Related papers: Electric Field Propagation Through Singular Value …
Smooth vector fields on $\mathbb{R}^n$ can be decomposed into the sum of a gradient vector field and divergence-free (solenoidal) vector field under suitable hypotheses. This is called the Helmholtz-Hodge decomposition (HHD), which has been…
We present an algorithm for the forward propagation of intervals through the discrete Fourier transform. The algorithm yields best-possible bounds when computing the amplitude of the Fourier transform for real and complex valued sequences.…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse fields. In regard to the special characteristics of such field types we derive modified…
Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…
A simple calculation method for photon statistics of frequency-filtered fields is proposed. This method, based on eigenvalue decompositions of superoperators, allows us to study effects on the photon statistics of spectral filtering by…
We consider application of the discrete Fourier transform-spread orthogonal frequency-division multiplexing (DFT-spread OFDM) technique to high-speed fiber optic communications. The DFT-spread OFDM is a form of single-carrier technique that…
The deconvolution algorithm for measuring distribution of space charge under dc by the pressure wave propagation (PWP) method is studied in this paper. A new Fredholm integral equation of first kind, including a space charge distribution…
Determining the electric field (E-field) distribution on the Sun's photosphere is essential for quantitative studies of how energy flows from the Sun's photosphere, through the corona, and into the heliosphere. This E-field also provides…
An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the…
Inertia-gravity mode and Rossby mode dispersion properties are examined for discretisations of the linearized rotating shallow-water equations using the $P1_{DG}$-$P2$ finite element pair on arbitrary triangulations in planar geometry. A…
Helmholtz decomposition theorem for vector fields is presented usually with too strong restrictions on the fields. Based on the work of Blumenthal of 1905 it is shown that the decomposition of vector fields is not only possible for…
This paper introduces a novel method to extend the Helmholtz Decomposition to n-dimensional sufficiently smooth and fast decaying vector fields. The rotation is described by a superposition of n(n-1)/2 rotations within the coordinate…
We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant electric field…
We present a two-timescale Floquet method that allows one to apply the Kramers-Henneberger approach to short pulses and arbitrary laser frequencies. An efficient numerical procedure to propagate the Floquet Hamiltonian is provided that…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
In this work we present a variant of the fast multipole method (FMM) for efficiently evaluating standard layer potentials on geometries with complex coordinates in two and three dimensions. The complex scaled boundary integral method for…
In this note, we report the back propagation formula for complex valued singular value decompositions (SVD). This formula is an important ingredient for a complete automatic differentiation(AD) infrastructure in terms of complex numbers,…
We present a generic scheme to construct corrected trapezoidal rules with spectral accuracy for integral operators with weakly singular kernels in arbitrary dimensions. We assume that the kernel factorization of the form,…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…