A Genetic Algorithm for Pointwise Source Reconstruction by the Method of Fundamental Solutions
DOI:
https://doi.org/10.5540/tcam.2022.023.03.00401Keywords:
Inverse Problems, Method of Fundamental Solutions, Genetic Algorithms, Source ReconstructionAbstract
Inverse source reconstruction problems offer great potential for applications of interest to engineering, such as the identification of polluting sources, and to medicine, such as electroencephalography, to cite at least two relevant examples. From a mathematical point of view, the identification of a concentrated source (intensity and location) corresponds to the identification of the centroid (location) and size (intensity) of a distributed source. On the other hand, from a numerical point of view, it is observed that the use of domain discretization methods is intrinsically associated with the introduction of numerical noise in reconstruction algorithms, which is strongly inadvisable since inverse problems are reckoned to be ill-posed. The objective of this work is to explore, in the context of a Poisson problem and taking into account a numerical point of view, a new reconstruction algorithm based on the method of fundamental solutions, where a source point adequately represents the pointwise source within the domain. The inverse problem is reformulated as an optimization problem solved through a genetic algorithm. Finally, numerical examples are performed to analyze the accuracy of the proposed algorithm for two and three dimensions.Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.