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Abdulle, Assyr (b. 1971 d. 2021)

Author ID: abdulle.assyr Recent zbMATH articles by "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
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

Publications by Year

Citations contained in zbMATH Open

94 Publications have been cited 1,451 times in 679 Documents Cited by Year
The heterogeneous multiscale method. Zbl 1255.65224
Abdulle, Assyr; Weinan, E.; Engquist, Björn; Vanden-Eijnden, Eric
166
2012
Second order Chebyshev methods based on orthogonal polynomials. Zbl 0997.65094
Abdulle, Assyr; Medovikov, Alexei A.
67
2001
On a priori error analysis of fully discrete heterogeneous multiscale FEM. Zbl 1092.65093
Abdulle, Assyr
62
2005
Fourth order Chebyshev methods with recurrence relation. Zbl 1009.65048
Abdulle, Assyr
57
2002
The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs. Zbl 1372.65266
Abdulle, A.
50
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
41
2003
Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems. Zbl 1284.65161
Abdulle, Assyr; Bai, Yun
35
2012
S-ROCK methods for stiff Itô SDEs. Zbl 1162.60330
Abdulle, Assyr; Li, Tiejun
34
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
32
2013
Heterogeneous multiscale FEM for diffusion problems on rough surfaces. Zbl 1160.65337
Abdulle, Assyr; Schwab, Christoph
31
2005
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
Localized orthogonal decomposition method for the wave equation with a continuum of scales. Zbl 1358.65064
Abdulle, Assyr; Henning, Patrick
29
2017
High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
27
2014
A short and versatile finite element multiscale code for homogenization problems. Zbl 1229.74125
Abdulle, Assyr; Nonnenmacher, Achim
27
2009
Analysis of a heterogeneous multiscale FEM for problems in elasticity. Zbl 1095.74029
Abdulle, Assyr
26
2006
Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales. Zbl 1243.65134
Abdulle, Assyr
26
2012
Finite element heterogeneous multiscale method for the wave equation: long-time effects. Zbl 1315.65084
Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian
26
2014
Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
26
2015
Effectiveness of implicit methods for stiff stochastic differential equations. Zbl 1199.65010
Li, Tiejun; Abdulle, Assyr; E, Weinan
24
2008
Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs. Zbl 1296.65008
Abdulle, Assyr; Barth, Andrea; Schwab, Christoph
21
2013
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146
Abdulle, Assyr; Vilmart, Gilles
21
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
High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
21
2012
Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
20
2013
Finite element heterogeneous multiscale methods with near optimal computational complexity. Zbl 1155.65096
Abdulle, Assyr; Engquist, Bjorn
20
2008
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
14
2013
A posteriori error analysis of the heterogeneous multiscale method for homogenization problems. Zbl 1172.65060
Abdulle, Assyr; Nonnenmacher, Achim
14
2009
Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis. Zbl 1426.76208
Abdulle, Assyr; Vilmart, Gilles
14
2012
Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013
Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles
14
2018
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
14
2015
FE heterogeneous multiscale method for long-time wave propagation. Zbl 1273.76263
Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian
13
2013
Stabilized methods for stiff stochastic systems. Zbl 1128.65004
Abdulle, Assyr; Cirilli, Stéphane
13
2007
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245
Abdulle, Assyr; Bai, Yun; Vilmart, Gilles
12
2015
Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration. Zbl 1505.62010
Abdulle, Assyr; Garegnani, Giacomo
12
2020
Stabilized multilevel Monte Carlo method for stiff stochastic differential equations. Zbl 1349.65028
Abdulle, Assyr; Blumenthal, Adrian
12
2013
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
11
2016
A reduced basis localized orthogonal decomposition. Zbl 1349.65609
Abdulle, Assyr; Henning, Patrick
11
2015
Numerical methods for stochastic partial differential equations with multiple scales. Zbl 1429.65013
Abdulle, A.; Pavliotis, G. A.
11
2012
Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales. Zbl 1296.65150
Abdulle, A.; Huber, M. E.
10
2014
Spectral methods for multiscale stochastic differential equations. Zbl 1398.65313
Abdulle, Assyr; Pavliotis, G. A.; Vaes, U.
10
2017
Multiscale method based on discontinuous Galerkin methods for homogenization problems. Zbl 1133.65094
Abdulle, Assyr
10
2008
Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems. Zbl 1357.65169
Abdulle, Assyr; Huber, Martin E.
10
2016
A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method. Zbl 1274.65289
Abdulle, Assyr; Nonnenmacher, Achim
9
2013
Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization. Zbl 1362.35033
Abdulle, Assyr; Pouchon, Timothée
9
2016
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
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
8
2019
Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063
Abdulle, A.; Huber, M. E.; Vilmart, G.
8
2015
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.
8
2014
Multiscale methods for advection-diffusion problems. Zbl 1144.65315
Abdulle, Assyr
7
2005
Reduced-order modelling numerical homogenization. Zbl 1353.74067
Abdulle, A.; Bai, Y.
7
2014
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
Fully discrete analysis of the heterogeneous multiscale method for elliptic problems with multiple scales. Zbl 1311.65140
Abdulle, Assyr; Bai, Yun
6
2015
Chebyshev methods with discrete noise: the \(\tau\)-rock methods. Zbl 1224.65009
Abdulle, Assyr; Hu, Yucheng; Li, Tiejun
6
2010
Explicit methods for stiff stochastic differential equations. Zbl 1246.65007
Abdulle, Assyr
6
2012
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
6
2017
On roots and error constants of optimal stability polynomials. Zbl 0956.65068
Abdulle, Assyr
5
2000
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
Numerical methods for multilattices. Zbl 1255.74025
Abdulle, Assyr; Lin, Ping; Shapeev, Alexander V.
5
2012
A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media. Zbl 1436.76018
Abdulle, Assyr; Budáč, Ondrej
5
2016
Chebyshev methods based on orthogonal polynomials. Zbl 1026.65076
Abdulle, Assyr
5
2001
An optimization-based, heterogeneous to homogeneous coupling method. Zbl 1326.65074
Abdulle, Assyr; Jecker, Orane
5
2015
Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization. Zbl 1350.65112
Abdulle, Assyr; Huber, Martin E.
5
2016
Multiscale methods for wave problems in heterogeneous media. Zbl 1368.65184
Abdulle, A.; Henning, P.
5
2017
Heterogeneous multiscale methods with quadrilateral finite elements. Zbl 1118.65382
Abdulle, Assyr
4
2006
A Bayesian numerical homogenization method for elliptic multiscale inverse problems. Zbl 1436.62089
Abdulle, Assyr; Blasio, Andrea Di
4
2020
Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales. Zbl 1456.35015
Abdulle, Assyr; Pouchon, Timothée
4
2020
Ensemble Kalman filter for multiscale inverse problems. Zbl 1453.65393
Abdulle, Assyr; Garegnani, Giacomo; Zanoni, Andrea
4
2020
Explicit stabilized multirate method for stiff differential equations. Zbl 1500.65034
Abdulle, Assyr; Grote, Marcus J.; De Souza, Giacomo Rosilho
4
2022
Effective models for long time wave propagation in locally periodic media. Zbl 1404.35020
Abdulle, Assyr; Pouchon, Timothée
4
2018
Numerical homogenization and model order reduction for multiscale inverse problems. Zbl 1412.65195
Abdulle, Assyr; Blasio, Andrea Di
3
2019
The role of numerical integration in numerical homogenization. Zbl 1382.65375
Abdulle, Assyr
3
2015
Numerical experiments for multiscale problems in linear elasticity. Zbl 1388.74099
Jecker, Orane; Abdulle, Assyr
3
2016
Multiscale adaptive method for Stokes flow in heterogenenous media. Zbl 1321.76034
Abdulle, Assyr; Budáč, Ondrej
3
2015
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
Homogenization method for transport of DNA particles in heterogeneous arrays. Zbl 1140.92300
Abdulle, Assyr; Attinger, Sabine
2
2004
200 years of least squares method. Zbl 1003.01008
Abdulle, Assyr; Wanner, G.
2
2002
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
2
2019
A probabilistic finite element method based on random meshes: a posteriori error estimators and Bayesian inverse problems. Zbl 1506.65200
Abdulle, Assyr; Garegnani, Giacomo
2
2021
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
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
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
Numerical methods for transport problems in microdevices. Zbl 1142.65436
Abdulle, Assyr; Attinger, Sabine
1
2006
Multiple scales problems in biomathematics, mechanics, physics and numerics, CIMPA school, Cape Town, South Africa, August 6–18, 2007. Zbl 1171.65002
1
2009
A parabolic local problem with exponential decay of the resonance error for numerical homogenization. Zbl 07466873
Abdulle, Assyr; Arjmand, Doghonay; Paganoni, Edoardo
1
2021
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
Numerical homogenization method for parabolic advection-diffusion multiscale problems with large compressible flows. Zbl 1397.76118
Abdulle, A.; Huber, M. E.
1
2017
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
Improved stabilized multilevel Monte Carlo method for stiff stochastic differential equations. Zbl 1328.65013
Abdulle, Assyr; Blumenthal, Adrian
1
2015
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
2
2021
A parabolic local problem with exponential decay of the resonance error for numerical homogenization. Zbl 07466873
Abdulle, Assyr; Arjmand, Doghonay; Paganoni, Edoardo
1
2021
Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration. Zbl 1505.62010
Abdulle, Assyr; Garegnani, Giacomo
12
2020
A Bayesian numerical homogenization method for elliptic multiscale inverse problems. Zbl 1436.62089
Abdulle, Assyr; Blasio, Andrea Di
4
2020
Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales. Zbl 1456.35015
Abdulle, Assyr; Pouchon, Timothée
4
2020
Ensemble Kalman filter for multiscale inverse problems. Zbl 1453.65393
Abdulle, Assyr; Garegnani, Giacomo; Zanoni, Andrea
4
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
8
2019
Numerical homogenization and model order reduction for multiscale inverse problems. Zbl 1412.65195
Abdulle, Assyr; Blasio, Andrea Di
3
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
2
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
14
2018
Effective models for long time wave propagation in locally periodic media. Zbl 1404.35020
Abdulle, Assyr; Pouchon, Timothée
4
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.
10
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
6
2017
Multiscale methods for wave problems in heterogeneous media. Zbl 1368.65184
Abdulle, A.; Henning, P.
5
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
11
2016
Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems. Zbl 1357.65169
Abdulle, Assyr; Huber, Martin E.
10
2016
Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization. Zbl 1362.35033
Abdulle, Assyr; Pouchon, Timothée
9
2016
A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media. Zbl 1436.76018
Abdulle, Assyr; Budáč, Ondrej
5
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.
5
2016
Numerical experiments for multiscale problems in linear elasticity. Zbl 1388.74099
Jecker, Orane; Abdulle, Assyr
3
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.
26
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
14
2015
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245
Abdulle, Assyr; Bai, Yun; Vilmart, Gilles
12
2015
A reduced basis localized orthogonal decomposition. Zbl 1349.65609
Abdulle, Assyr; Henning, Patrick
11
2015
Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063
Abdulle, A.; Huber, M. E.; Vilmart, G.
8
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.
27
2014
Finite element heterogeneous multiscale method for the wave equation: long-time effects. Zbl 1315.65084
Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian
26
2014
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146
Abdulle, Assyr; Vilmart, Gilles
21
2014
Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales. Zbl 1296.65150
Abdulle, A.; Huber, M. E.
10
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.
8
2014
Reduced-order modelling numerical homogenization. Zbl 1353.74067
Abdulle, A.; Bai, Y.
7
2014
Adaptive reduced basis finite element heterogeneous multiscale method. Zbl 1286.74088
Abdulle, Assyr; Bai, Yun
32
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
14
2013
FE heterogeneous multiscale method for long-time wave propagation. Zbl 1273.76263
Abdulle, Assyr; Grote, Marcus J.; Stohrer, Christian
13
2013
Stabilized multilevel Monte Carlo method for stiff stochastic differential equations. Zbl 1349.65028
Abdulle, Assyr; Blumenthal, Adrian
12
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
166
2012
Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems. Zbl 1284.65161
Abdulle, Assyr; Bai, Yun
35
2012
Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales. Zbl 1243.65134
Abdulle, Assyr
26
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
High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
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
14
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.
50
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
34
2008
Effectiveness of implicit methods for stiff stochastic differential equations. Zbl 1199.65010
Li, Tiejun; Abdulle, Assyr; E, Weinan
24
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
26
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
62
2005
Heterogeneous multiscale FEM for diffusion problems on rough surfaces. Zbl 1160.65337
Abdulle, Assyr; Schwab, Christoph
31
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
41
2003
Fourth order Chebyshev methods with recurrence relation. Zbl 1009.65048
Abdulle, Assyr
57
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.
67
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 top 5

Cited by 1,036 Authors

65 Abdulle, Assyr
29 Chung, Tsz Shun Eric
20 Efendiev, Yalchin R.
18 Vilmart, Gilles
17 Henning, Patrick
12 Cui, Junzhi
12 Leung, Wingtat
12 Ohlberger, Mario
12 Peterseim, Daniel
11 Ma, Qiang
11 Verfürth, Barbara
11 Yang, Zhiqiang
10 Målqvist, Axel
9 Engquist, Bjorn E.
8 Arjmand, Doghonay
8 Burrage, Kevin
8 Hoang, Viet Ha
8 Martín-Vaquero, Jesús
8 Sun, Yi
8 Zygalakis, Konstantinos C.
7 Barth, Andrea
7 Brown, Donald L.
7 Dong, Hao
7 Hong, Jialin
7 Legoll, Frédéric
7 Pavliotis, Grigorios A.
7 Schweizer, Ben
7 Vasilyeva, Maria V.
7 Zhang, Zhiwen
6 Cheung, Siu Wun
6 De Souza, Giacomo Rosilho
6 Heydari, Mohammad Hossein
6 Huber, Martin E.
6 Komori, Yoshio
6 Maier, Roland
6 Shang, Xiaocheng
6 Zhang, Lei
5 Bai, Yun
5 Cattani, Carlo
5 Grote, Marcus J.
5 Hooshmandasl, Mohammad Reza
5 Li, Zhihui
5 Lu, Jianfeng
5 Pun, Saimang
5 Runborg, Olof
5 Samaey, Giovanni
5 Schwab, Christoph
5 Stohrer, Christian
5 Stoltz, Gabriel
4 Almuslimani, Ibrahim
4 Bréhier, Charles-Edouard
4 Budáč, Ondrej
4 Bunder, J. E.
4 Chamoin, Ludovic
4 Chartier, Philippe
4 Chen, Chuchu
4 Ciarlet, Patrick jun.
4 Crouseilles, Nicolas
4 Deparis, Simone
4 Eidel, Bernhard
4 Fu, Shubin
4 Gan, Siqing
4 Jecker, Orane
4 Kleefeld, B.
4 Kornhuber, Ralf
4 Laurent, Adrien
4 Lee, Yoonsang
4 Liu, Yizhi
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 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 Fischer, Andreas
3 Garegnani, Giacomo
3 Guan, Xiaofei
3 Hennig, Philipp
3 Hochbruck, Marlis
3 Kevrekidis, Ioannis George
3 Khaliq, Abdul Q. M.
3 Kleefeld, Andreas
3 Kreiss, Gunilla
3 Kurganov, Alexander
3 Lamacz, Agnes
3 Larsson, Fredrik
...and 936 more Authors
all top 5

Cited in 130 Serials

82 Journal of Computational Physics
58 Multiscale Modeling & Simulation
44 Computer Methods in Applied Mechanics and Engineering
44 Journal of Computational and Applied Mathematics
27 SIAM Journal on Scientific Computing
22 BIT
21 SIAM Journal on Numerical Analysis
20 Journal of Scientific Computing
18 Computers & Mathematics with Applications
18 Numerische Mathematik
17 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 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
8 International Journal for Numerical Methods in Engineering
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
4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
4 Computational and Applied Mathematics
4 European Journal of Mechanics. A. Solids
4 Foundations of Computational Mathematics
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 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 Networks and Heterogeneous Media
3 SIAM Journal on Imaging Sciences
3 Stochastic and Partial Differential Equations. Analysis and Computations
3 Research in the Mathematical Sciences
2 Archive for Rational Mechanics and Analysis
2 Inverse Problems
2 Computational Mathematics and Mathematical Physics
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 SIAM Journal on Applied Dynamical Systems
2 Advances in Difference Equations
2 Acta Mechanica Sinica
1 Acta Mechanica
1 Applicable Analysis
1 Computers and Fluids
1 Computer Physics Communications
1 International Journal for Numerical Methods in Fluids
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Journal of Fluid Mechanics
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 Applied Mathematics Letters
1 Mathematical and Computer Modelling
1 Japan Journal of Industrial and Applied Mathematics
1 The Annals of Applied Probability
1 Journal of Elasticity
1 SIAM Journal on Mathematical Analysis
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 Complexity
1 Electronic Journal of Probability
1 Mathematical Problems in Engineering
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
1 Multibody System Dynamics
1 Nonlinear Dynamics
...and 30 more Serials
all top 5

Cited in 36 Fields

545 Numerical analysis (65-XX)
284 Partial differential equations (35-XX)
132 Probability theory and stochastic processes (60-XX)
128 Mechanics of deformable solids (74-XX)
102 Fluid mechanics (76-XX)
47 Ordinary differential equations (34-XX)
34 Statistical mechanics, structure of matter (82-XX)
32 Optics, electromagnetic theory (78-XX)
31 Statistics (62-XX)
29 Dynamical systems and ergodic theory (37-XX)
19 Computer science (68-XX)
17 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)
8 Linear and multilinear algebra; matrix theory (15-XX)
8 Systems theory; control (93-XX)
7 Mechanics of particles and systems (70-XX)
7 Geophysics (86-XX)
5 General and overarching topics; collections (00-XX)
4 Integral equations (45-XX)
4 Functional analysis (46-XX)
4 Operations research, mathematical programming (90-XX)
3 History and biography (01-XX)
3 Global analysis, analysis on manifolds (58-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 Approximations and expansions (41-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Operator theory (47-XX)
2 Differential geometry (53-XX)
2 Information and communication theory, circuits (94-XX)
1 Combinatorics (05-XX)
1 Real functions (26-XX)
1 Measure and integration (28-XX)
1 Special functions (33-XX)
1 Geometry (51-XX)

Citations by Year

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