MATH 273A: Scientific Computation
Fall quarter, 2005


Instructor: Bo Li


General: Crystalline Defects, Elasticity, Fluid Mechanics, Numerical ODE and PDE

Multiscale Methods

  1. The quasicontinuum method
    • R. E. Miller and E. B. Tadmor, The quasicontinuum method: Overview, applications and current directions, J. Computer-Aided Materials Design, 9, 203-239, 2002.
    • V. B. Shenoy, R. Miller, E. B. Tadmor, D. Rodney, R. Phillips and M. Ortiz, An adaptive finite element approach to atomic-scale mechanics - the quasicontinuum method, J. Mech. Phys. Solids, 47, 611-642, 1999.
    • J. Knap J and M. Ortiz, An analysis of the quasicontinuum method, J. Mech. Phys. Solids, 49, 1899-1923, 2001.
  2. The heterogeneous multiscale method
    • A. Abdulle and W. E, Finite difference heterogeneous multi-scale method for homogenization problems, J. Comput. Phys., 191, 18-39, 2003.
    • W. E, Analysis of the heterogeneous multiscale method for ordinary differential equations, Comm. Math. Sci., 1(3), 423-436, 2003.
    • W. E, B. Engquist, X. Li, W. Ren, E. Vanden-Eijnden, The heterogeneous multiscale method: A review, preprint, 2005.
    • W. E, P. Ming, and P. Zhang, Analysis of the heterogeneous multiscale method for elliptic homogenization problems, J. Amer. Math Soc., 8, 121-156, 2004.
    • B. Engquist and R. Tsai, Heterogeneous multiscale methods for stiff ordinary differential equations, preprint, 2004.
    • X. Yue and W. E, The local microscale problem in the multiscale modelling of strongly heterogeneous media: effect of boundary conditions and cell size, preprint, 2005.
  3. Coupling molecular dynamics and continuum simulations
    • E. B. Tadmor, G. S. Smith, N. Bernstein, and E. Kaxiras, Mixed finite element and atomistic formulation for complex crystals, Phys. Rev. B, 59, 235-245, 1999.
    • J. Q. Broughton, F. F. Abraham, N. Bernstein, and E. Kaxiras, Concurrent coupling of length scales: Methodology and application, Phys. Rev. B, 60(4), 2391-2403, 1999.
    • W. E and Z. Huang, Matching conditions in atomistic-continuum modeling of materials, Phys. Rev. Lett., 87(13), 135501, 2001.
    • X. B. Nie, S. Y. Chen, W. E., and M. O. Robbins, A continuum and molecular dynamics hybrid method for micro-and nano-fluid flow, J. Fluid Mech., 500, 55-64, 2004.
    • T. Qian and X.-P. Wang, Driven cavity flow: From molecular dynamics to continuum hydrodynamics, Multiscale Model. Simul., 3(4), 749-763, 2005.

Interface Dynamics

Energy Minimization

Last updated by Bo Li on October 17, 2005.