Abstract
The objective of this article is to investigate, analytically and numerically, the exact control problem associated with a mathematical model that describes the vertical vibrations of elastic strings, with moving contours. To determine the approximate numerical solution, following the description of the HUM (Hilbert Uniqueness Method), the finite element method associated with the Newmark method was used for the adjunct problem and the backward problem. To calculate the optimal control, the conjugated gradient method is used. The properties of a numerical problem must be consistent with the theoretical mathematical one. However, in order to obtain the numerical control, the grid is of fundamental importance, so we used the Bi-Grid technique. In this way, we developed an algorithm to solve this problem. Numerical simulations were performed for different initial data and moving contours, with and without the Bi-Grid algorithm and the numerical results confirmed the consistency between the theoretical and numerical results.
Funder
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
Publisher
Sociedade Paranaense de Matemática
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