Browsing by Author "E, Weinan"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Ergodicity for the navier-stokes equation with degenerate random forcing: Finite-dimensional approximation
    (Communications on Pure and Applied Mathematics, 2001-11-01) E, Weinan; Mattingly, Jonathan C
    We study Galerkin truncations of the two-dimensional Navier-Stokes equation under degenerate, large-scale, stochastic forcing. We identify the minimal set of modes that has to be forced in order for the system to be ergodic. Our results rely heavily on the structure of the nonlinearity. © 2001 John Wiley & Sons, Inc.
  • Thumbnail Image
    ItemOpen Access
    Pole-based approximation of the Fermi-dirac function
    (Chinese Annals of Mathematics. Series B, 2009-12-01) Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan
    Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations. © Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2009.