A cost function involving the eigenvalues of an elastic structure is optimized using a phase-
field approach, which allows for topology changes and multiple materials. We show …

This paper introduces a novel topology optimization framework by combining the phase-field
method and optimality criteria approach. This novel approach allows for the automatical …

This paper deals with the numerical optimization of the first three eigenvalues of the Laplace-
Beltrami operator of domains in the Euclidean sphere of R 3 with Neumann boundary …

We consider an optimization problem for the eigenvalues of a multi-material elastic structure
that was previously introduced by Garcke et al.(Adv. Nonlinear Anal. 11: 159–197, 2022) …

We investigate a phase-field version of the Faber–Krahn theorem based on a phase-field
optimization problem introduced by Garcke et al. in their 2023 paper formulated for the …

We derive a model for the optimization of the bending and torsional rigidities of
nonhomogeneous elastic rods. This is achieved by studying a sharp interface shape …

In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization
problem in a phase-field setting by a conforming finite element method. An adaptive …

This dissertation considers the modelling of geometrical shapes and structures regarding
three different mathematical applications. The first two parts focus on perimeter penalized …

In this paper, we study adaptive approximations of an elliptic eigenvalue optimization
problem in a phasefield setting by a conforming finite element method. An adaptive …

This manuscript is the outcome of my long research project, conducted as part of the
conclusion of my Ensimag engineering training and the preparation for my MSIAM double …