Matthew Dobson Department of Mathematics and Statistics, UMass Amherst 710 N. Pleasant Street Amherst, MA 01003, USA Room: LGRT 1430 Phone 413-545-7194 E-mail: my last name at math.umass.edu UMass Research Experiences for Undergrduates Research Interests and Publications Seminars Teaching

Research and Publications

Atomistic-to-Continuum Schemes

1. Matthew Dobson, Ryan Elliott, and Ellad Tadmor. A quasicontinuum for complex crystals, In Peter Gumbsch, ed., Third International Conference on Multiscale Materials Modeling 889-896, Freiburg, Germany, 2006.
2. Matthew Dobson, Ryan Elliott, Mitchell Luskin, and Ellad Tadmor. A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics. J. Comput. Aided Mater. Des., 14(Supplement 1):219--237, 2007. article
3. Matthew Dobson and Mitchell Luskin. Analysis of a force-based quasicontinuum method. M2AN Math. Model. Numer. Anal., 42(1):113--139, 2008. pdf
4. Matthew Dobson and Mitchell Luskin. Iterative solution of the quasicontinuum equilibrium equations with continuation. J. Sci. Comput., 37:19--41, 2008. preprint
5. Matthew Dobson and Mitchell Luskin. An analysis of the effect of ghost force oscillation on quasicontinuum error. M2AN Math. Model. Numer. Anal., 43(3):591--604, 2009. preprint pdf
6. Matthew Dobson and Mitchell Luskin. An optimal order error analysis of the one-dimensional quasicontinuum approximation. SIAM J. Numer. Anal., 47(4):2455--2475, 2009. preprint.
7. Matthew Dobson, Mitchell Luskin, and Christoph Ortner. Stability, instability, and error of the force-based quasicontinuum approximation. Archive for Rational Mechanics and Analysis, 197(1):179--202, 2010. preprint
8. Matthew Dobson, Mitchell Luskin, and Christoph Ortner. Sharp stability estimates for force-based quasicontinuum methods. SIAM J. Multiscale Modeling and Simulation, 8(3):782--802, 2010. preprint
9. Matthew Dobson, Mitchell Luskin, and Christoph Ortner. Accuracy of quasicontinuum approximations near instabilities. Journal of the Mechanics and Physics of Solids, 58(10):1741--1757, 2010.preprint
10. Matthew Dobson, Mitchell Luskin, and Christoph Ortner. Iterative methods for the force-based quasicontinuum approximation. Computer Methods in Applied Mechanics and Engineering, Volume 200, Issues 37--40, 2011.preprint
11. Matthew Dobson, Christoph Ortner, and Alexander V. Shapeev. The spectrum of the force-based quasicontinuum operator for a homogeneous periodic chain. Multiscale Modeling and Simulation, Volume 10, Issue 3, 2012, Pp. 744-765. preprint.
12. Matthew Dobson. There is no pointwise consistent quasicontinuum energy. IMA Journal of Numerical Analysis, 34 (4): 1541-1553, 2014. preprint.
13. Matthew Dobson, Manh Hong Duong, and Christoph Ortner. On assessing the accuracy of defect free energy computations. ESAIM: Mathematical Modelling and Numerical Analysis, Volume 52, Number 4, July-August 2018 Accepted.preprint

Nonlinear Dynamical Systems

1. Matthew Dobson, Claude Le Bris, and Frederic Legoll. Symplectic schemes for highly oscillatory Hamiltonian systems with varying fast frequencies. Note aux Comptes Rendus de l'Academie des Sciences, 348(17-18):1033--1038, 2010.preprint
2. Matthew Dobson, Claude Le Bris, and Frederic Legoll. Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case. IMA Journal of Numerical Analysis Volume 33, Issue 1, 2012 Pp. 30-56. preprint.
3. A. S. Rodrigues, P. Kevrekidis, M. Dobson. N-break states in a chain of nonlinear oscillators. Physical Review E, vol 99, 2019, 022201. preprint

Nonequilibrium Molecular Dynamics

1. Matthew Dobson, Frederic Legoll, Tony Lelievre, Gabriel Stoltz. Derivation of Langevin Dynamics in a non-Uniform Background Flow Field. Mathematical Modelling and Numerical Analysis, Volume 47, Issue 06, November 2013, pp 1583-1626.preprint
2. Matthew Dobson. Periodic boundary conditions for long-time nonequilibrium molecular dynamics simulations of incompressible flows. Journal of Chemical Physics, Volume 141, Issue 18, 184103 (2014).preprint
3. Matthew Dobson, Ian Fox, Alexandra Saracino. Cell List Algorithm for Nonequilibrium Molecular Dynamics. Journal of Computational Physics, Volume 315, Pages 211-220, 2016.preprint
4. Matthew Dobson and Abdel Kader Geraldo. Strong Convergence of Integrators for Nonequilibrium Langevin Dynamics. Molecular Simulation, Volume 45, Issue 11 (2019) 912--920.. preprint
5. Matthew Dobson and Abdel Kader Geraldo. Simple Periodic Boundary Conditions for Molecular Simulation of Uniaxial Flow. manuscript. preprint

Data Driven Solvers for Fokker-Planck Equations

1. M. Dobson, Y. Li, and J. Zhai, An efficient data-driven solver for {F}okker-{P}lanck equations: algorithm and analysis, arXiv preprint arXiv:1906.02600 (2019).
2. J. Zhai, M. Dobson, and Y. Li, A deep learning method for solving Fokker-Planck equations, arXiv preprint arXiv:2012.10696 (2020).
3. M. Dobson, Y. Li, and J. Zhai, Using coupling methods to estimate sample quality of stochastic differential equations, SIAM/ASA Journal on Uncertainty Quantification Volume 9, no 1, (2021) 135--162.

Seminars

Teaching