photo

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, 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. manuscript. 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. manuscript. preprint

Seminars

Applied Mathematics and Computation

Teaching

Fall 2018, Math 551 Introduction to Scientific Computing
Fall 2018, Honors 391AH Discovering Mathematics through Computer Experiments

Spring 2018, Math 697AM Applied Math and Mathematical Modeling

Fall 2017, Math 235, Introduction to Linear Algebra
Fall 2017, Math 645, ODE and Dynamical Systems

Spring 2017, Math 697, Multiscale Methods

Fall 2016, Math 235, Introduction to Linear Algebra
Fall 2016, Math 551, Introduction to Scientific Computing

Spring 2016, Math 545, Linear Algebra for Applied Mathematics

Fall 2015, Math 545, Linear Algebra for Applied Mathematics
Fall 2015, Math 691Y, Applied Math Project Seminar