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

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

doi:10.1155/1998/90420

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

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

^*Corresponding author for this work

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	111-115
Number of pages	5
Journal	VLSI Design
Volume	6
Issue number	1-4
DOIs	https://doi.org/10.1155/1998/90420
State	Published - 1998

Keywords

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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10.1155/1998/90420

Cite this

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abstract = "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.",

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T1 - Gridding and discretization for divergence form (semiconductor-like) PDEs

AU - Kao, Ming Y.

AU - Rose, Donald J.

AU - Shao, Hai

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - Boundary value problems

KW - Box method

KW - Divergence form partial differential equations

KW - Grid generation

KW - Voronoi diagram

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DO - 10.1155/1998/90420

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EP - 115

JO - VLSI Design

JF - VLSI Design

IS - 1-4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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