Related papers: Phase-Field Methods for Spectral Shape and Topolog…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…
The NEPv approach has been increasingly used lately for optimization on the Stiefel manifold arising from machine learning. General speaking, the approach first turns the first order optimality condition, also known as the KKT condition,…
We prove the existence of an optimal partition for the multiphase shape optimization problem which consists in minimizing the sum of the first Robin Laplacian eigenvalue of $k$ mutually disjoint {\it open} sets which have a $\mathcal H ^…
We investigate multi-physical topology optimization for microfluidic mixers employing the phase-field model. The optimization problem is formulated using a modified Ginzburg-Landau free energy functional. To eliminate fluid blockage in…
This article is an expanded version of the plenary talk given by Evans Harrell at QMath98, a meeting in Prague, June 1998. We consider Laplace operators and Schr\"odinger operators with potentials containing curvature on certain regions of…
We study three types of fourth-order Steklov eigenvalue problems. For the first two of them, we derive the asymptotic expansion of their spectra on Euclidean annular domains $\mathbb{B}^n_1\setminus \overline{\mathbb{B}^n_\epsilon}$ as…
This article discusses an optimal control problem for a phase field model of two immiscible incompressible fluid flow, incorporating surface tension effects. The optimal control problem is defined with a $L^2$-cost functional and subject to…
Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem…
We investigate the Dirichlet boundary control of the Laplace equation, considering the control in $H^{1/2}(\partial \Omega)$, which is the natural space for Dirichlet data when the state belongs to $H^1(\Omega)$. The cost of the control is…
In this paper we prove the existence of an optimal domain $\Omega_{opt}$ for the shape optimization problem $$\max\Big\{\lambda_q(\Omega)\ :\ \Omega\subset D,\ \lambda_p(\Omega)=1\Big\},$$ where $q<p$ and $D$ is a prescribed bounded subset…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
The optimal control of two-level systems by time-dependent laser fields is studied using a variational theory. We obtain, for the first time, general analytical expressions for the optimal pulse shapes leading to global maximization or…
We consider a finite volume scheme with two-point flux approximation (TPFA) to approximate a Laplace problem when the solution exhibits no more regularity than belonging to $H^1_0(\Omega)$. We establish in this case some error bounds for…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…
This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral…
A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal…
This paper demonstrates the impact of a phase field method on shape registration to align shapes of possibly different topology. It yields new insights into the building of discrepancy measures between shapes regardless of topology, which…
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…