Papers Published

1. Rose, DJ; Shao, H; Henriquez, CS, Discretization of anisotropic convection-diffusion equations, convective M-matrices and their iterative solution, Vlsi Design, vol. 10 no. 4 (January, 2000), pp. 485-529, Hindawi Limited [doi] .
   (last updated on 2023/06/01)

   Abstract:
   We derive the constant-j box method discretization for the convection-diffusion equation, ▽j = f, with j = -α▽u+βu. In two dimensions, α is a 2×2 symmetric, positive definite tensor field and β is a two-dimensional vector field. This derivation generalizes the well-known Scharfetter-Gummel discretization of the continuity equations in semiconductor device simulation. We define the anisotropic Delaunay condition and show that under this condition and appropriate evaluations of α and β, the stiffness matrix, M, of the discretization is a convective M-matrix. We then examine classical iterative splittings of M and show that convection (even convection dominance) does not degrade the rate of convergence of such iterations relative to the purely diffusive, (β = 0) problem under certain conditions.

   Keywords:
   iterative methods;matrix algebra;semiconductor device models;