Gridding and discretization for divergence form (semiconductor-like) PDEs

Ming Y. Kao, Donald J. Rose, Hai Shao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We develop the box method for solving partial differential equations in the divergence (or conservation law) form. We first use graphic theoretical approaches to generate grids, i.e. partition the governing domain into boxes. Then we apply Green's theorem box-wisely and the constant-j assumption edge-pair-wisely to obtain the discretization system of equations, which lead to the numerical solution to the problem. We show that the box method is inherently more efficient than the traditional finite element method for linear (or convection-diffusion) problems in 1 and 2 dimensions. We also present some potential thoughts on implementing the box method for problems in higher dimensions and with nonlinearity.

Original languageEnglish (US)
Pages (from-to)111-115
Number of pages5
JournalVLSI Design
Issue number1-4
StatePublished - 1998


  • Boundary value problems
  • Box method
  • Divergence form partial differential equations
  • Grid generation
  • Voronoi diagram

ASJC Scopus subject areas

  • Hardware and Architecture
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering


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