Related papers: Computational design of nanophotonic structures us…
The classical adjoint-based topology optimization (TO) method, based on the use of a random continuous dielectric function as an adjoint variable distribution, is known to be one of the most efficient optimization methods that enable the…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
Image retargeting, which resizes images to one with a prescribed aspect ratio by determining an optimal warping map, has gained substantial interest in imaging science. Despite significant advances, existing methods often fail to ensure…
The interaction of electromagnetic waves with metallic nanostructures generates resonant oscillations of the conduction-band electrons at the metal surface. These resonances can lead to large enhancements of the incident field and to the…
Hybrid nanophotonics based on metal-dielectric nanostructures unifies the advantages of plasmonics and all-dielectric nanophotonics providing strong localization of light, magnetic optical response and specifically designed scattering…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
Recent advancements in computational inverse design have begun to reshape the landscape of structures and techniques available to nanophotonics. Here, we outline a cross section of key developments at the intersection of these two fields:…
We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
For all applications of plasmonics to technology it is required to tailor the resonance to the optical system in question. This chapter gives an understanding of the design considerations for nanoparticles needed to tune the resonance.…
A new domain decomposition method for Maxwell's equations in conductive media is presented. Using this method reconstruction algorithms are developed for determination of dielectric permittivity function using time-dependent scattered data…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
We show that an optimal finite element mesh refinement algorithm for a prototypical elliptic PDE can be learned by a recurrent neural network with a fixed number of trainable parameters independent of the desired accuracy and the input…
A method is created to automatically increase the threshold projection parameter in three-field density-based topology optimization to achieve a near binary design. The parameter increase each iteration is based on an exponential growth…
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
We propose a new algorithm for the design of topologically optimized lightweight structures, under a minimum compliance requirement. The new process enhances a standard level set formulation in terms of computational efficiency, thanks to…
This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…