相关论文: Analysis of two-phase shape optimization problems …
In this paper, which corresponds to an updated version of the author's Habilitation lecture in Mathematics, we do an overview of several topics in elliptic problems. We review some old and new results regarding the Lane-Emden equation, both…
We present an initial implementation of a probabilistic PDE-constrained shape optimization algorithm. Our method is based on a novel probabilistic representation of the shape derivative, which is evaluated using Monte Carlo sampling; and…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
The paper is concerned with the minimal drag problem in shape optimization of merchant ships exposed to turbulent two-phase flows. Attention is directed to the solution of Reynolds Averaged Navier-Stokes equations using a Finite Volume…
In this paper we present a framework for automated shape differentiation in the finite element software NGSolve. Our approach combines the mathematical Lagrangian approach for differentiating PDE constrained shape functions with the…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
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…
In this thesis, we explore several related topics broadly regarding the symmetry and geometric properties of nonlocal partial differential equations (PDE). This thesis is split into three parts. In the first part, we study two…
Second derivative pinching estimates are proved for a class of elliptic and parabolic equations, including motion of hypersurfaces by curvature functions such as quotients of elementary symmetric functions of curvature. The estimates imply…
Infinitesimal bendings for classes of two-dimensional surfaces in $\mathbb{R}^3$ are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers-Vekua type equations and systems of differential…
This paper implements topology optimization on two-dimensional manifolds. In this paper, the material interpolation is implemented on a material parameter in the partial differential equation used to describe a physical field, when this…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…
A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the…
In this work, we investigate a novel approach for the simulation of two-dimensional, brittle, quasi-static fracture problems based on a shape optimization approach. In contrast to the commonly-used phase-field approach, this proposed…
We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, Chinese Academy of Sciences, Beijing, 2012] of the author…
The book contains the results obtained by the author in 1975-1982 and presents new constructive methods of the topological analysis of integrable systems having non-linear integrals in involution. The phase topology of the classical…
We study a class of degenerate parabolic equations with boundary point degeneracy in dimensions N>=2 and investigate the associated boundary observability problem by means of shape design. While one-dimensional degenerate models have been…
We investigate an overdetermined Torsion problem, with a non-constant positively homogeneous boundary constraint on the gradient. We interpret this problem as the Euler equation of a shape optimization problems, we prove existence and…
Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems…
A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…