Journal of Applied Mathematics
Volume 2013 (2013), Article ID 493483, 14 pages
http://dx.doi.org/10.1155/2013/493483
Research Article

First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation

Marco Pedro Ramirez-Tachiquin,1 Cesar Marco Antonio Robles Gonzalez,2 Rogelio Adrian Hernandez-Becerril,2 and Ariana Guadalupe Bucio Ramirez3

1Communications and Digital Signal Processing Group, Faculty of Engineering, La Salle University, B. Franklin 47, Mexico City 06140, Mexico
2SEPI, ESIME Culhuacan, National Polytechnic Institute, Avenue Santa Ana No. 1000, Mexico City 04430, Mexico
3SEPI, UPIITA, National Polytechnic Institute, Avenue IPN 2580, Mexico City 07340, Mexico

Received 13 March 2013; Accepted 31 May 2013

Academic Editor: Yansheng Liu

Copyright © 2013 Marco Pedro Ramirez-Tachiquin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Based upon the elements of the modern pseudoanalytic function theory, we analyze a new method for numerically solving the forward Dirichlet boundary value problem corresponding to the two-dimensional electrical impedance equation. The analysis is performed by introducing interpolating piecewise separable-variables conductivity functions in the unit circle. To warrant the effectiveness of the posed method, we consider several examples of conductivity functions, whose boundary conditions are exact solutions of the electrical impedance equation, performing a brief comparison with the finite element method. Finally, we discuss the possible contributions of these results to the field of the electrical impedance tomography.