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

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Marco Pedro Ramirez-Tachiquin ◽  
Cesar Marco Antonio Robles Gonzalez ◽  
Rogelio Adrian Hernandez-Becerril ◽  
Ariana Guadalupe Bucio Ramirez
Keyword(s):  
Electrical Impedance ◽  
Dirichlet Boundary ◽  
Function Theory ◽  
New Method ◽  
Two Dimensional ◽  
Dirichlet Boundary Value Problem ◽  
The Finite Element Method ◽  
Impedance Tomography ◽  
Pseudoanalytic Function

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.

scholarly journals Numerical Method for Dirichlet Problem with Degeneration of the Solution on the Entire Boundary

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1455
Author(s):  
Viktor A. Rukavishnikov ◽  
Elena I. Rukavishnikova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dirichlet Boundary ◽  
Symmetric Domain ◽  
Two Dimensional ◽  
Dirichlet Boundary Value Problem ◽  
The Finite Element Method ◽  
Entire Boundary ◽  
Dimensional Domain ◽  
Element Method

The finite element method (FEM) with a special graded mesh is constructed for the Dirichlet boundary value problem with degeneration of the solution on the entire boundary of the two-dimensional domain. A comparative numerical analysis is performed for the proposed method and the classical finite element method for a set of model problems in symmetric domain. Experimental confirmation of theoretical estimates of accuracy is obtained and conclusions are made.

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