M\'etodo de Regularizaci\'on para Identificar una Fuente en una Ecuaci\'on El\'iptica

TL;DR

This paper evaluates a regularization method for solving ill-posed inverse problems in a 2D Poisson equation, analyzing its performance with various parameters and noise levels to improve source estimation accuracy.

Contribution

It introduces and assesses a regularization technique tailored for source identification in elliptic equations, highlighting its effectiveness and implementation considerations.

Findings

Optimal regularization parameters depend on noise levels.

The method improves source estimation accuracy.

Implementation guidelines are discussed.

Abstract

The aim of this paper is to numerically study the performance of a method of regularization. This technique was developed to solve the illposed problem of estimating a source-dimensional Poisson equation for two dimensions from measurements taken over a line inside the domain. The proposed method consists in adding a regularization term to the equation that depends on a parameter, which is called regularization parameter. In this paper we show the results for different values of this parameter as well as for different levels of noise in the data used for estimation. After analyzing the results some considerations on its effective implementation are discussed.