Related papers: A frequency-dependent $p$-adaptive technique for s…
A $p$-adaptive discontinuous Galerkin time-domain method is developed to obtain high-order solutions to electromagnetic scattering problems. A novel feature of the proposed method is the use of divergence error to drive the $p$-adaptive…
This paper investigates the spectral structure, numerical dispersion, and observability of fully discrete approximations of the one-dimensional wave equation by $P^k$ (local) discontinuous Galerkin methods. Characterizing the coupled…
Electromagnetic waves in a system with a space and time dependent boundary experience both diffraction and Doppler-like frequency conversion. In order to analyse such situations, conventional methods call for either the eigenmodes or the…
We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral…
We develop the theoretical procedures for shifting the frequency of a single soliton and of a sequence of solitons of the nonlinear Schr\"odinger equation. The procedures are based on simple transformations of the soliton pattern in the…
In this article we develop an $hp$-adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not only mesh subdivision (h-refinement) and local basis…
We propose an adaptive finite element method to approximate the solutions to reaction-diffusion systems on time-dependent domains and surfaces. We derive a computable error estimator that provides an upper bound for the error in the…
This paper presents a gradient-based method for on-the-fly optimization for both per-frame and per-frequency window length of the short-time Fourier transform (STFT), related to previous work in which we developed a differentiable version…
Vectorial structured light with spatially varying amplitude, phase, and polarization is reshaping many areas of modern optics, including nonlinear optics, as diverse parametric processes can be used to explore interactions between such…
In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller…
Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the…
It is an interesting open problem to achieve adaptive prescribed-time control for strict-feedback systems with unknown and fast or even abrupt time-varying parameters. In this paper we present a solution with the aid of several design and…
Any frequency selective device with an ongoing drift will cause observed spectra to be variously and simultaneously scaled in proportion to their source distances. The reason is that detectors after the drifting selection will integrate…
It was recently demonstrated that time-dependent PDE problems can numerically be solved with a fully pseudospectral scheme, i.e. using spectral expansions with respect to both spatial and time directions (Hennig and Ansorg, 2009 [15]). This…
We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for…
High-frequency solutions of one or several Schr\"odinger-type equations are well known to differ very little from the plane wave solutions $\exp[\pm ik x]$. That is, the potential terms impact the envelope of a high-frequency plane wave by…
Variational perturbation expansions have recently been used to calculate directly the strong-coupling expansion coefficients of the anharmonic oscillator. The convergence is exponentially fast with superimposed oscillations, as recently…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
Consistent distillation methods have evolved into effective techniques that significantly accelerate the sampling process of diffusion models. Although existing methods have achieved remarkable results, the selection of target timesteps…
Interest in inverse dynamical, spectral and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguides and by a variety of other classical and quantum…