Related papers: Computational design of nanophotonic structures us…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
Inverse design has enabled the systematic design of ultra-compact and high-performance nanophotonic components. Yet enforcing foundry design rules during inverse design remains a major challenge, as optimized devices frequently violate…
Adjoint optimization is an effective method in the inverse design of nanophotonic devices. In order to ensure the manufacturability, one would like to have control over the minimal feature sizes. Here we propose utilizing a level-set method…
We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…
Dynamic reconfiguration is crucial for nanoplasmonic structures to achieve diversified functions and optimize performances; however, the dynamic reconfiguration of spatial arrangements remains a formidable technological challenge. Here, we…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
Nanophotonic device design aims to optimize photonic structures to meet specific requirements across various applications. Inverse design has unlocked non-intuitive, high-dimensional design spaces, enabling the discovery of high-performance…
Inverse design has greatly expanded nanophotonic devices and brought optimized performance. However, the use of inverse design for plasmonic structures has been challenging due to local field concentrations that can lead to errors in…
This paper has presented inversely determining the resonant configuration of the bilateral nanostructures for periodic metallic slits with extraordinary optical transmission performance. The topology optimization approach is utilized to…
Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not…
We present a locally adapted parametric finite element method for interface problems. For this adapted finite element method we show optimal convergence for elliptic interface problems with a discontinuous diffusion parameter. The method is…
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…
We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we…
We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse…
A computational nanophotonic design library for gradient-based optimization called SPINS is presented. Borrowing the concept of computational graphs, SPINS is a design framework that emphasizes flexibility and reproducible results. The…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…