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

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 sepa...

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Main Authors:	Marco Pedro Ramirez-Tachiquin, Cesar Marco Antonio Robles Gonzalez, Rogelio Adrian Hernandez-Becerril, Ariana Guadalupe Bucio Ramirez
Format:	Article
Language:	English
Published:	Hindawi Limited 2013-01-01
Series:	Journal of Applied Mathematics
Online Access:	http://dx.doi.org/10.1155/2013/493483

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spelling	doaj-c2bb14a867c4410da987069da823dbee2020-11-25T01:05:25ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/493483493483First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance EquationMarco Pedro Ramirez-Tachiquin0Cesar Marco Antonio Robles Gonzalez1Rogelio Adrian Hernandez-Becerril2Ariana Guadalupe Bucio Ramirez3Communications and Digital Signal Processing Group, Faculty of Engineering, La Salle University, B. Franklin 47, Mexico City 06140, MexicoSEPI, ESIME Culhuacan, National Polytechnic Institute, Avenue Santa Ana No. 1000, Mexico City 04430, MexicoSEPI, ESIME Culhuacan, National Polytechnic Institute, Avenue Santa Ana No. 1000, Mexico City 04430, MexicoSEPI, UPIITA, National Polytechnic Institute, Avenue IPN 2580, Mexico City 07340, MexicoBased 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.http://dx.doi.org/10.1155/2013/493483
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Marco Pedro Ramirez-Tachiquin Cesar Marco Antonio Robles Gonzalez Rogelio Adrian Hernandez-Becerril Ariana Guadalupe Bucio Ramirez
spellingShingle	Marco Pedro Ramirez-Tachiquin Cesar Marco Antonio Robles Gonzalez Rogelio Adrian Hernandez-Becerril Ariana Guadalupe Bucio Ramirez First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation Journal of Applied Mathematics
author_facet	Marco Pedro Ramirez-Tachiquin Cesar Marco Antonio Robles Gonzalez Rogelio Adrian Hernandez-Becerril Ariana Guadalupe Bucio Ramirez
author_sort	Marco Pedro Ramirez-Tachiquin
title	First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation
title_short	First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation
title_full	First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation
title_fullStr	First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation
title_full_unstemmed	First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation
title_sort	first characterization of a new method for numerically solving the dirichlet problem of the two-dimensional electrical impedance equation
publisher	Hindawi Limited
series	Journal of Applied Mathematics
issn	1110-757X 1687-0042
publishDate	2013-01-01
description	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.
url	http://dx.doi.org/10.1155/2013/493483
work_keys_str_mv	AT marcopedroramireztachiquin firstcharacterizationofanewmethodfornumericallysolvingthedirichletproblemofthetwodimensionalelectricalimpedanceequation AT cesarmarcoantonioroblesgonzalez firstcharacterizationofanewmethodfornumericallysolvingthedirichletproblemofthetwodimensionalelectricalimpedanceequation AT rogelioadrianhernandezbecerril firstcharacterizationofanewmethodfornumericallysolvingthedirichletproblemofthetwodimensionalelectricalimpedanceequation AT arianaguadalupebucioramirez firstcharacterizationofanewmethodfornumericallysolvingthedirichletproblemofthetwodimensionalelectricalimpedanceequation
_version_	1725194715598422016

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

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