scholarly journals Discussion: “Extension of a Method of Solution for Poisson’s Equation” (Cobble, M. H., and Ames, W. F., 1963, ASME J. Appl. Mech., 30, pp. 415–418)

1964 ◽  
Vol 31 (3) ◽  
pp. 568-568
Author(s):  
Robert Schmidt
Keyword(s):  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Method Of Solution

Extension of a Method of Solution for Poisson’s Equation

1963 ◽  
Vol 30 (3) ◽  
pp. 415-418 ◽  
Author(s):  
M. H. Cobble ◽  
W. F. Ames
Keyword(s):  
Functional Form ◽  
Fluid Velocity ◽  
Velocity Fields ◽  
Poisson’S Equation ◽  
Coordinate Transformations ◽  
Poisson's Equation ◽  
Method Of Solution ◽  
Substitution Procedure

A classical substitution procedure for solving Poisson’s equation ∇2φ = −K is extended by application of certain coordinate transformations suggested by the functional form of K. The method is applied to the determination of fluid-velocity fields in two curvilinear geometries.

scholarly journals A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Yaw Kyei ◽  
John Paul Roop ◽  
Guoqing Tang
Keyword(s):  
Finite Difference ◽  
High Performance ◽  
Three Dimensional ◽  
Difference Schemes ◽  
Poisson’S Equation ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Poisson's Equation ◽  
Compact Finite Difference ◽  
Compact Finite Difference Schemes

We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson's equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson's equation on a compact stencil, and thus the schemes can be easily implemented and resulting linear systems are solved in a high-performance computing environment. The resulting discretization is a one-parameter family of finite-difference schemes which may be further optimized for accuracy and stability. Computational experiments are implemented which illustrate the theoretically demonstrated truncation errors.

Electric field distribution and voltage breakdown modeling for any PN junction

2016 ◽  
Vol 35 (1) ◽  
pp. 137-156 ◽  
Author(s):  
N. Rouger
Keyword(s):  
Numerical Methods ◽  
Electric Field ◽  
Field Distribution ◽  
Electric Field Distribution ◽  
Poisson’S Equation ◽  
Doping Profile ◽  
Distribution Analysis ◽  
Poisson's Equation ◽  
Content Type ◽  
Pn Junction

Purpose – Scientists and engineers have been solving Poisson’s equation in PN junctions following two approaches: analytical solving or numerical methods. Although several efforts have been accomplished to offer accurate and fast analyses of the electric field distribution as a function of voltage bias and doping profiles, so far none achieved an analytic or semi-analytic solution to describe neither a double diffused PN junction nor a general case for any doping profile. The paper aims to discuss these issues. Design/methodology/approach – In this work, a double Gaussian doping distribution is first considered. However, such a doping profile leads to an implicit problem where Poisson’s equation cannot be solved analytically. A method is introduced and successfully applied, and compared to a finite element analysis. The approach is then generalized, where any doping profile can be considered. 2D and 3D extensions are also presented, when symmetries occur for the doping profile. Findings – These results and the approach here presented offer an efficient and accurate alternative to numerical methods for the modeling and simulation of mathematical equations arising in physics of semiconductor devices. Research limitations/implications – A general 3D extension in the case where no symmetry exists can be considered for further developments. Practical implications – The paper strongly simplify and ease the optimization and design of any PN junction. Originality/value – This paper provides a novel method for electric field distribution analysis.

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