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

[摘要] Based upon the elements of the modern pseudoanalytic function theory, we analyze a new method for numerically solving the forward Dirichletboundary value problem corresponding to the two-dimensional electricalimpedance equation. The analysis is performed by introducing interpolating piecewise separable-variables conductivity functions in the unitcircle. To warrant the effectiveness of the posed method, we considerseveral examples of conductivity functions, whose boundary conditionsare exact solutions of the electrical impedance equation, performing abrief comparison with the finite element method. Finally, we discussthe possible contributions of these results to the field of the electricalimpedance tomography.

[学科分类] 应用数学