Control problem applied to the Helmholtz problem
Welerson Fernandes Kneipp1; Alan Alves Santana Amad2; Thiago José Machado2; Antonio André Novotny2
1 Centro Federal de Educação Tecnológica Celso Suckow da Fonseca - CEFET-RJ; 2 Laboratório Nacional de Computação Científica - LNCC
doi:10.20906/CPS/CILAMCE2017-0616
Resumo
In this work, the optimal control problem for concentrated sources is studied. In particular, the control is given by a finite linear combination of Dirac mass and the state is a solution of an Helmholtz equation. The purpose is thus to minimize a functional, which measures the distance between the state and the target function, relative to the amount, intensities, and locations of pointwise loads that constitute the source term of the boundary value problem. To this end, applies a method that consists in calculating the sensitivity of functional with respect to the set of admissible solutions. The result is used to devise a non-iterative second order method, independent of any initial guess and without introducing regularization techniques. The optimization problem is used to solve the problem of reconstruction concentrated sources from the reading data inside a subset of the domain. Finally, the devised reconstruction algorithm is verified numerically.
Palavras-chave: control problem; inverse problem; Helmholtz equation; sensitivity analysis