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Topological Optimization and Optimal Transport by Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux

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Anca-Maria Toader and Cristian Barbarosie

6 Optimization of eigenvalues and eigenmodes by using the adjoint method

Anca-Maria Toader and Cristian Barbarosie, Centro de Matemática e Aplicações Fundamentais, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal. atoader@fc.ul.pt, cabarbarosie@fc.ul.pt

Abstract: Application of the adjoint method has proven successful in shape optimization and topology optimization. In the present chapter the adjoint method is applied to the optimization of eigenvalues and eigenmodes (eigenvectors). The general case of an arbitrary cost function depending on the first n eigenvalues and eigenmodes is detailed. The direct problem does not involve a bilinear form and a linear form as usual in other ...

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