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We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…

Optimization and Control · Mathematics 2024-06-04 Jochen Schmid , Philipp Seufert , Michael Bortz

The merger between integrated photonics and quantum optics promises new opportunities within photonic quantum technology with the very significant progress on excellent photon-emitter interfaces and advanced optical circuits. A key missing…

We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…

Numerical Analysis · Mathematics 2010-05-27 Thomas Witkowski , Axel Voigt

The complexity of applications addressed with photonic integrated circuits is steadily rising and poses increasingly challenging demands on individual component functionality, performance and footprint. Inverse design methods have recently…

Optics · Physics 2023-05-10 Marco Butz , Adrian S. Abazi , Rene Ross , Benjamin Risse , Carsten Schuck

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…

Numerical Analysis · Mathematics 2017-11-20 Gregor Gantner , Daniel Haberlik , Dirk Praetorius

The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale space-frame structures, as the individual design of…

Computational Engineering, Finance, and Science · Computer Science 2023-12-05 Oguz Oztoprak , Alexander Paolini , Pierluigi D'Acunto , Ernst Rank , Stefan Kollmannsberger

We present an efficient adaptive refinement procedure that preserves analysis-suitability of the T-mesh, this is, the linear independence of the T-spline blending functions. We prove analysis-suitability of the overlays and boundedness of…

Numerical Analysis · Mathematics 2016-05-04 Philipp Morgenstern , Daniel Peterseim

Optical metasurfaces are planar arrangements of subwavelength meta-atoms that implement a wide range of transformations on incident light. The design of efficient metasurfaces requires that the responses of and interactions among meta-atoms…

Optics · Physics 2021-01-19 Mahdad Mansouree , Andrew McClung , Sarath Samudrala , Amir Arbabi

Nanophotonic structures have versatile applications including solar cells, anti-reflective coatings, electromagnetic interference shielding, optical filters, and light emitting diodes. To design and understand these nanophotonic structures,…

Machine Learning · Computer Science 2023-10-31 Jungtaek Kim , Mingxuan Li , Oliver Hinder , Paul W. Leu

Design of nanoscale structures with desired nanophotonic properties are key tasks for nanooptics and nanophotonics. Here, the correlative relationship between local nanoparticle geometries and their plasmonic responses is established using…

Materials Science · Physics 2021-03-29 Kevin M. Roccapriore , Maxim Ziatdinov , Shin Hum Cho , Jordan A. Hachtel , Sergei V. Kalinin

The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces…

Numerical Analysis · Mathematics 2023-04-05 Michael Feischl , Hubert Hackl

Self-assembled nano and micro-structures, particularly those capable of responsive erasure and regeneration, have garnered significant interest for their applications in smart photonics and electronics. However, current techniques for…

Removing geometrical details from a complex domain is a classical operation in computer aided design. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the…

Numerical Analysis · Mathematics 2024-07-18 Annalisa Buffa , Ondine Chanon , Rafael Vázquez

As an increasingly powerful technique in integrated photonics, inverse design uses optimization algorithms to automatically create compact, high-performance photonic structures, often yielding non-intuitive layouts far more compact than…

Optics · Physics 2026-03-03 Junho Park , Taehan Kim , Mohammad Ali , Di Liang

Nanophotonics has been an active research field over the past two decades, triggered by the rising interests in exploring new physics and technologies with light at the nanoscale. As the demands of performance and integration level keep…

Optics · Physics 2019-01-28 Kan Yao , Rohit Unni , Yuebing Zheng

We present a method of creation of photonic structures whose optical spectrum of the reflection coefficient has an arbitrary shape and has predetermined features. We develop an algorithm for the construction of a photonic crystal structure,…

Optics · Physics 2023-05-16 S. E. Svyakhovskiy , N. I. Pyshkov

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…

Numerical Analysis · Mathematics 2022-02-25 Qichen Hong , Hehu Xie , Fei Xu

To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…

Applied Physics · Physics 2026-04-07 Hongxin Wang , Jie Liu , Guilin Wen

In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…

Numerical Analysis · Mathematics 2022-03-16 Chiu Ling Chan , Felix Scholz , Thomas Takacs

Plasmonic resonances in metallic nanoparticles are exploited to create efficient optical filtering functions. A Finite Element Method is used to model metallic nanoparticles gratings. The accuracy of this method is shown by comparing…

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