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A Geometrical Comparison between Cell Method and Finite Element Method in Electrostatics

M. Heshmatzadeh, G. E. Bridges1
1 ECE Department, University of Manitoba, MB, CA

Computer Modeling in Engineering & Sciences 2007, 18(1), 45-58. https://doi.org/10.3970/cmes.2007.018.045

Abstract

Cell Method, a Finite Formulation technique, is compared in detail with the Finite Element Method (FEM), a differential-based numerical technique. In the finite formulation technique, Poisson's equation is described starting from a topological foundation. The final set of algebraic equations resulting from the two approaches are compared in matrix form. The equivalence of the coefficient matrices is proven for a Voronoi dual mesh and linear shape functions in the FEM. The difference between the source (charge) vectors in the two approaches is described. It is shown that the use of linear shape functions in the FEM is equivalent to the use of a barycentric dual mesh for charge vectors. Also, it is shown that the coefficient matrix derived from a variational technique, FEM, can be interpreted using the simple geometrical concept of a parallel plate capacitor. As an example, a Schottky barrier diode with a non-uniform doping profile is considered. The results demonstrate the differences between the two approaches in the case of a non-zero electric charge density.

Keywords

Cell Method, Electrostatics, Finite Element Method, Numerical techniques, Poisson's Equation.

Cite This Article

Heshmatzadeh,, M. (2007). A Geometrical Comparison between Cell Method and Finite Element Method in Electrostatics. CMES-Computer Modeling in Engineering & Sciences, 18(1), 45–58.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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