First characterization of a new method for numerically solving the Dirichlet problem of the two-dimensional Electrical Impedance Equation

TL;DR

This paper introduces a novel numerical method based on Pseudoanalytic Function Theory for solving the 2D Electrical Impedance Equation's Dirichlet problem, demonstrating its effectiveness through multiple conductivity examples.

Contribution

It presents a new approach using piecewise separable-variables conductivity functions and orthonormal functions to numerically solve the Dirichlet problem for the Electrical Impedance Equation.

Findings

Successfully approximated boundary conditions for six conductivity cases.

Validated the method's effectiveness with exact solution comparisons.

Contributed to advancements in Electrical Impedance Tomography.

Abstract

Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation. The analysis is performed by interpolating piecewise separable-variables conductivity functions, that are eventually used in the numerical calculations in order to obtain finite sets of orthonormal functions, whose linear combinations succeed to approach the imposed boundary conditions. To warrant the effectiveness of the numerical method, we study six different examples of conductivity. The boundary condition for every case is selected considering one exact solution of the Electrical Impedance Equation. The work intends to discuss the contributions of these results into the field of the Electrical Impedance Tomography.