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Within the framework of numerical simulation and optimal control of partial differential equations, in this work we deal with the mathematical modelling and control of the processes related to the urban heat island effect. In particular, we are interested in finding the optimal locations of green zones inside metropolitan areas in order to mitigate the consequences of this harmful phenomenon. So, we consider a three-dimensional climate model and formulate a constrained optimal control problem, that is extensively analyzed in the first part of the paper. Then, we propose a complete numerical algorithm for its resolution, interfacing the interior point algorithm IPOPT with the FreeFem++ software package. Finally, we present several numerical tests for a simple realistic case, where the advantages of our approach are shown. [ABSTRACT FROM AUTHOR]

This paper proposes an identification algorithm for identifying multipolar sources F in the elliptic equation Δ u + μ u = F from boundary measurements. The reconstruction question of this class of sources appears naturally in Helmholtz equation ( μ > 0 ) and in biomedical phenomena particularly in EEG/MEG problems ( μ = 0 ) and bioluminescence tomography (BLT) applications ( μ < 0 ) . Previous works have treated the inverse multipolar source problems, only for equations with μ = 0 , using algebraic approaches depending on the complex calculation of determinants. Knowing that the novelty in our method concerns several points, the principal one is its simplicity where its proof is not founded on the determinants calculation and its ease in implementation. Moreover, this work involves the general form of equations considering μ ∈ R and at the same time considers a more general type of sources than former related works including sources having small compact support within a finite number of subdomains. Finally, some numerical results are shown to prove the robustness of our identification algorithm. [ABSTRACT FROM AUTHOR]