Related papers: An hp-Adaptive Sampling Algorithm for Dispersion R…
An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing the bias of the spectrum. Smooth…
Optoelectronic functionalities of photodection and light harnessing rely on the band-to-band excitation of semiconductors, thus the spectral response of the devices is dictated and limited by their bandgap. A novel approach, free from this…
We introduce a new $hp$-adaptive strategy for self-adjoint elliptic boundary value problems that does not rely on using classical a posteriori error estimators. Instead, our approach is based on a generally applicable prediction strategy…
We study numerically the reflectivity of three-dimensional (3D) photonic crystals with a complete 3D photonic band gap, with the aim to interpret recent experiments. We employ the finite element method to study crystals with the cubic…
Methods of three-dimensional deconvolution (3DD) or volumetric deconvolution of optical complex-valued wavefronts diffracted by 3D samples with the 3D point spread function are presented. Particularly, the quantitative correctness of the…
We suggest an inverse dispersion method for calculating photonic band diagram for materials with arbitrary frequency-dependent dielectric functions. The method is able to calculate the complex wave vector for a given frequency by solving…
We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical…
Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving…
We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strategy which…
Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…
We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized by means of a Karhunen-Lo\`eve expansion. The approximation…
In this paper a new hp-adaptive strategy for elliptic problems based on refinement history is proposed, which chooses h-, p- or hp-refinement on individual elements according to a posteriori error estimate, as well as smoothness estimate of…
In this work, we investigate the sampling and reconstruction of spectrally $s$-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as {randomized} dynamical…
Photonic crystals (PCs) offer unique ways to control light-matter interactions. The measurement of dispersion relations is a fundamental prerequisite if we are to create novel functionalities in PC devices. Angle-resolved spectroscopic…
In this paper, we propose a method for tailoring the absorption in a photonic crystal membrane. For that purpose, we first applied Time Domain Coupled Mode Theory to such a subwavelength membrane and demonstrated that 100% resonant…
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
We obtain a convergent power series expansion for the first branch of the dispersion relation for subwavelength plasmonic crystals consisting of plasmonic rods with frequency-dependent dielectric permittivity embedded in a host medium with…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
We have developed a three-dimensional radiative transfer method designed specifically for use with parallel adaptive mesh refinement hydrodynamics codes. This new algorithm, which we call hybrid characteristics, introduces a novel form of…
High-dimensional interpolation problems appear in various applications of uncertainty quantification, stochastic optimization and machine learning. Such problems are computationally expensive and request the use of adaptive grid generation…