Edit Profile (opens in new tab) Abdulle, Assyr (b. 1971 d. 2021) Co-Author Distance Author ID: abdulle.assyr Published as: Abdulle, Assyr; Abdulle, A. Homepage: https://www.epfl.ch/labs/anmc/home/professor-assyr-abdulle/ External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef Documents Indexed: 111 Publications since 2000, including 1 Book and 3 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 46 Co-Authors with 95 Joint Publications 1,574 Co-Co-Authors all top 5 Co-Authors 18 single-authored 16 Vilmart, Gilles 7 Bai, Yun 6 Budáč, Ondrej 6 De Souza, Giacomo Rosilho 6 Huber, Martin E. 5 Grote, Marcus J. 5 Jecker, Orane 5 Nonnenmacher, Achim 5 Pavliotis, Grigorios A. 5 Pouchon, Timothée 5 Zygalakis, Konstantinos C. 4 Arjmand, Doghonay 4 Garegnani, Giacomo 4 Li, Tiejun 4 Paganoni, Edoardo 4 Shapeev, Alexander V. 3 Attinger, Sabine 3 E, Weinan 3 Henning, Patrick 3 Lin, Ping 3 Zanoni, Andrea 2 Blasio, Andrea Di 2 Blumenthal, Adrian 2 Cirilli, Stéphane 2 Engquist, Bjorn E. 2 Hu, Yucheng 2 Schwab, Christoph 2 Stohrer, Christian 2 Wanner, Gerhard 1 Almuslimani, Ibrahim 1 Banasiak, Jacek 1 Barth, Andrea 1 Bréhier, Charles-Edouard 1 Damlamian, Alain 1 Deparis, Simone 1 Gander, Lia 1 Imboden, Antoine 1 Kressner, Daniel 1 Lemaire, Simon 1 Medovikov, Alexei A. 1 Nobile, Fabio 1 Picasso, Marco 1 Sango, Mamadou 1 Stuart, Andrew M. 1 Vaes, Urbain 1 Vanden-Eijnden, Eric all top 5 Serials 12 Multiscale Modeling & Simulation 9 Journal of Computational Physics 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Computer Methods in Applied Mechanics and Engineering 6 SIAM Journal on Scientific Computing 5 SIAM Journal on Numerical Analysis 4 Mathematics of Computation 4 Numerische Mathematik 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 PAMM. Proceedings in Applied Mathematics and Mechanics 3 SIAM/ASA Journal on Uncertainty Quantification 2 IMA Journal of Numerical Analysis 2 BIT 2 Numerical Methods for Partial Differential Equations 2 Foundations of Computational Mathematics 2 Communications in Mathematical Sciences 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Communications in Computational Physics 2 Statistics and Computing 1 International Journal for Numerical Methods in Engineering 1 Journal of Computational Mathematics 1 Elemente der Mathematik 1 Pokroky Matematiky, Fyziky & Astronomie 1 Physics of Fluids 1 Discrete and Continuous Dynamical Systems 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Acta Numerica 1 GAKUTO International Series. Mathematical Sciences and Applications 1 Lecture Notes in Computational Science and Engineering 1 Discrete and Continuous Dynamical Systems. Series S 1 Research in the Mathematical Sciences 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys all top 5 Fields 102 Numerical analysis (65-XX) 52 Partial differential equations (35-XX) 28 Mechanics of deformable solids (74-XX) 23 Probability theory and stochastic processes (60-XX) 16 Fluid mechanics (76-XX) 10 Ordinary differential equations (34-XX) 6 Statistics (62-XX) 4 Biology and other natural sciences (92-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 96 Publications have been cited 1,523 times in 712 Documents Cited by ▼ Year ▼ The heterogeneous multiscale method. Zbl 1255.65224 Abdulle, Assyr; Weinan, E.; Engquist, Björn; Vanden-Eijnden, Eric 176 2012 Second order Chebyshev methods based on orthogonal polynomials. Zbl 0997.65094 Abdulle, Assyr; Medovikov, Alexei A. 68 2001 On a priori error analysis of fully discrete heterogeneous multiscale FEM. Zbl 1092.65093 Abdulle, Assyr 63 2005 Fourth order Chebyshev methods with recurrence relation. Zbl 1009.65048 Abdulle, Assyr 58 2002 The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs. Zbl 1372.65266 Abdulle, A. 53 2009 S-ROCK: Chebyshev methods for stiff stochastic differential equations. Zbl 1159.60329 Abdulle, Assyr; Cirilli, Stephane 44 2008 Finite difference heterogeneous multi-scale method for homogenization problems. Zbl 1034.65067 Abdulle, Assyr; E, Weinan 42 2003 Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems. Zbl 1284.65161 Abdulle, Assyr; Bai, Yun 38 2012 S-ROCK methods for stiff Itô SDEs. Zbl 1162.60330 Abdulle, Assyr; Li, Tiejun 35 2008 Adaptive finite element heterogeneous multiscale method for homogenization problems. Zbl 1230.74165 Abdulle, A.; Nonnenmacher, A. 34 2011 Adaptive reduced basis finite element heterogeneous multiscale method. Zbl 1286.74088 Abdulle, Assyr; Bai, Yun 34 2013 Heterogeneous multiscale FEM for diffusion problems on rough surfaces. Zbl 1160.65337 Abdulle, Assyr; Schwab, Christoph 33 2005 Finite element heterogeneous multiscale method for the wave equation. Zbl 1298.65145 Abdulle, Assyr; Grote, Marcus J. 31 2011 Localized orthogonal decomposition method for the wave equation with a continuum of scales. Zbl 1358.65064 Abdulle, Assyr; Henning, Patrick 29 2017 A priori and a posteriori error analysis for numerical homogenization: a unified framework. Zbl 1300.65076 Abdulle, Assyr 29 2011 Analysis of a heterogeneous multiscale FEM for problems in elasticity. Zbl 1095.74029 Abdulle, Assyr 28 2006 High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 28 2014 Finite element heterogeneous multiscale method for the wave equation: long-time effects. Zbl 1315.65084 Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian 28 2014 A short and versatile finite element multiscale code for homogenization problems. Zbl 1229.74125 Abdulle, Assyr; Nonnenmacher, Achim 27 2009 Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 27 2015 Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales. Zbl 1243.65134 Abdulle, Assyr 26 2012 Effectiveness of implicit methods for stiff stochastic differential equations. Zbl 1199.65010 Li, Tiejun; Abdulle, Assyr; E, Weinan 25 2008 High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008 Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C. 22 2012 Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146 Abdulle, Assyr; Vilmart, Gilles 22 2014 A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Zbl 1251.65151 Abdulle, Assyr; Vilmart, Gilles 21 2012 Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs. Zbl 1296.65008 Abdulle, Assyr; Barth, Andrea; Schwab, Christoph 21 2013 Finite element heterogeneous multiscale methods with near optimal computational complexity. Zbl 1155.65096 Abdulle, Assyr; Engquist, Bjorn 20 2008 Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 20 2013 Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013 Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles 16 2018 Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis. Zbl 1426.76208 Abdulle, Assyr; Vilmart, Gilles 15 2012 PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise. Zbl 1297.65110 Abdulle, Assyr; Vilmart, Gilles 15 2013 A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries. (Une méthode d’éléments finis de type Petrov-Galerkin pour l’approximation en base réduite du probléme de Stokes.) Zbl 1320.76057 Abdulle, Assyr; Budáč, Ondrej 15 2015 A posteriori error analysis of the heterogeneous multiscale method for homogenization problems. Zbl 1172.65060 Abdulle, Assyr; Nonnenmacher, Achim 14 2009 Stabilized methods for stiff stochastic systems. Zbl 1128.65004 Abdulle, Assyr; Cirilli, Stéphane 13 2007 A reduced basis localized orthogonal decomposition. Zbl 1349.65609 Abdulle, Assyr; Henning, Patrick 13 2015 Stabilized multilevel Monte Carlo method for stiff stochastic differential equations. Zbl 1349.65028 Abdulle, Assyr; Blumenthal, Adrian 13 2013 Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245 Abdulle, Assyr; Bai, Yun; Vilmart, Gilles 13 2015 Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration. Zbl 1505.62010 Abdulle, Assyr; Garegnani, Giacomo 13 2020 FE heterogeneous multiscale method for long-time wave propagation. Zbl 1273.76263 Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian 13 2013 Spectral methods for multiscale stochastic differential equations. Zbl 1398.65313 Abdulle, Assyr; Pavliotis, G. A.; Vaes, U. 12 2017 A priori error analysis of the finite element heterogeneous multiscale method for the wave equation over long time. Zbl 1382.65303 Abdulle, Assyr; Pouchon, Timothée 12 2016 Numerical methods for stochastic partial differential equations with multiple scales. Zbl 1429.65013 Abdulle, A.; Pavliotis, G. A. 11 2012 Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems. Zbl 1357.65169 Abdulle, Assyr; Huber, Martin E. 11 2016 Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales. Zbl 1296.65150 Abdulle, A.; Huber, M. E. 11 2014 Multiscale method based on discontinuous Galerkin methods for homogenization problems. Zbl 1133.65094 Abdulle, Assyr 10 2008 Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization. Zbl 1362.35033 Abdulle, Assyr; Pouchon, Timothée 10 2016 Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems. (Décroissance exponentielle de l’erreur de résonance en homogénéisation numerique via des problèmes de cellules paraboliques et elliptiques.) Zbl 1422.65362 Abdulle, Assyr; Arjmand, Doghonay; Paganoni, Edoardo 10 2019 An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems. Zbl 1352.65462 Abdulle, A.; Bai, Y.; Vilmart, G. 9 2014 Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063 Abdulle, A.; Huber, M. E.; Vilmart, G. 9 2015 A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method. Zbl 1274.65289 Abdulle, Assyr; Nonnenmacher, Achim 9 2013 Reduced-order modelling numerical homogenization. Zbl 1353.74067 Abdulle, A.; Bai, Y. 8 2014 Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. Zbl 1367.65011 Abdulle, A.; Vilmart, G.; Zygalakis, K. C. 8 2013 An optimization-based numerical method for diffusion problems with sign-changing coefficients. (Une méthode d’optimisation pour des problèmes de diffusion avec changement de signe.) Zbl 1362.65120 Abdulle, Assyr; Huber, Martin E.; Lemaire, Simon 7 2017 Multiscale methods for advection-diffusion problems. Zbl 1144.65315 Abdulle, Assyr 7 2005 Chebyshev methods with discrete noise: the \(\tau\)-rock methods. Zbl 1224.65009 Abdulle, Assyr; Hu, Yucheng; Li, Tiejun 6 2010 The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. Zbl 1230.65122 Abdulle, Assyr; Vilmart, Gilles 6 2011 Explicit methods for stiff stochastic differential equations. Zbl 1246.65007 Abdulle, Assyr 6 2012 Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales. Zbl 1311.65140 Abdulle, Assyr; Bai, Yun 6 2015 Multiscale methods for wave problems in heterogeneous media. Zbl 1368.65184 Abdulle, A.; Henning, P. 6 2017 Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization. Zbl 1350.65112 Abdulle, Assyr; Huber, Martin E. 6 2016 Numerical homogenization and model order reduction for multiscale inverse problems. Zbl 1412.65195 Abdulle, Assyr; Blasio, Andrea Di 6 2019 On roots and error constants of optimal stability polynomials. Zbl 0956.65068 Abdulle, Assyr 5 2000 An optimization-based, heterogeneous to homogeneous coupling method. Zbl 1326.65074 Abdulle, Assyr; Jecker, Orane 5 2015 Chebyshev methods based on orthogonal polynomials. Zbl 1026.65076 Abdulle, Assyr 5 2001 Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales. Zbl 1456.35015 Abdulle, Assyr; Pouchon, Timothée 5 2020 A priori and a posteriori \(W^{1,\infty}\) error analysis of a QC method for complex lattices. Zbl 1279.65126 Abdulle, Assyr; Lin, Ping; Shapeev, Alexander V. 5 2013 A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media. Zbl 1436.76018 Abdulle, Assyr; Budáč, Ondrej 5 2016 A Bayesian numerical homogenization method for elliptic multiscale inverse problems. Zbl 1436.62089 Abdulle, Assyr; Blasio, Andrea Di 5 2020 Effective models for long time wave propagation in locally periodic media. Zbl 1404.35020 Abdulle, Assyr; Pouchon, Timothée 5 2018 Numerical methods for multilattices. Zbl 1255.74025 Abdulle, Assyr; Lin, Ping; Shapeev, Alexander V. 5 2012 Ensemble Kalman filter for multiscale inverse problems. Zbl 1453.65393 Abdulle, Assyr; Garegnani, Giacomo; Zanoni, Andrea 5 2020 Heterogeneous multiscale methods with quadrilateral finite elements. Zbl 1118.65382 Abdulle, Assyr 4 2006 Numerical experiments for multiscale problems in linear elasticity. Zbl 1388.74099 Jecker, Orane; Abdulle, Assyr 4 2016 Explicit stabilized multirate method for stiff differential equations. Zbl 1500.65034 Abdulle, Assyr; Grote, Marcus J.; De Souza, Giacomo Rosilho 4 2022 Boosted hybrid method for solving chemical reaction systems with multiple scales in time and population size. Zbl 1403.92357 Hu, Yucheng; Abdulle, Assyr; Li, Tiejun 3 2012 The role of numerical integration in numerical homogenization. Zbl 1382.65375 Abdulle, Assyr 3 2015 Multiscale adaptive method for Stokes flow in heterogenenous media. Zbl 1321.76034 Abdulle, Assyr; Budáč, Ondrej 3 2015 A probabilistic finite element method based on random meshes: a posteriori error estimators and Bayesian inverse problems. Zbl 1506.65200 Abdulle, Assyr; Garegnani, Giacomo 3 2021 A parabolic local problem with exponential decay of the resonance error for numerical homogenization. Zbl 07466873 Abdulle, Assyr; Arjmand, Doghonay; Paganoni, Edoardo 3 2021 Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations. (Convergence accélérée vers l’équilibre et variance asymptotique réduite pour la dynamique de Langevin à l’aide de perturbations de Stratonovich.) Zbl 07066212 Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles 3 2019 Homogenization method for transport of DNA particles in heterogeneous arrays. Zbl 1140.92300 Abdulle, Assyr; Attinger, Sabine 2 2004 An optimization based coupling method for multiscale problems. Zbl 1352.65463 Abdulle, Assyr; Jecker, Orane; Shapeev, Alexander 2 2016 A discontinuous Galerkin reduced basis numerical homogenization method for fluid flow in porous media. Zbl 1381.76149 Abdulle, Assyr; Budáč, Ondrej 2 2017 200 years of least squares method. Zbl 1003.01008 Abdulle, Assyr; Wanner, G. 2 2002 A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations. Zbl 1448.65211 Abdulle, Assyr; De Souza, Giacomo Rosilho 2 2019 Explicit stabilized multirate method for stiff stochastic differential equations. Zbl 1491.60115 Abdulle, Assyr; Rosilho de Souza, Giacomo 2 2022 Multiple scales problems in biomathematics, mechanics, physics and numerics, CIMPA school, Cape Town, South Africa, August 6–18, 2007. Zbl 1171.65002 1 2009 Numerical methods for transport problems in microdevices. Zbl 1142.65436 Abdulle, Assyr; Attinger, Sabine 1 2006 Numerical mathematics and advanced applications – ENUMATH 2013. Proceedings of ENUMATH 2013, the 10th European conference on numerical mathematics and advanced applications, Lausanne, Switzerland, August 26–30, 2013. Zbl 1304.65003 1 2015 Multiscale model reduction methods for flow in heterogeneous porous media. Zbl 1387.76045 Abdulle, Assyr; Budáč, Ondrej 1 2016 Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows. Zbl 1397.76118 Abdulle, A.; Huber, M. E. 1 2017 Numerical homogenization methods for parabolic monotone problems. Zbl 1357.65168 Abdulle, Assyr 1 2016 Improved stabilized multilevel Monte Carlo method for stiff stochastic differential equations. Zbl 1328.65013 Abdulle, Assyr; Blumenthal, Adrian 1 2015 Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions. Zbl 1484.62001 Abdulle, Assyr; Pavliotis, Grigorios A.; Zanoni, Andrea 1 2022 Finite element heterogeneous multiscale method for elastic waves in heterogeneous media. Zbl 1440.74165 Abdulle, Assyr; Grote, Marcus J.; Jecker, Orane 1 2018 Drift estimation of multiscale diffusions based on filtered data. Zbl 07654468 Abdulle, Assyr; Garegnani, Giacomo; Pavliotis, Grigorios A.; Stuart, Andrew M.; Zanoni, Andrea 1 2023 Drift estimation of multiscale diffusions based on filtered data. Zbl 07654468 Abdulle, Assyr; Garegnani, Giacomo; Pavliotis, Grigorios A.; Stuart, Andrew M.; Zanoni, Andrea 1 2023 Explicit stabilized multirate method for stiff differential equations. Zbl 1500.65034 Abdulle, Assyr; Grote, Marcus J.; De Souza, Giacomo Rosilho 4 2022 Explicit stabilized multirate method for stiff stochastic differential equations. Zbl 1491.60115 Abdulle, Assyr; Rosilho de Souza, Giacomo 2 2022 Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions. Zbl 1484.62001 Abdulle, Assyr; Pavliotis, Grigorios A.; Zanoni, Andrea 1 2022 A probabilistic finite element method based on random meshes: a posteriori error estimators and Bayesian inverse problems. Zbl 1506.65200 Abdulle, Assyr; Garegnani, Giacomo 3 2021 A parabolic local problem with exponential decay of the resonance error for numerical homogenization. Zbl 07466873 Abdulle, Assyr; Arjmand, Doghonay; Paganoni, Edoardo 3 2021 Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration. Zbl 1505.62010 Abdulle, Assyr; Garegnani, Giacomo 13 2020 Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales. Zbl 1456.35015 Abdulle, Assyr; Pouchon, Timothée 5 2020 A Bayesian numerical homogenization method for elliptic multiscale inverse problems. Zbl 1436.62089 Abdulle, Assyr; Blasio, Andrea Di 5 2020 Ensemble Kalman filter for multiscale inverse problems. Zbl 1453.65393 Abdulle, Assyr; Garegnani, Giacomo; Zanoni, Andrea 5 2020 Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems. (Décroissance exponentielle de l’erreur de résonance en homogénéisation numerique via des problèmes de cellules paraboliques et elliptiques.) Zbl 1422.65362 Abdulle, Assyr; Arjmand, Doghonay; Paganoni, Edoardo 10 2019 Numerical homogenization and model order reduction for multiscale inverse problems. Zbl 1412.65195 Abdulle, Assyr; Blasio, Andrea Di 6 2019 Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations. (Convergence accélérée vers l’équilibre et variance asymptotique réduite pour la dynamique de Langevin à l’aide de perturbations de Stratonovich.) Zbl 07066212 Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles 3 2019 A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations. Zbl 1448.65211 Abdulle, Assyr; De Souza, Giacomo Rosilho 2 2019 Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013 Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles 16 2018 Effective models for long time wave propagation in locally periodic media. Zbl 1404.35020 Abdulle, Assyr; Pouchon, Timothée 5 2018 Finite element heterogeneous multiscale method for elastic waves in heterogeneous media. Zbl 1440.74165 Abdulle, Assyr; Grote, Marcus J.; Jecker, Orane 1 2018 Localized orthogonal decomposition method for the wave equation with a continuum of scales. Zbl 1358.65064 Abdulle, Assyr; Henning, Patrick 29 2017 Spectral methods for multiscale stochastic differential equations. Zbl 1398.65313 Abdulle, Assyr; Pavliotis, G. A.; Vaes, U. 12 2017 An optimization-based numerical method for diffusion problems with sign-changing coefficients. (Une méthode d’optimisation pour des problèmes de diffusion avec changement de signe.) Zbl 1362.65120 Abdulle, Assyr; Huber, Martin E.; Lemaire, Simon 7 2017 Multiscale methods for wave problems in heterogeneous media. Zbl 1368.65184 Abdulle, A.; Henning, P. 6 2017 A discontinuous Galerkin reduced basis numerical homogenization method for fluid flow in porous media. Zbl 1381.76149 Abdulle, Assyr; Budáč, Ondrej 2 2017 Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows. Zbl 1397.76118 Abdulle, A.; Huber, M. E. 1 2017 A priori error analysis of the finite element heterogeneous multiscale method for the wave equation over long time. Zbl 1382.65303 Abdulle, Assyr; Pouchon, Timothée 12 2016 Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems. Zbl 1357.65169 Abdulle, Assyr; Huber, Martin E. 11 2016 Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization. Zbl 1362.35033 Abdulle, Assyr; Pouchon, Timothée 10 2016 Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization. Zbl 1350.65112 Abdulle, Assyr; Huber, Martin E. 6 2016 A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media. Zbl 1436.76018 Abdulle, Assyr; Budáč, Ondrej 5 2016 Numerical experiments for multiscale problems in linear elasticity. Zbl 1388.74099 Jecker, Orane; Abdulle, Assyr 4 2016 An optimization based coupling method for multiscale problems. Zbl 1352.65463 Abdulle, Assyr; Jecker, Orane; Shapeev, Alexander 2 2016 Multiscale model reduction methods for flow in heterogeneous porous media. Zbl 1387.76045 Abdulle, Assyr; Budáč, Ondrej 1 2016 Numerical homogenization methods for parabolic monotone problems. Zbl 1357.65168 Abdulle, Assyr 1 2016 Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 27 2015 A Petrov-Galerkin reduced basis approximation of the Stokes equation in parameterized geometries. (Une méthode d’éléments finis de type Petrov-Galerkin pour l’approximation en base réduite du probléme de Stokes.) Zbl 1320.76057 Abdulle, Assyr; Budáč, Ondrej 15 2015 A reduced basis localized orthogonal decomposition. Zbl 1349.65609 Abdulle, Assyr; Henning, Patrick 13 2015 Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245 Abdulle, Assyr; Bai, Yun; Vilmart, Gilles 13 2015 Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063 Abdulle, A.; Huber, M. E.; Vilmart, G. 9 2015 Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales. Zbl 1311.65140 Abdulle, Assyr; Bai, Yun 6 2015 An optimization-based, heterogeneous to homogeneous coupling method. Zbl 1326.65074 Abdulle, Assyr; Jecker, Orane 5 2015 The role of numerical integration in numerical homogenization. Zbl 1382.65375 Abdulle, Assyr 3 2015 Multiscale adaptive method for Stokes flow in heterogenenous media. Zbl 1321.76034 Abdulle, Assyr; Budáč, Ondrej 3 2015 Numerical mathematics and advanced applications – ENUMATH 2013. Proceedings of ENUMATH 2013, the 10th European conference on numerical mathematics and advanced applications, Lausanne, Switzerland, August 26–30, 2013. Zbl 1304.65003 1 2015 Improved stabilized multilevel Monte Carlo method for stiff stochastic differential equations. Zbl 1328.65013 Abdulle, Assyr; Blumenthal, Adrian 1 2015 High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 28 2014 Finite element heterogeneous multiscale method for the wave equation: long-time effects. Zbl 1315.65084 Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian 28 2014 Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146 Abdulle, Assyr; Vilmart, Gilles 22 2014 Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales. Zbl 1296.65150 Abdulle, A.; Huber, M. E. 11 2014 An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems. Zbl 1352.65462 Abdulle, A.; Bai, Y.; Vilmart, G. 9 2014 Reduced-order modelling numerical homogenization. Zbl 1353.74067 Abdulle, A.; Bai, Y. 8 2014 Adaptive reduced basis finite element heterogeneous multiscale method. Zbl 1286.74088 Abdulle, Assyr; Bai, Yun 34 2013 Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs. Zbl 1296.65008 Abdulle, Assyr; Barth, Andrea; Schwab, Christoph 21 2013 Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005 Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 20 2013 PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise. Zbl 1297.65110 Abdulle, Assyr; Vilmart, Gilles 15 2013 Stabilized multilevel Monte Carlo method for stiff stochastic differential equations. Zbl 1349.65028 Abdulle, Assyr; Blumenthal, Adrian 13 2013 FE heterogeneous multiscale method for long-time wave propagation. Zbl 1273.76263 Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian 13 2013 A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method. Zbl 1274.65289 Abdulle, Assyr; Nonnenmacher, Achim 9 2013 Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. Zbl 1367.65011 Abdulle, A.; Vilmart, G.; Zygalakis, K. C. 8 2013 A priori and a posteriori \(W^{1,\infty}\) error analysis of a QC method for complex lattices. Zbl 1279.65126 Abdulle, Assyr; Lin, Ping; Shapeev, Alexander V. 5 2013 The heterogeneous multiscale method. Zbl 1255.65224 Abdulle, Assyr; Weinan, E.; Engquist, Björn; Vanden-Eijnden, Eric 176 2012 Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems. Zbl 1284.65161 Abdulle, Assyr; Bai, Yun 38 2012 Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales. Zbl 1243.65134 Abdulle, Assyr 26 2012 High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008 Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C. 22 2012 A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Zbl 1251.65151 Abdulle, Assyr; Vilmart, Gilles 21 2012 Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis. Zbl 1426.76208 Abdulle, Assyr; Vilmart, Gilles 15 2012 Numerical methods for stochastic partial differential equations with multiple scales. Zbl 1429.65013 Abdulle, A.; Pavliotis, G. A. 11 2012 Explicit methods for stiff stochastic differential equations. Zbl 1246.65007 Abdulle, Assyr 6 2012 Numerical methods for multilattices. Zbl 1255.74025 Abdulle, Assyr; Lin, Ping; Shapeev, Alexander V. 5 2012 Boosted hybrid method for solving chemical reaction systems with multiple scales in time and population size. Zbl 1403.92357 Hu, Yucheng; Abdulle, Assyr; Li, Tiejun 3 2012 Adaptive finite element heterogeneous multiscale method for homogenization problems. Zbl 1230.74165 Abdulle, A.; Nonnenmacher, A. 34 2011 Finite element heterogeneous multiscale method for the wave equation. Zbl 1298.65145 Abdulle, Assyr; Grote, Marcus J. 31 2011 A priori and a posteriori error analysis for numerical homogenization: a unified framework. Zbl 1300.65076 Abdulle, Assyr 29 2011 The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. Zbl 1230.65122 Abdulle, Assyr; Vilmart, Gilles 6 2011 Chebyshev methods with discrete noise: the \(\tau\)-rock methods. Zbl 1224.65009 Abdulle, Assyr; Hu, Yucheng; Li, Tiejun 6 2010 The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs. Zbl 1372.65266 Abdulle, A. 53 2009 A short and versatile finite element multiscale code for homogenization problems. Zbl 1229.74125 Abdulle, Assyr; Nonnenmacher, Achim 27 2009 A posteriori error analysis of the heterogeneous multiscale method for homogenization problems. Zbl 1172.65060 Abdulle, Assyr; Nonnenmacher, Achim 14 2009 Multiple scales problems in biomathematics, mechanics, physics and numerics, CIMPA school, Cape Town, South Africa, August 6–18, 2007. Zbl 1171.65002 1 2009 S-ROCK: Chebyshev methods for stiff stochastic differential equations. Zbl 1159.60329 Abdulle, Assyr; Cirilli, Stephane 44 2008 S-ROCK methods for stiff Itô SDEs. Zbl 1162.60330 Abdulle, Assyr; Li, Tiejun 35 2008 Effectiveness of implicit methods for stiff stochastic differential equations. Zbl 1199.65010 Li, Tiejun; Abdulle, Assyr; E, Weinan 25 2008 Finite element heterogeneous multiscale methods with near optimal computational complexity. Zbl 1155.65096 Abdulle, Assyr; Engquist, Bjorn 20 2008 Multiscale method based on discontinuous Galerkin methods for homogenization problems. Zbl 1133.65094 Abdulle, Assyr 10 2008 Stabilized methods for stiff stochastic systems. Zbl 1128.65004 Abdulle, Assyr; Cirilli, Stéphane 13 2007 Analysis of a heterogeneous multiscale FEM for problems in elasticity. Zbl 1095.74029 Abdulle, Assyr 28 2006 Heterogeneous multiscale methods with quadrilateral finite elements. Zbl 1118.65382 Abdulle, Assyr 4 2006 Numerical methods for transport problems in microdevices. Zbl 1142.65436 Abdulle, Assyr; Attinger, Sabine 1 2006 On a priori error analysis of fully discrete heterogeneous multiscale FEM. Zbl 1092.65093 Abdulle, Assyr 63 2005 Heterogeneous multiscale FEM for diffusion problems on rough surfaces. Zbl 1160.65337 Abdulle, Assyr; Schwab, Christoph 33 2005 Multiscale methods for advection-diffusion problems. Zbl 1144.65315 Abdulle, Assyr 7 2005 Homogenization method for transport of DNA particles in heterogeneous arrays. Zbl 1140.92300 Abdulle, Assyr; Attinger, Sabine 2 2004 Finite difference heterogeneous multi-scale method for homogenization problems. Zbl 1034.65067 Abdulle, Assyr; E, Weinan 42 2003 Fourth order Chebyshev methods with recurrence relation. Zbl 1009.65048 Abdulle, Assyr 58 2002 200 years of least squares method. Zbl 1003.01008 Abdulle, Assyr; Wanner, G. 2 2002 Second order Chebyshev methods based on orthogonal polynomials. Zbl 0997.65094 Abdulle, Assyr; Medovikov, Alexei A. 68 2001 Chebyshev methods based on orthogonal polynomials. Zbl 1026.65076 Abdulle, Assyr 5 2001 On roots and error constants of optimal stability polynomials. Zbl 0956.65068 Abdulle, Assyr 5 2000 all cited Publications top 5 cited Publications all top 5 Cited by 1,072 Authors 66 Abdulle, Assyr 31 Chung, Tsz Shun Eric 20 Efendiev, Yalchin R. 18 Vilmart, Gilles 17 Henning, Patrick 13 Cui, Junzhi 13 Ohlberger, Mario 13 Peterseim, Daniel 12 Leung, Wingtat 12 Ma, Qiang 11 Målqvist, Axel 11 Verfürth, Barbara 11 Yang, Zhiqiang 9 Arjmand, Doghonay 9 Engquist, Bjorn E. 8 Burrage, Kevin 8 Hoang, Viet Ha 8 Martín-Vaquero, Jesús 8 Pavliotis, Grigorios A. 8 Sun, Yi 8 Zygalakis, Konstantinos C. 7 Barth, Andrea 7 Brown, Donald L. 7 Cheung, Siu Wun 7 Dong, Hao 7 Hong, Jialin 7 Komori, Yoshio 7 Legoll, Frédéric 7 Maier, Roland 7 Schweizer, Ben 7 Vasilyeva, Maria V. 7 Zhang, Zhiwen 6 Bréhier, Charles-Edouard 6 De Souza, Giacomo Rosilho 6 Eidel, Bernhard 6 Heydari, Mohammad Hossein 6 Huber, Martin E. 6 Pun, Saimang 6 Samaey, Giovanni 6 Shang, Xiaocheng 6 Zhang, Lei 5 Bai, Yun 5 Cattani, Carlo 5 Ciarlet, Patrick jun. 5 Crouseilles, Nicolas 5 Deparis, Simone 5 Grote, Marcus J. 5 Hooshmandasl, Mohammad Reza 5 Laurent, Adrien 5 Li, Zhihui 5 Lu, Jianfeng 5 Runborg, Olof 5 Schwab, Christoph 5 Stohrer, Christian 5 Stoltz, Gabriel 4 Almuslimani, Ibrahim 4 Budáč, Ondrej 4 Chamoin, Ludovic 4 Chartier, Philippe 4 Chen, Chuchu 4 Fischer, Andreas 4 Fu, Shubin 4 Gan, Siqing 4 Garegnani, Giacomo 4 Hennig, Philipp 4 Jecker, Orane 4 Kleefeld, B. 4 Kornhuber, Ralf 4 Lee, Yoonsang 4 Li, Qin 4 Liu, Yizhi 4 Ljung, Per 4 Ming, Pingbing 4 Nonnenmacher, Achim 4 Pollock, Sara 4 Pouchon, Timothée 4 Roberts, Anthony John 4 Tang, Xiao 4 Vaes, Urbain 4 Valentin, Frédéric 4 Xiao, Aiguo 4 Yamada, Takayuki 4 Ye, Changqing 4 Zanoni, Andrea 4 Zhao, Xiaofei 4 Zielinski, Przemyslaw 3 Allaire, Grégoire 3 Ben Hammouda, Chiheb 3 Cao, Liqun 3 Dal Santo, Niccolò 3 Debrabant, Kristian 3 Deng, Weibing 3 Dong, Qiaoli 3 E, Weinan 3 Ekre, Fredrik 3 Engwer, Christian 3 Guan, Xiaofei 3 Haghighi, Amir 3 Hochbruck, Marlis 3 Kevrekidis, Ioannis George ...and 972 more Authors all top 5 Cited in 136 Serials 83 Journal of Computational Physics 62 Multiscale Modeling & Simulation 46 Computer Methods in Applied Mechanics and Engineering 45 Journal of Computational and Applied Mathematics 30 SIAM Journal on Scientific Computing 23 BIT 22 SIAM Journal on Numerical Analysis 20 Journal of Scientific Computing 18 Computers & Mathematics with Applications 18 Numerische Mathematik 18 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 14 Applied Numerical Mathematics 12 Mathematics of Computation 11 Computational Mechanics 11 Statistics and Computing 10 International Journal for Numerical Methods in Engineering 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 9 Advances in Computational Mathematics 9 Discrete and Continuous Dynamical Systems. Series S 8 Applied Mathematics and Computation 7 Numerical Methods for Partial Differential Equations 7 Numerical Algorithms 7 International Journal of Computer Mathematics 7 SIAM/ASA Journal on Uncertainty Quantification 5 Applied Mathematical Modelling 5 Computational and Applied Mathematics 5 Foundations of Computational Mathematics 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 European Journal of Mechanics. A. Solids 4 Acta Numerica 4 Oberwolfach Reports 4 Communications in Computational Physics 4 Advances in Applied Mathematics and Mechanics 4 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Computer Physics Communications 3 Mathematics and Computers in Simulation 3 Asymptotic Analysis 3 SIAM Journal on Applied Mathematics 3 SIAM Review 3 Computational Geosciences 3 Discrete and Continuous Dynamical Systems. Series B 3 SIAM Journal on Applied Dynamical Systems 3 Networks and Heterogeneous Media 3 SIAM Journal on Imaging Sciences 3 Stochastic and Partial Differential Equations. Analysis and Computations 3 Journal of Computational Dynamics 3 Research in the Mathematical Sciences 2 Archive for Rational Mechanics and Analysis 2 Inverse Problems 2 Journal of Fluid Mechanics 2 The Annals of Applied Probability 2 Computational Mathematics and Mathematical Physics 2 SIAM Journal on Mathematical Analysis 2 ETNA. Electronic Transactions on Numerical Analysis 2 Discrete and Continuous Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Communications in Nonlinear Science and Numerical Simulation 2 Combustion Theory and Modelling 2 Computational Methods in Applied Mathematics 2 Journal of Machine Learning Research (JMLR) 2 Journal of Numerical Mathematics 2 Advances in Difference Equations 2 Acta Mechanica Sinica 1 Acta Mechanica 1 Applicable Analysis 1 Computers and Fluids 1 International Journal for Numerical Methods in Fluids 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical Analysis and Applications 1 Journal of the Mechanics and Physics of Solids 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nonlinearity 1 Bulletin of Mathematical Biology 1 Acta Mathematica Vietnamica 1 The Annals of Probability 1 The Annals of Statistics 1 Calcolo 1 Journal of Differential Equations 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Journal of Computational Mathematics 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Japan Journal of Industrial and Applied Mathematics 1 Journal of Elasticity 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Stochastic Processes and their Applications 1 Computational Statistics and Data Analysis 1 SIAM Journal on Optimization 1 Journal of Nonlinear Science 1 Potential Analysis 1 Turkish Journal of Mathematics 1 Georgian Mathematical Journal 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Computational Neuroscience 1 Complexity 1 Electronic Journal of Probability ...and 36 more Serials all top 5 Cited in 37 Fields 569 Numerical analysis (65-XX) 293 Partial differential equations (35-XX) 141 Probability theory and stochastic processes (60-XX) 136 Mechanics of deformable solids (74-XX) 105 Fluid mechanics (76-XX) 47 Ordinary differential equations (34-XX) 36 Statistical mechanics, structure of matter (82-XX) 34 Statistics (62-XX) 34 Optics, electromagnetic theory (78-XX) 31 Dynamical systems and ergodic theory (37-XX) 20 Computer science (68-XX) 19 Biology and other natural sciences (92-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 14 Classical thermodynamics, heat transfer (80-XX) 9 Quantum theory (81-XX) 9 Systems theory; control (93-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 Mechanics of particles and systems (70-XX) 7 Geophysics (86-XX) 6 Approximations and expansions (41-XX) 5 General and overarching topics; collections (00-XX) 5 Operations research, mathematical programming (90-XX) 4 Integral equations (45-XX) 4 Functional analysis (46-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 History and biography (01-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 Differential geometry (53-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Geometry (51-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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