Related papers: Single freeform surface design for prescribed inpu…
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…
Designing a freeform surface to reflect or refract light to achieve a target distribution is a challenging inverse problem. In this paper, we propose an end-to-end optimization strategy for an optical surface mesh. Our formulation leverages…
The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the…
An accurate method for designing transmissive metasurfaces is presented that provides perfect transmission while transforming the amplitude and phase of the wavefront. The designed metasurfaces consist of three spatially-varying, electric…
In this paper, we propose an efficient joint precoding design method to maximize the weighted sum-rate in wideband intelligent reflecting surface (IRS)-assisted cell-free networks by jointly optimizing the active beamforming of base…
This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
A novel space-discretized Finite Differences-based model reduction, introduced in (Liu,Guo,2020) is extended to the partial differential equations (PDE) model of a multi-layer Mead-Marcus-type sandwich beam with clamped-free boundary…
This paper introduces a novel partial differential equation (PDE) framework for single-image dehazing. We embed the atmospheric scattering model into a PDE featuring edge-preserving diffusion and a nonlocal operator to maintain both local…
The efficient design of continuous freeform surfaces, which transform a given source into an arbitrary target intensity, remains a challenging problem. A popular approach are ray-mapping methods, where first a ray mapping between the…
In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface corrugation in 1+1…
Starting from the general modal solutions for a homogeneous layer of arbitrary material and crystalline symmetry, a matrix formalism is developed to establish the semi analytical expressions of the surface impedance matrices (SIM) for a…
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams,…
Designing freeform surfaces to control light based on real-world illumination patterns is challenging, as existing caustic lens designs often assume oversimplified point or parallel light sources. We propose representing surface light…
For more than 150 years, scientists have advanced aberration theory to describe, analyse, and eliminate imperfections that disturb the imaging quality of optical components and systems. Simultaneously, they have developed optical design…
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method allows a surface to be given implicitly as a zero level of a level set function. A surface equation…
Metasurfaces, with their ability to control electromagnetic waves, hold immense potential in optical device design, especially for applications requiring precise control over dispersion. This work introduces an approach to dispersion…
In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of…
In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the…
In this paper, we propose a computational framework for the optimal design of broadband absorbing materials composed of plasmonic nanoparticle arrays. This design problem poses several key challenges: (1) the complex multi-particle…