Related papers: Shape and topology optimization for variational in…
In this study, we describe a procedure of topology optimization in the framework of the linear Boltzmann equation, implemented using a reference Monte-Carlo particle transport code. This procedure can design complex structures that optimize…
Adjoint-based shape optimization most often relies on Eulerian flow field formulations. However, since Lagrangian particle methods are the natural choice for solving sedimentation problems in oceanography, extensions to the Lagrangian…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
The problem of covering a region of the plane with a fixed number of minimum-radius identical balls is studied in the present work. An explicit construction of bi-Lipschitz mappings is provided to model small perturbations of the union of…
Motivated by the recent theoretical and experimental progress in implementing topological orders with photons, we analyze photonic systems with different topologies and present a scheme to probe their topological features. Specifically, we…
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
We review typical design problems encountered in the planning of observational studies and propose a unifying framework that allows us to use the same concepts and notation for different problems. In the framework, the design is defined as…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…
The note focuses on the differential geometric approach to the study of nonlinear systems that are affine in control. We first develop normal forms for nonlinear system affine in control. Based on these normal forms, we then address the…
Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However,…
This paper investigates a shape optimization problem involving the Signorini unilateral conditions in a linear elastic model, without any penalization procedure. The shape sensitivity analysis is performed using tools from convex and…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
We consider the problem of optimal location of a Dirichlet region in a $d$-dimensional domain $\Omega$ subjected to a given right-hand side $f$ in order to minimize some given functional of the configuration. While in the literature the…
Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of…
It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…
The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The extension is based on optimization on Riemannian vector space…
We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…