Related papers: Frequency extraction for BEM-matrices arising from…
While fast multipole methods (FMMs) are in widespread use for the rapid evaluation of potential fields governed by the Laplace, Helmholtz, Maxwell or Stokes equations, their coupling to high-order quadratures for evaluating layer potentials…
We develop a parametric high-resolution method for the estimation of the frequency nodes of linear combinations of complex exponentials with exponential damping. We use Kronecker's theorem to formulate the associated nonlinear least squares…
In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched…
Multichannel frequency estimation with incomplete data and miscellaneous noises arises in array signal processing, modal analysis, wireless communications, and so on. In this paper, we consider maximum-likelihood(-like) optimization methods…
The boundary element method (BEM) enables the efficient electromagnetic modelling of lossy conductors with a surface-based discretization. Existing BEM techniques for conductor modelling require either expensive dual basis functions or the…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…
The combination of the effects of Doppler frequency shifts (due to mobility) and phase noise (due to the imperfections of oscillators operating at a high carrier frequency) poses serious challenges to Orthogonal Frequency Division…
Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…
In this paper, we develop fast multipole methods for 3D Helmholtz kernel in layered media. Two algorithms based on different forms of Taylor expansion of layered media Green's function are developed. A key component of the first algorithm…
Para-Hermitian polynomial matrices obtained by matrix spectral factorization lead to functions useful in control theory systems, basis functions in numerical methods or multiscaling functions used in signal processing. We introduce a fast…
Modeling large dependent datasets in modern time series analysis is a crucial research area. One effective approach to handle such datasets is to transform the observations into density functions and apply statistical methods for further…
Combinig the harmonic balance method (HBM) and a continuation method is a well-known technique to follow the periodic solutions of dynamical systems when a control parameter is varied. However, since deriving the algebraic system containing…
In $d$ dimensions, approximating an arbitrary function oscillating with frequency $\lesssim k$ requires $\sim k^d$ degrees of freedom. A numerical method for solving the Helmholtz equation (with wavenumber $k$) suffers from the pollution…
We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion models have excelled at capturing data distributions, they still suffer from…
The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…
A frequency beam splitter (FBS) with the split ratio of 0.5 or 1 can be used as the frequency-mode Hadamard gate (FHG) for frequency-encoded photonic qubits or as the quantum frequency converter (QFC) for frequency up or down conversion of…