Gridding and Discretization For Divergence Form(Semiconductor‐Like) PDEs | Zendy

Ming Y. Kao | Zendy; Donald J. Rose | Zendy; Hai Shao | Zendy

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Gridding and Discretization For Divergence Form(Semiconductor‐Like) PDEs

Author(s) -

Ming Y. Kao,

Donald J. Rose,

Hai Shao

Publication year - 1998

Publication title -

vlsi design

Language(s) - English

Resource type - Journals

eISSN - 1065-514X

pISSN - 1026-7123

DOI - 10.1155/1998/90420

Subject(s) - discretization , divergence (linguistics) , partial differential equation , mathematics , domain (mathematical analysis) , conservation law , divergence theorem , nonlinear system , partition (number theory) , finite element method , ordinary differential equation , mathematical analysis , differential equation , physics , philosophy , linguistics , brouwer fixed point theorem , quantum mechanics , combinatorics , fixed point theorem , thermodynamics

We develop the box method for solving partial differential equations in the divergence (orconservation law) form. We first use graphic theoretical approaches to generate grids, i.e. partitionthe 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 inherentlymore efficient than the traditional finite element method for linear (or convection-diffusion)problems in and 2 dimensions. We also present some potential thoughts onimplementing the box method for problems in higher dimensions and with nonlinearity

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