Related papers: Shape optimizations for body-assisted light-matter…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
A quantitative and predictive theory of quantum light-matter interactions in ultra thin materials involves several fundamental challenges. Any realistic model must simultaneously account for the ultra-confined plasmonic modes and their…
Nanophotonic freeform design has the potential to push the performance of optical components to new limits, but there remains a challenge to effectively perform optimization while reliably enforcing design and manufacturing constraints. We…
Since the seminal work of Idelsohn, O\~nate and Del-Pin (2004), the Particle Finite Element Method (PFEM) has relied on a Delaunay triangulation and the Alpha--Shape (AS) algorithm in the remeshing process. This approach guarantees a good…
Optimal transport methods have recently established state of the art accuracy and efficiency for holographic laser beam shaping. However, use of such methods is hindered by severe $\mathcal{O}(N^2)$ memory and $\mathcal{O}(N^2)$ time…
Atomic nuclei are self-organized, many-body quantum systems bound by strong nuclear forces within femtometer-scale space. These complex systems manifest a variety of shapes, traditionally explored using non-invasive spectroscopic techniques…
Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…
As humans, we regularly associate shape of an object with its built material. In the context of geometric modeling, however, this interrelation between form and material is rarely explored. In this work, we propose a novel data-driven…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the…
The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is formulated by introducing a tracking-type cost functional…
We build a new mathematical model of shape optimization for maximizing ionic concentration governed by the multi-physical coupling steady-state Poisson-Nernst-Planck system. Shape sensitivity analysis is performed to obtain the Eulerian…
Using adaptive algorithms, the design of nano-scale dielectric structures for photonic applications is explored. Widths of dielectric layers in a linear array are adjusted to match target responses of optical transmission as a function of…
Knowing a biomolecule's structure is inherently linked to and a prerequisite for any detailed understanding of its function. Significant effort has gone into developing technologies for structural characterization. These technologies do not…
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 work discusses the problem of optimal excitation of a three-level atom of ladder-configuration by light in the two-photon state and coherent light carrying an average of two photons. The applied atom-light interaction model is based on…
This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a…
Metasurfaces mold the flow of classical light waves by engineering sub-wavelength patterns from dielectric or metallic thin films. We describe and analyze a method in which quantum operator-valued reflectivity can be used to control both…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
We introduce an algorithm aimed to reduce the dimensions of Hilbert space. It is used here in order to study the behaviour of low energy states of strongly interacting quantum many-body systems at first order transitions and avoided…