Alifanov’s Iterative Regularization Method for the Poisson Source Term on Spherical Surfaces using Icosahedral Meshes

Authors

DOI:

https://doi.org/10.5902/2179460X91903

Keywords:

Poisson equation, Icosahedral mesh, Inverse problem, Alifanov, Source term

Abstract

In the Poisson problem, given measurements at specific points on the sphere, the goal is to determine the source term that maintains a stationary distribution. The forward problem was solved using a dual icosahedral mesh, chosen for its quasi-regularity, which is beneficial for a wide range of applications. The objective of this work is to solve the inverse problem in order to obtain the source term of the Poisson equation defined on the sphere. To solve the inverse problem, Alifanov’s iterative regularization method is applied. The inverse problem solution was validated using synthetic experimental data, which successfully recovered the source term. Perturbations of up to 10% preserved the overall behavior of the source term, albeit with amplified values.

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Author Biographies

Fábio Freitas Ferreira, Universidade Federal Fluminense

He holds a degree in Mathematics Education from the State University of Rio de Janeiro (2000), a master's degree in Computational Modeling from the State University of Rio de Janeiro (2003), a doctorate in Computational Modeling from the State University of Rio de Janeiro (2008), and a postdoctoral degree in Computational Modeling from IPRJ/UERJ (2019). He is currently an associate professor 2 at the Fluminense Federal University.

Francisco Duarte Moura Neto, Universidade do Estado do Rio de Janeiro

He holds a bachelor's degree in Mathematics from the Pontifical Catholic University of Rio de Janeiro (1980), a master's degree in Mathematics from the Pontifical Catholic University of Rio de Janeiro (1982) and a PhD in Mathematics from the University of California, Berkeley (1987). He is currently a Full Professor at the State University of Rio de Janeiro, was coordinator of the postgraduate program in Computational Modeling at the Polytechnic Institute (2011-2013).

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Published

2026-07-23

Issue

Vol. 48 (2026): Publicação contínua

Section

Applied Mathematics

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