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Shape sensitivity analysis of eigenvalues revisited

100%

Nazarov S. A. , Sokolowski J.

Control and Cybernetics

2008

tom Vol. 37, no 4

999-1012

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.

Topological derivatives for semilinear elliptic equations

70%

Iguernane M. , Nazarov S. A. , Roche J. R. , Sokolowski J. , Szulc K.

tom Vol. 19, no 2

191-205

The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L [...] norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.