| Analysis of a force-based quasicontinuum approximation M Dobson, M Luskin ESAIM: Mathematical Modelling and Numerical Analysis 42 (1), 113-139, 2008 | 91 | 2008 |
| Stability, instability, and error of the force-based quasicontinuum approximation M Dobson, M Luskin, C Ortner Archive for Rational Mechanics and Analysis 197, 179-202, 2010 | 79 | 2010 |
| An analysis of the effect of ghost force oscillation on quasicontinuum error M Dobson, M Luskin ESAIM: Mathematical Modelling and Numerical Analysis 43 (3), 591-604, 2009 | 69 | 2009 |
| Accuracy of quasicontinuum approximations near instabilities M Dobson, M Luskin, C Ortner Journal of the Mechanics and Physics of Solids 58 (10), 1741-1757, 2010 | 66 | 2010 |
| An optimal order error analysis of the one-dimensional quasicontinuum approximation M Dobson, M Luskin SIAM Journal on Numerical Analysis 47 (4), 2455-2475, 2009 | 62 | 2009 |
| Periodic boundary conditions for long-time nonequilibrium molecular dynamics simulations of incompressible flows M Dobson The Journal of chemical physics 141 (18), 2014 | 56 | 2014 |
| Sharp stability estimates for the force-based quasicontinuum approximation of homogeneous tensile deformation M Dobson, M Luskin, C Ortner Multiscale Modeling & Simulation 8 (3), 782-802, 2010 | 56 | 2010 |
| A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics M Dobson, RS Elliott, M Luskin, EB Tadmor Journal of Computer-Aided Materials Design 14, 219-237, 2007 | 55 | 2007 |
| A deep learning method for solving Fokker-Planck equations J Zhai, M Dobson, Y Li Mathematical and scientific machine learning, 568-597, 2022 | 31 | 2022 |
| Iterative solution of the quasicontinuum equilibrium equations with continuation M Dobson, M Luskin Journal of Scientific Computing 37 (1), 19-41, 2008 | 23 | 2008 |
| The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain M Dobson, C Ortner, AV Shapeev Multiscale Modeling & Simulation 10 (3), 744-765, 2012 | 18 | 2012 |
| Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem M Dobson, M Luskin, C Ortner Computer Methods in Applied Mechanics and Engineering 200 (37-40), 2697-2709, 2011 | 18 | 2011 |
| Derivation of Langevin dynamics in a nonzero background flow field M Dobson, F Legoll, T Lelièvre, G Stoltz ESAIM: Mathematical Modelling and Numerical Analysis 47 (6), 1583-1626, 2013 | 15 | 2013 |
| An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis M Dobson, Y Li, J Zhai arXiv preprint arXiv:1906.02600, 2019 | 14 | 2019 |
| Cell list algorithms for nonequilibrium molecular dynamics M Dobson, I Fox, A Saracino Journal of Computational Physics 315, 211-220, 2016 | 14 | 2016 |
| Using coupling methods to estimate sample quality of stochastic differential equations M Dobson, Y Li, J Zhai SIAM/ASA Journal on Uncertainty Quantification 9 (1), 135-162, 2021 | 12 | 2021 |
| Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case M Dobson, C Le Bris, F Legoll IMA Journal of Numerical Analysis 33 (1), 30-56, 2013 | 9 | 2013 |
| A quasicontinuum for complex crystals M Dobson, RS Elliott, EB Tadmor Proceedings of the Third International Conference on Multiscale Materials …, 2006 | 7 | 2006 |
| There is no pointwise consistent quasicontinuum energy M Dobson IMA Journal of Numerical Analysis 34 (4), 1541-1553, 2014 | 6 | 2014 |
| Sharp stability estimates for the accurate prediction of instabilities by the quasicontinuum method M Dobson, M Luskin, C Ortner arXiv preprint arXiv:0905.2914, 2009 | 6 | 2009 |
