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In this investigation we address the problem of adjoint–based optimization of PDE systems in moving domains. As an example we consider the one–dimensional heat equation with prescribed boundary temperatures and heat fluxes. We discuss two methods of deriving an adjoint system necessary to obtain a gradient of a cost functional. In the first approach we… (More)

In this work we investigate a technique for accelerating convergence of adjoint–based optimization of PDE systems based on a nonlinear change of variables in the control space. This change of variables is accomplished in the differentiate–then–discretize approach by constructing the descent directions in a control space not equipped with the Hilbert… (More)

The inverse natural convection problem (INCP) in a porous medium is a highly non-linear problem because of the nonlinear convection and Forchheimer terms. The INCP can be converted into the minimization of a least-squares discrepancy between the observed and the modelled data. It has been solved using different classical optimization strategies that require… (More)

In this investigation we propose a computational approach for solution of optimal control problems for vortex systems with compactly supported vorticity. The problem is formulated as PDE–constrained optimization in which the solutions are found using a gradient–based descent method. Recognizing such Euler flows as free– boundary problems, the proposed… (More)

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