Assyr Abdulle
EPFL SB MATH ANMC
MA C2 657 (Bâtiment MA)
Station 8
CH-1015 Lausanne
Unité: SMA-ENS
EPFL SB MATH MATH-GE
MA C2 657 (Bâtiment MA)
Station 8
CH-1015 Lausanne
Biographie
Assyr Abdulle est professeur ordinaire de mathématiques a l'EPFL et titulaire de la chaire d'analyse numérique et de mathématiques computationnelles.
Originaire de Laconnex (Genève), Assyr Abdulle est né en 1971. Il a obtenu un diplôme professionnel de violon au Conservatoire de Musique de Genève en 1993 et un Doctorat en Mathématiques à l'Université de Genève en 2001.
Il effectue sa première année post-doctorale à l'Université de Princeton (Etats-Unis) et a occupé successivement des postes de chercheur associé, professeur assistant et professeur associé à l'ETH de Zurich, l'Université de Bâle ainsi qu'a l'Université d'Edimbourg.
Il a reçu le prix "SciCADE new talent" en 2005, un "Advanced Research Fellowship" (ARF) du conseil de recherche "Engineering and Physical Sciences Research Council" (EPSRC, Royaume-Uni) en 2007 ainsi que le prix Wilkinson (SIAM) en analyse numérique et calcul scientifique en 2009.
Ses recherches portent sur le développement, l'analyse et la mise en uvre de méthodes numériques pour les équations différentielles multi-échelles ordinaires, aux dérivées partielles ou stochastiques. Assyr Abdulle élabore des méthodes computationnelles applicables à la simulation de nombreux problèmes dans les domaines des sciences naturelles et de l'ingénieur.
Collaborateurs scientifiques
Patrick Henning
Alexander Shapeev
Gilles Vilmart
Konstantinos Zygalakis
Publications
Publications
A. Abdulle; I. Almuslimani; G. Vilmart : Optimal Explicit Stabilized Integrator of Weak Order 1 for Stiff and Ergodic Stochastic Differential Equations; SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION. 2018. DOI : 10.1137/17M1145859.
A. Abdulle; M. Grote; O. Jecker : Finite element heterogeneous multiscale method for elastic waves in heterogeneous media; COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. 2018. DOI : 10.1016/j.cma.2018.01.038.
A. Abdulle; G. Rosilho De Souza : A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations. 2018.
A. Abdulle; A. Di Blasio : A Bayesian numerical homogenization method for elliptic multiscale inverse problems; publication. 2018.
A. Abdulle; T. N. Pouchon : Effective Models for Long Time Wave Propagation in Locally Periodic Media; SIAM Journal on Numerical Analysis. 2018. DOI : 10.1137/17M113678X.
A. Abdulle; G. Garegnani : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration; publication. 2017.
T. N. Pouchon / A. Abdulle (Dir.) : Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7881.
A. Abdulle; M. J. Grote; O. Jecker : FE-HMM for elastic waves in heterogeneous media; publication. 2017.
A. Abdulle; I. Almuslimani; G. Vilmart : Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations; publication. 2017.
O. C. Jecker / A. Abdulle (Dir.) : Optimization based methods for highly heterogeneous multiscale problems and multiscale methods for elastic waves. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7467.
A. Abdulle; G. A. Pavliotis; U. Vaes : Spectral methods for multiscale stochastic differential equations; SIAM/ASA Journal on Uncertainty Quantification. 2017. DOI : 10.1137/16M1094117.
A. Abdulle; M. E. Huber; S. Lemaire : An optimization-based numerical method for diffusion problems with sign-changing coefficients; C. R. Acad. Sci. Paris, Série I. 2017. DOI : 10.1016/j.crma.2017.02.010.
A. Abdulle; O. Budác; A. Imboden : Multiscale methods and model order reduction for flow problems in three-scale porous media; Journal of Computational Physics. 2017.
A. Abdulle; O. C. Jecker : On heterogeneous coupling of multiscale methods for problems with and without scale separation; Research in the mathematical Sciences. 2017. DOI : 10.1186/s40687-017-0118-9.
A. Abdulle; P. Henning : Multiscale methods for wave problems in heterogenous media; Handbook of Numerical Analysis. 2017.
A. Abdulle; M. E. Huber : Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows; Numerische Mathematik. 2017. DOI : 10.1007/s00211-016-0854-6.
A. Abdulle; O. Budác : A discontinuous Galerkin reduced basis numerical homogenization method for fluid flow in porous media; Siam Journal on Scientific Computing. 2017. DOI : 10.1137/15M1050690.
A. Abdulle; P. Henning : Localized orthogonal decomposition method for the wave equation with a continuum of scales; Mathematics of Computation. 2017. DOI : 10.1090/mcom/3114.
A. Abdulle; O. C. Jecker; A. Shapeev : An Optimization Based Coupling Method For Multiscale Problems; Multiscale Modeling & Simulation. 2016. DOI : 10.1137/15M105389X.
A. Abdulle; M. E. Huber : Finite Element Heterogeneous Multiscale Method For Nonlinear Monotone Parabolic Homogenization Problems; Esaim-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique. 2016. DOI : 10.1051/m2an/2016003.
O. Budáč / A. Abdulle (Dir.) : Multiscale methods for Stokes flow in heterogeneous media. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7135.
A. Abdulle; A. Di Blasio : Numerical homogenization and model order reduction for multiscale inverse problems; publication. 2016.
A. Abdulle; O. Budác : Multiscale model reduction methods for flow in heterogeneous porous media; publication. 2016.
A. E. Grandchamp / J. Maddocks (Dir.) : On the statistical physics of chains and rods, with application to multi-scale sequence-dependent DNA modelling. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6977.
A. Abdulle : Numerical methods for wave equation in heterogenous media. 2016. Oberwolfach Workshop, Oberwolfach, March 20-26, 2016.
A. Abdulle; O. C. Jecker : Numerical experiments for multiscale problems in linear elasticity. 2016. Numerical Mathematics and Advanced Applications ‐ ENUMATH 2015, Ankara.
A. Abdulle; T. N. Pouchon : Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization; Mathematical Models and Methods in Applied Sciences. 2016. DOI : 10.1142/S0218202516500627.
F. Tesei / F. Nobile (Dir.) : Numerical Approximation of Flows in Random Porous Media. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6860.
A. Abdulle : Numerical homogenization methods for parabolic monotone problems; Springer, Lecture Notes in Computational Science and Engineering. 2016. DOI : 10.1007/978-3-319-41640-3_1.
A. Abdulle; O. Budác : A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media; Computer Methods in Applied Mechanics and Engineering. 2016. DOI : 10.1016/j.cma.2016.03.016.
A. Abdulle; T. N. Pouchon : A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time; SIAM Journal on Numerical Analysis. 2016. DOI : 10.1137/15M1025633.
A. Abdulle; M. E. Huber : Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization; Numerical Methods for Partial Differential Equations. 2016. DOI : 10.1002/num.22037.
A. Blumenthal / A. Abdulle (Dir.) : Stabilized Numerical Methods for Stochastic Differential Equations driven by Diffusion and Jump-Diffusion Processes. Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6771.
M. E. Huber / A. Abdulle (Dir.) : Numerical homogenization methods for advection-diffusion and nonlinear monotone problems with multiple scales. Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6769.
A. Abdulle; S. Deparis; D. Kressner; F. Nobile; M. Picasso : Numerical Mathematics and Advanced Applications - ENUMATH 2013. 2015.
A. Abdulle; O. Budác : A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries; Comptes Rendus Mathematique. 2015. DOI : 10.1016/j.crma.2015.03.019.
A. Abdulle : Reduced basis heterogeneous multiscale methods. 2015. Euromech Colloquium 559 - Multi-scale computational methods for bridging scales in materials and structures, Eindhoven, The Netherlands, February 23-25, 2015.
A. Abdulle : Reduced basis techniques for multiscale methods. 2015. Oberwolfach Workshop, Oberwolfach, January 11-17, 2015.
A. Abdulle : The role of numerical integration in numerical homogenization; ESAIM: Proceedings. 2015.
G. Migliorati : Adaptive polynomial approximation by means of random discrete least squares. 2015. ENUMATH 2013, Lausanne, August 26-30, 2013. p. 547-554. DOI : 10.1007/978-3-319-10705-9_54.
A. Abdulle; P. Henning : A reduced basis localized orthogonal decomposition; Journal of Computational Physics. 2015. DOI : 10.1016/j.jcp.2015.04.016.
A. Abdulle; M. E. Huber; G. Vilmart : Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems; Multiscale Modeling and Simulation. 2015. DOI : 10.1137/140975504.
A. Abdulle; O. C. Jecker : An optimization-based multiscale coupling method; Communication in Mathematical Sciences. 2015. DOI : 10.4310/CMS.2015.v13.n6.a13.
A. Abdulle; G. Vilmart; K. C. Zygalakis : Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics; SIAM Journal on Numerical Analysis. 2015. DOI : 10.1137/140962644.
A. Abdulle; O. Budác : Multiscale adaptive method for Stokes fow in heterogenenous media. 2015. Enumath 2013, EPFL, Lausanne, Switzerland, August 26-30,2013.
A. Abdulle; Y. Bai; T. N. Pouchon : Reduced basis numerical homogenization method for the multiscale wave equation. 2015. Enumath 2013, EPFL,Lausanne, Switzerland, August 26-30,2013. p. 397-405.
A. Abdulle; A. Blumenthal : Improved stabilized multilevel Monte Carlo method for stiff stochastic differential equations. 2015. Enumath 2013, EPFL, Lausanne, Switzerland, August 26-30,2013.
A. Abdulle; O. Budác : An adaptive finite element heterogeneous multiscale method for Stokes flow in porous media; Multiscale Modeling and Simulation. 2015. DOI : 10.1137/130950136.
A. Abdulle; Y. Bai; G. Vilmart : Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems; Discrete and Continuous Dynamical Systems. 2015. DOI : 10.3934/dcdss.2015.8.91.
A. Abdulle : Numerical homogenization; Encyclopedia of Applied and Computational Mathematics; Berlin: Springer, 2015. p. 1066-1074.
A. Abdulle; Y. Bai : Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales; IMA, Journal of Numerical Analysis. 2015. DOI : 10.1093/imanum/drt066.
A. Abdulle : Explicit stabilized Runge-Kutta methods; Encyclopedia of Applied and Computational Mathematics; Berlin: Springer, 2015. p. 460-468.
A. Abdulle : Numerical techniques for differential equations with multiple scales in space or time. 2014. Oberwolfach Workshop, Oberwolfach. p. 48-50.
A. Abdulle : Numerical methods for multiscale parabolic and hyperbolic problems. 2014. Oberwolfach Workshop, Oberwolfach. p. 1631-1633.
A. Abdulle; M. E. Huber : Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems; publication. 2014.
A. Abdulle; Y. Bai : Reduced order modelling numerical homogenization; Philosophical Transactions of the Royal Society A. 2014. DOI : 10.1098/rsta.2013.0388.
A. Abdulle; M. J. Grote; C. Stohrer : Finite element heterogeneous multiscale method for the wave equation: long-time effects; Multiscale Modeling and Simulation. 2014. DOI : 10.1137/13094195X.
A. Abdulle; G. Vilmart; K. C. Zygalakis : High order numerical approximation of the invariant measure of ergodic SDEs; Siam Journal on Numerical Analysis. 2014. DOI : 10.1137/130935616.
A. Abdulle; Y. Bai; G. Vilmart : An online-offline homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems; International Journal for Numerical Methods in Engineering. 2014. DOI : 10.1002/nme.4682.
A. Abdulle; M. E. Huber : Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales; Numerische Mathematik. 2014. DOI : 10.1007/s00211-013-0578-9.
A. Abdulle; G. Vilmart : Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems; Mathematics of Computation. 2014. DOI : 10.1090/S0025-5718-2013-02758-5.
Y. Bai / A. Abdulle (Dir.) : Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems. Lausanne, EPFL, 2013. DOI : 10.5075/epfl-thesis-5922.
A. Abdulle; M. J. Grote; C. Stohrer : FE heterogeneous multiscale method for long time wave propagation; Comptes Rendus Mathématique (Académie des Sciences). 2013. DOI : 10.1016/j.crma.2013.06.002.
A. Abdulle : Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems. 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.
A. Abdulle; M. J. Grote; C. M. Stohrer : Finite element heterogeneous multiscale method for the wave equation: dispersive effects. 2013. 11th International Conference on the Mathematical and Numerical Aspects of Waves.
A. Abdulle; A. Blumenthal : Stabilized multilevel Monte Carlo method for stiff stochastic differential equations; Journal of Computational Physics. 2013. DOI : 10.1016/j.jcp.2013.05.039.
A. Abdulle; G. Vilmart; K. Zygalakis : Weak second order explicit stabilized methods for stiff stochastic differential equations; SIAM Journal on Scientific Computing. 2013. DOI : 10.1137/12088954X.
A. Abdulle; Y. Bai : Adaptive reduced basis finite element heterogeneous multiscale method; Computer Methods in Applied Mechanics and Engineering. 2013. DOI : 10.1016/j.cma.2013.01.002.
A. Abdulle; G. Vilmart; K. Zygalakis : Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations; BIT Numerical Mathematics. 2013. DOI : 10.1007/s10543-013-0430-8.
A. Abdulle; A. Barth; C. Schwab : Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs; SIAM Multiscale Modeling & Simulation. 2013. DOI : 10.1137/120894725.
A. Abdulle; G. Vilmart : PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise; Journal of Computational Physics. 2013. DOI : 10.1016/j.jcp.2013.02.009.
A. Abdulle; P. Lin; A. Shapeev : A priori and a posteriori $W^{1,\infty}$ error analysis of a QC method for complex lattices; SIAM, Journal on Numerical Analysis. 2013. DOI : 10.1137/120894300.
A. Abdulle; A. Nonnenmacher : A posteriori error estimate in quantities of interest for the finite element heterogeneous multiscale method; Numerical Methods for Partial Differential Equations. 2013. DOI : 10.1002/num.21769.
J. Rochat : An Implicit Finite Element Method for the Landau-Lifshitz-Gilbert Equation with Exchange and Magnetostriction ; 2012.
A. Abdulle; Y. Bai : Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems; Journal of Computational Physics. 2012. DOI : 10.1016/j.jcp.2012.02.019.
A. Abdulle : Explicit stabilized integration of stiff determinisitic or stochastic problems. 2012. AIP Conference Proceedings, vol. 1479, p.11-15. p. 11-15. DOI : 10.1063/1.4756050.
A. Abdulle; P. Lin; A. Shapeev : Numerical methods for multilattices; SIAM, Multiscale Modeleling Simulation. 2012. DOI : 10.1137/110841163.
A. Abdulle; D. Cohen; G. Vilmart; K. Zygalakis : High weak order methods for stochastic equations based on modified equations; SIAM Journal of Scientific Computing. 2012. DOI : 10.1137/110846609.
A. Abdulle; W. E.; B. Engquist; E. Vanden-Eijnden : The heterogeneous multiscale method; Acta Numerica. 2012. DOI : 10.1017/S0962492912000025.
A. Abdulle : Explicit methods for stiff stochastic differential equations; Lecture Notes in Computational Science and Engineering, Springer. 2012. DOI : 10.1007/978-3-642-21943-6_1.
Y. Hu; A. Abdulle; T. Li : Boosted Hybrid Method for Solving Chemical Reaction Systems with Multiple Scales in Time and Population Size; Communications in Computational Physics. 2012. DOI : 10.4208/cicp.190411.301111a.
A. Abdulle : Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales; Mathematics of Computation. 2012. DOI : 10.1090/S0025-5718-2011-02527-5.
A. Abdulle; G. Vilmart : Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: A fully discrete spacetime analysis; Mathematical Models & Methods in Applied Sciences. 2012. DOI : 10.1142/S0218202512500029.
A. Abdulle; G. A. Pavliotis : Numerical methods for stochastic partial differential equations with multiple scales; Journal of Computational Physics. 2012. DOI : 10.1016/j.jcp.2011.11.039.
A. Abdulle; G. Vilmart : A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems; Numerische Mathematik. 2012. DOI : 10.1007/s00211-011-0438-4.
J. Rochat : Splitting Methods with Modified Potentials and Application to the Damped Wave Equation ; 2011.
A. Abdulle; A. Blumenthal; E. Buckwar : The multilevel Monte Carlo method for stochastic differential equations driven by jump-diffusion processes. 2011.
A. Abdulle : A priori and a posteriori error analysis for numerical homogenization: a unified framework; Series in Contemporary Applied Mathematics, CAM. 2011.
A. Abdulle; M. J. Grote; C. Stohrer : Finite element heterogeneous multiscale method for transient wave propagation. 2011. 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. 2011. Oberwolfach Workshop on Geometric Numerical Integration, Oberwolfach, March 20-26, 2011. p. 857-859. DOI : 10.4171/OWR/2011/16.
A. Abdulle; M. J. Grote : Finite element heterogeneous multiscale method for the wave equation; SIAM, Multiscale Modeling & Simulation. 2011. DOI : 10.1137/100800488.
A. Abdulle; G. Vilmart : The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods; Comptes Rendus Mathématique, (Académie des Sciences). 2011. DOI : 10.1016/j.crma.2011.09.005.
A. Abdulle; A. Nonnenmacher : Adaptive finite element heterogeneous multiscale method for homogenization problems; Computer Methods in Applied Mechanics and Engineering. 2011. DOI : 10.1016/j.cma.2010.06.012.
A. Nonnenmacher / A. Abdulle (Dir.) : Adaptive Finite Element Methods for Multiscale Partial Differential Equations. Lausanne, EPFL, 2011. DOI : 10.5075/epfl-thesis-5097.
A. Abdulle; A. Nonnenmacher : Erratum to “A short and versatile finite element multiscale code for homogenization problems” [Comput. Methods Appl. Mech. Engrg. 198 (2009) 2839–2859]; Computer Methods in Applied Mechanics and Engineering. 2010. DOI : 10.1016/j.cma.2009.11.020.
A. Abdulle; A. Shapeev; P. Lin : Homogenization-based analysis of quasicontinuum method for complex crystals. 2010.
A. Abdulle; Y. Hu; T. Li : Chebyshev methods with discrete noise: the tau-ROCK methods; Journal of Computational Mathematics. 2010. DOI : 10.4208/jcm.2009.10-m1004.
A. Abdulle; A. Nonnenmacher : A short and versatile finite element multiscale code for homogenization problems (vol 198, pg 2839, 2009); Computer Methods In Applied Mechanics And Engineering. 2010. DOI : 10.1016/j.cma.2009.11.020.
A. Abdulle : The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs; GAKUTO International Series Mathematical Sciences and Applications. 2009.
A. Abdulle; A. Nonnenmacher : A short and versatile finite element multiscale code for homogenization problems; Computer Methods in Applied Mechanics and Engineering. 2009. DOI : 10.1016/j.cma.2009.03.019.
Enseignement & Phd
Enseignement
- Mathematics,
Programmes doctoraux
- Doctoral Program in Mathematics
Doctorants
Di Blasio Andrea
Garegnani Giacomo
Paganoni Edoardo
Rosilho De Souza Giacomo
Blumenthal Adrian ...
Budác Ondrej ...
Huber Martin Ernst ...
Jecker Orane Camille ...
Nonnenmacher Achim ...
Pouchon Timothée Noé ...
Garegnani Giacomo
Paganoni Edoardo
Rosilho De Souza Giacomo
A dirigé les thèses de
Bai Yun ...Blumenthal Adrian ...
Budác Ondrej ...
Huber Martin Ernst ...
Jecker Orane Camille ...
Nonnenmacher Achim ...
Pouchon Timothée Noé ...
Cours
Numerical integration of stochastic differential equations
Nous étudions des méthodes numériques pour des équations différentielles stochastiques. Ces méthodes numériques sont importantes pour de nombreuses applications. 