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

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.