : 10.1007/978-3-319-39929-4_13.

Theses

Multiscale methods for Stokes flow in heterogeneous media

O. Budáč / A. Abdulle (Dir.)  

Lausanne, EPFL, 2016. 

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.

Working Papers

MATHICSE Technical Report : Spectral methods for multiscale stochastic differential equations

A. Abdulle; G. A. Pavliotis; U. Vaes 

2016-09

MATHICSE Technical Report : Numerical homogenization and model order reduction for multiscale inverse problems

A. Abdulle; A. Di Blasio 

2016-08

MATHICSE Technical Report : An optimization-based numerical method for diffusion problems with sign-changing coefficients

A. Abdulle; M. E. Huber; S. Lemaire 

2016-08

MATHICSE Technical Report : Multiscale methods and model order reduction for flow problems in three-scale porous media

A. Abdulle; O. Budác; A. Imboden 

2016-07

MATHICSE Technical Report : On heterogeneous coupling of multiscale methods for problems with and without scale separation

A. Abdulle; O. Jecker 

2016-07

MATHICSE Technical Report : Multiscale methods for wave problems in heterogeneous media

A. Abdulle; P. Henning 

2016-07

MATHICSE Technical Report : Multiscale model reduction methods for flow in heterogeneous porous media

A. Abdulle; O. Budác 

2016-07

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

A. Abdulle; T. N. Pouchon 

2016-02-12

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.

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. p. 95-98. DOI : 10.4171/OWR/2015/2.

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. 

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

M. E. Huber / A. Abdulle (Dir.)  

Lausanne, EPFL, 2015. 

Book Chapters

The role of numerical integration in numerical homogenization

A. Abdulle 

ESAIM: Proceedings; 2015. p. 1-20.

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. 

Working Papers

MATHICSE Technical Report: An optimization based coupling method for multiscale problems

A. Abdulle; O. Jecker; A. Shapeev 

2015-12

MATHICSE Technical Report: Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows

A. Abdulle; M. Huber 

2015-12

MATHICSE Technical Report: Numerical homogenization methods for parabolic monotone problems

A. Abdulle 

2015-12

MATHICSE Technical Report: A discontinuous Galerkin reduced basis numerical homogenization method for fluid flow in porous media

A. Abdulle; O. Budác 

2015-12

MATHICSE Technical Report : A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media

A. Abdulle; O. Budác 

2015-07

MATHICSE Technical Report : A priori error analysis of the finite element heterogenenous multiscale method for the wave equation in heterogenenous media over long time

A. Abulle; T. N. Pouchon 

2015-06

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.

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. 2457-2459. DOI : 10.4171/OWR/2014/43.

Numerical methods for multiscale parabolic and hyperbolic problems

A. Abdulle 

2014. Oberwolfach Workshop, Oberwolfach, p. 1631-1633. DOI : 10.4171/OWR/2014/30.

Working Papers

MATHICSE Technical Report : Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems

A. Abdulle; M. E. Huber 

2014-07-01

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. 

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.

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.

Book Chapters

The heterogeneous multiscale method

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

Acta Numerica; Cambridge University Press, 2012. p. 1-87.

Explicit methods for stiff stochastic differential equations

A. Abdulle 

Lecture Notes in Computational Science and Engineering, Springer; Berlin: Springer-Verlag Berlin, 2012. p. 1-22.

Student Projects

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

J. Rochat 

2012.

2011

Journal Articles

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.

Theses

Adaptive Finite Element Methods for Multiscale Partial Differential Equations

A. Nonnenmacher / A. Abdulle (Dir.)  

Lausanne, EPFL, 2011. 

Book Chapters

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

A. Abdulle 

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

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.

2010

Journal Articles

Erratum to “A short and versatile finite element multiscale code for homogenization problems” [Comput. Methods Appl. Mech. Engrg. 198 (2009) 2839–2859]

A. Abdulle; A. Nonnenmacher 

Computer Methods in Applied Mechanics and Engineering. 2010. Vol. 199, num. 17-20, p. 1240. DOI : 10.1016/j.cma.2009.11.020.

Algebraic Structures of B-series

P. Chartier; E. Hairer; G. Vilmart 

Foundations Of Computational Mathematics. 2010. Vol. 10, p. 407-427. DOI : 10.1007/s10208-010-9065-1.

Chebyshev methods with discrete noise: the tau-ROCK methods

A. Abdulle; Y. Hu; T. Li 

Journal of Computational Mathematics. 2010. Vol. 28, num. 2, p. 195-217. DOI : 10.4208/jcm.2009.10-m1004.

Reports

Homogenization-based analysis of quasicontinuum method for complex crystals

A. Abdulle; A. Shapeev; P. Lin 

2010

2009

Journal Articles

A short and versatile finite element multiscale code for homogenization problems

A. Abdulle; A. Nonnenmacher 

Computer Methods in Applied Mechanics and Engineering. 2009. Vol. 198, p. 2839-2859. DOI : 10.1016/j.cma.2009.03.019.

A posteriori error analysis of the heterogeneous multiscale method for homogenization problems

A. Abdulle; A. Nonnenmacher 

Comptes Rendus Mathematique. 2009. Vol. 347, num. 17-18, p. 1081-1086. DOI : 10.1016/j.crma.2009.07.004.

Book Chapters

The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs

A. Abdulle 

GAKUTO International Series Mathematical Sciences and Applications; 2009. p. 135-184.

2008

Journal Articles

Effective velocity for transport in heterogeneous compressible flows with mean drift

A. Abdulle; S. Attinger 

Physics of Fluids. 2008. Vol. 20, num. 016102-12, p. 12. DOI : 10.1063/1.2827584.

S-ROCK methods for stiff Itô SDEs

A. Abdulle; T. Li 

Communications in Mathematical Sciences. 2008. Vol. 6, num. 4, p. 845-868. DOI : 10.4310/CMS.2008.v6.n4.a3.

Effectiveness of implicit methods for stiff stochastic differential equations

T. Li; A. Abdulle; W. E. 

Communication in Computational Physics. 2008. Vol. 3, num. 2, p. 295-307.

S-ROCK: Chebyshev methods for stiff stochastic differential equations

A. Abdulle; S. Cirilli 

SIAM Journal on Scientific Computing. 2008. Vol. 30, num. 2, p. 997-1014. DOI : 10.1137/070679375.

Multiscale method based on discontinuous Galerkin methods for homogenization problems

A. Abdulle 

Comptes Rendus Mathématique (Académie des Sciences). 2008. Vol. 346, num. 1-2, p. 97-102. DOI : 10.1016/j.crma.2007.11.029.

2007

Journal Articles

Finite element heterogeneous multiscale methods with near optimal computational complexity

A. Abdulle; B. Engquist 

SIAM Multiscale modeling & simulation. 2007. Vol. 6, num. 4, p. 1059-1084. DOI : 10.1137/060676118.

Stabilized methods for stiff stochastic systems

A. Abdulle; S. Cirilli 

Comptes Rendus Mathématique (Académie des Sciences). 2007. Vol. 345, num. 10, p. 593-598. DOI : 10.1016/j.crma.2007.10.009.

2006

Journal Articles

Heterogeneous multiscale methods with quadrilateral finite elements

A. Abdulle 

Numerical Mathematics and Advanced Applications. 2006.  p. 743-751. DOI : 10.1007/978-3-540-34288-5_72.

Analysis of a heterogeneous multiscale FEM for problems in elasticity

A. Abdulle 

Mathematical Models & Methods in Applied Sciences. 2006. Vol. 16, num. 4, p. 615-635. DOI : 10.1142/S0218202506001285.

Conference Papers

Numerical methods for multiscale problems

A. Abdulle 

2006. Oberwolfach Workshop on Geometric Numerical Integration, Oberwolfach-Walke, March 19-25, 2006. p. 834-837. DOI : 10.4171/OWR/2006/14.

Numerical methods for transport problems in microdevices

A. Abdulle; S. Attinger 

2006. LSSC: International Conference on Large-Scale Scientific Computing, Sozopol, Bulgaria, June 6-10, 2005. p. 67-75. DOI : 10.1007/11666806_6.

2005

Journal Articles

Heterogeneous multiscale FEM for diffusion problems on rough surfaces

A. Abdulle; C. Schwab 

SIAM Multiscale modeling & simulation. 2005. Vol. 3, num. 1, p. 195-220. DOI : 10.1137/030600771.

Multiscale methods for advection-diffusion problems

A. Abdulle 

Discrete and Continuous Dynamical Systems Series A. 2005. Vol. 2005, num. Special Issue, p. 11-21. DOI : 10.3934/proc.2005.2005.11.

On a priori error analysis of fully discrete heterogeneous multiscale FEM

A. Abdulle 

SIAM Multiscale modeling & simulation. 2005. Vol. 4, num. 2, p. 447-459. DOI : 10.1137/040607137.

Conference Papers

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

A. Abdulle 

2005. Oberwolfach Workshop on Reactive Flow and Transport Through Complex Systems, Oberwolfach-Walke, October 30 – November 5, 2005. p. 2769-2771. DOI : 10.4171/OWR/2005/49.

2004

Conference Papers

Solving diffusions problems on rough surfaces with a hierarchical Multiscale FEM

A. Abdulle 

2004. Proceedings in Applied Mathematics and Mechanics, vol. 4, num. 1, p. 694-695, 2004. p. 694-695.

Book Chapters

Homogenization method for transport of DNA particles in heterogeneous arrays

A. Abdulle; S. Attinger 

Multiscale modelling and simulation; Springer, 2004. p. 23-33.

2003

Journal Articles

Finite difference heterogeneous multi-scale method for homogenization problems

A. Abdulle; W. E. 

Journal of Computational Physics. 2003. Vol. 191, num. 1, p. 18-39. DOI : 10.1016/S0021-9991(03)00303-6.

Conference Papers

Solving multi-scale problems with heterogeneous finite difference methods

A. Abdulle 

2003. Proceedings in Applied Mathematics and Mechanics, vol.3, num. 1, p. 575-576, 2003. p. 575-576.

2002

Journal Articles

200 let metodynejmenších čtverců [200 years of least squares method]

A. Abdulle; G. Wanner 

Pokroky Matematiky, Fyziky a Astronomie. 2002. Vol. 48, num. 2, p. 89-104.

200 years of least squares method

A. Abdulle; G. Wanner 

Elemente der Mathematik. 2002. Vol. 57, num. 2, p. 45-60. DOI : 10.1007/PL00000559.

Fourth order Chebyshev methods with recurrence relation

A. Abdulle 

SIAM Journal on Scientific Computing. 2002. Vol. 23, num. 6, p. 2041-2054 (electronic). DOI : 10.1137/S1064827500379549.

Conference Papers

Large stiff systems solved by Chebyshev methods

A. Abdulle 

2002. Proceedings in Applied Mathematics and Mechanics, vol.1, num. 1, p. 508-509, 2002. p. 508-509.

2001

Journal Articles

Second order Chebyshev methods based on orthogonal polynomials

A. Abdulle; A. A. Medovikov 

Numerische Mathematik. 2001. Vol. 90, num. 1, p. 1-18. DOI : 10.1007/s002110100292.

2000

Journal Articles

On roots and error constants of optimal stability polynomials

A. Abdulle 

BIT : Numerical Mathematics. 2000. Vol. 40, num. 1, p. 177-182. DOI : 10.1023/A:1022378621048.