相关论文: Hadamard integrators for wave equations in time an…
We present a time-frequency framework adapted to dispersive phase functions via a subdyadic geometry in phase space. On top of this geometry we construct stable Gabor frames with quantitative control of overlap, almost orthogonality, and…
A group of high order Gautschi-type exponential wave integrators (EWIs) Fourier pseudospectral method are proposed and analyzed for solving the nonlinear Klein-Gordon equation (KGE) in the nonrelativistic limit regime, where a parameter…
This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…
We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain,…
Solving the wave equation is essential to seismic imaging and inversion. The numerical solution of the Helmholtz equation, fundamental to this process, often encounters significant computational and memory challenges. We propose an…
We explore the unconventional wave scattering properties of non-Hermitian systems in which amplification or damping are induced by time-periodic modulation. These non- Hermitian time-Floquet systems are capable of non-reciprocal operations…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in…
The objective of this paper is to derive analytical solutions of fractional order Laplace, Poisson and Helmholtz equations in two variables derived from the corresponding standard equations in two dimensions by replacing the integer order…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…
We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in…
As an appropriate analog of the Euclidean short-time Fourier transform, we study a windowed version of the Helgason-Fourier transform on the complex unit ball and translate the theory of modulation/coorbit spaces. As a result, atomic…
In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The method employs structured grids of spectral elements in combination to a fictitious domain approach to represent…
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…
Sparse time-frequency (T-F) representations have been an important research topic for more than several decades. Among them, optimization-based methods (in particular, extensions of basis pursuit) allow us to design the representations…
An accurate treatment of electronic spectra in large systems with a technique such as time dependent density functional theory (TDDFT) is computationally challenging. Due to the Nyquist sampling theorem, direct real time simulations must be…
We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order $m$…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
In this article, we have studied the convergence behavior of the Dirichlet-Neumann and Neumann- Neumann waveform relaxation algorithms for time-fractional sub-diffusion and diffusion-wave equations in 1D & 2D for regular domains, where the…