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Authors
Alonso, Diego Hayashi https://orcid.org/0000-0002-6032-9989
Picelli, Renato https://orcid.org/0000-0003-4456-0213
Meneghini, Julio Romano https://orcid.org/0000-0003-3945-7916
Silva, EmÃlio Carlos Nelli https://orcid.org/0000-0003-1715-1713
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Article History
Received: 3 March 2025
Revised: 17 June 2025
Accepted: 21 June 2025
First Online: 29 July 2025
Declarations
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: The authors declare that they have no Conflict of interest.
: The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organizations.
: Data will be made available on request. The paper includes all necessary details of the numerical implementation, and all of the parameters used in the numerical examples are specified. The main implementation is done in the FEniCS platform, which means that the implementation is direct from the provided descriptions, because FEniCS is based on a high-level description of the equations, which automates the generation of the underlying matrices used for the computations. The specific details pertaining the implementation are described in detail in Appendices and . The pseudocode of the implementation is shown in Algorithm 1, where the main FEniCS/dolfin-adjoint functions are indicated between parentheses.
