Related papers: A multimaterial topology optimisation approach to …
We consider the shape-topological control of a singularly perturbed variational inequality. The geometry-dependent state problem that we address in this paper concerns a heterogeneous medium with a micro-object (defect) and a macro-object…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We present the Dirichlet-Neumann (DN) and Neumann-Neumann (NN) methods applied to the optimal control problems arising from elliptic partial differential equations (PDEs) under the $H^{-1}$ regularization. We use the Lagrange multiplier…
We consider a new fictitious domain approach of higher order accuracy. To implement Dirichlet conditions we apply the classical Nitsche method combined with a facet-based stabilization (ghost penalty). Both techniques are combined with a…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
Machine learning (ML) has been increasingly used for topology optimization (TO). However, most existing ML-based approaches focus on simplified benchmark problems due to their high computational cost, spectral bias, and difficulty in…
We present a variational optimization approach for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and conductivity functions in time-dependent Maxwell's system using limited…
We consider the Cauchy problem for non-autonomous forms inducing elliptic operators in divergence form with Dirichlet, Neumann, or mixed boundary conditions on an open subset $\Omega$ $\subseteq$ R n. We obtain maximal regularity in L 2…
The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in Reifenberg-flat domain is considered. The lower order terms supposed to satisfy controlled growth conditions. It is obtained…
This paper is focused on the Monotonicity Principle (MP) for nonlinear materials with piecewise growth exponent. This results are relevant because enables the use of a fast imaging method based on MP, to the wide class of problems with two…
This paper deals with optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which…
In this paper, we investigate a class of multiscale McKean-Vlasov stochastic systems, where the entire system depends on the distributions of both fast and slow components. First of all, by applying the Poisson equation method, we prove…
This paper proposes a new indirect solution method for solving state-constrained optimal control problems by revisiting the well-established optimal control theory and addressing the long-standing issue of discontinuous control and costate…
A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
This paper deals with generalized differentiability and second-order necessary optimality conditions for a box-constrained optimal control problem governed by an exponential semilinear elliptic equation with discrete measures as sources,…
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the…
This paper deals with a nonsmooth version of the connection between the maximum principle and dynamic programming principle, for the stochastic recursive control problem when the control domain is convex. By employing the notions of sub-…