The level set method for structural topology optimization has been proposed and studied
recently, which is basically a steepest descent method by combining the shape sensitivity …

A family of boundary value problems is considered in domains Ω (ε)= Ω⧹ ω ε⊂ R n, n⩾ 3,
with cavities ωε depending on a small parameter ε∈(0, ε0]. An approximation U (ε, x), x∈ Ω …

The problem of imaging objects embedded in a transparent homogeneous medium is
considered. It is assumed that the wavelength of the probing radiation is finite so that …

The topological derivative method is recognized as a robust numerical technique in
engineering applications such as topology optimization, inverse problems, imaging …

A new approach to solve the inverse problem in electrical capacitance tomography is
presented. The proposed method is based on an artificial neural network to estimate three …

New optimality conditions are derived for a class of shape optimization problems. The
conditions are established on the boundary by an application of the boundary variations …

The topological derivative measures the sensitivity of a shape functional with respect to an
infinitesimal singular domain perturbation, such as the insertion of holes, inclusions or …

The level set method is used for shape optimization of the energy functional for the Signorini
problem. The boundary variations technique is used in order to derive the shape gradients …

The problem of topology optimization is considered for free boundary problems of thin
obstacle types. The formulae for the first term of asymptotics for energy functionals are …

Topological derivatives are introduced for linear problems in (Sokolowski and Zochowski,
1999) and for variational inequalities in (Sokolowski and Zochowski, 2005). The …