Shape sensitivity analysis of eigenvalues revisited

Sergeï A. Nazarov (1) , Jan Sokolowski (2)

1 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
2 IECN - Institut Élie Cartan de Nancy

The paper can be considered as a complement to previous papers of the authors. An insight into applied asymptotic analysis of boundary value problems in singularly perturbed domains is presented. As a result, the asymptotic expansions of eigenvalues are obtained and discussed in terms of integral attributes of the geometrical perturbations including the virtual mass tensor, polarization tensor etc. The results are presented in such a way that can be easily employed in numerical methods for shape optimization and inverse problems.

Mots clés: singular perturbations; spectral problem; asymptotics of eigenfunctions and eigenvalues

Domaines: Equations aux dérivées partielles [math.AP]

Sergeï A. Nazarov, Jan Sokolowski. Shape sensitivity analysis of eigenvalues revisited. 2008. ⟨hal-00326017⟩