Study of the forward Dirichlet boundary value problem for the two-dimensional Electrical Impedance Equation

TL;DR

This paper introduces a novel numerical method leveraging Pseudoanalytic Function Theory to solve the 2D Electrical Impedance Equation with geometrically derived conductivity functions, expanding computational tools in this domain.

Contribution

It applies Modern Pseudoanalytic Function Theory to numerically solve the Dirichlet problem for the 2D Electrical Impedance Equation with geometrical conductivities, a first in the field.

Findings

Successful numerical solutions for geometrical conductivity functions

Demonstration of the method's applicability to bounded domains

Potential for improved impedance imaging techniques

Abstract

Using a conjecture that allows to approach separable-variables conductivity functions, the elements of the Modern Pseudoanalytic Function Theory are used, for the first time, to numerically solve the Dirichlet boundary value problem of the two-dimensional Electrical Impedance Equation, when the conductivity function arises from geometrical figures, located within bounded domains.