A topological derivative-based method for the reconstruction of multiple pollution sources

Lucas dos Santos Fernandez, Antonio André Novotny, Ravi Prakash, Jan Sokolowski

Resumo


The topological derivative method is used to solve a pollution sources reconstruction  problem governed by a steady-state convection-diffusion equation. The inverse problem consists in  the reconstruction of a set of pollution sources in a fluid médium by measuring the concentration  of the pollutants within some subregion of the reference domain. We rewrite the inverse problem  as a topology optimization problem which allows us to solve it by using the concept of topological  derivatives. The resulting algorithm is able to reconstruct the pollution sources in one step and is  independent of any initial guess. A numerical example is presented to show the effectiveness of our  reconstruction method.  


Palavras-chave


Inverse problem; pollution sources reconstruction; topological derivative method.

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Referências


A. A. Novotny and J. Sokolowski. Topological derivatives in shape optimization, Interactions of Mechanics and Mathematics. Springer-Verlag, Berlin, Heidelberg, 2013.

A. A. Novotny, J. Sokolowski and A. Zochowski. Applications of the topological derivative method, Studies in Systems, Decision and Control. Springer Nature, Switzerland, 2019.

T. J. Machado, J. S. Angelo and A. A. Novotny. A new one-shot pointwise source reconstruction method, Mathematical Methods in Applied Sciences, 40:1367-1381, 2017.

J. Sokolowski and A. Zochowski. On the topological derivative in shape optimization, SIAM Journal on Control and Optimization, 37(4): 1251-1272, 1999.




DOI: https://doi.org/10.5540/03.2021.008.01.0349

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