Related papers: Gabor-Type Holography Solved Analytically for Comp…
In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin…
This article presents novel numerical algorithms based on pseudodifferential operators for fast, direct, solution of the Helmholtz equation in 1D, 2D, and 3D inhomogeneous unbounded media. The proposed approach relies on an Operator Fourier…
We propose a practical tool for evaluating and comparing the accuracy of FDMs for the Helmholtz equation. The tool based on Fourier analysis makes it easy to find wavenumber explicit order of convergence, and can be used for rigorous proof.…
Off-axis X-ray holography is a lensless imaging technique that allows unambiguous retrieval of an object's exit-wave function with high fidelity. It has been used with great success to study nanoscale phenomena and spatio-temporal dynamics…
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the high-frequency regime. Among the available numerical…
Fourier ptychographic microscopy (FPM) is a recently developed imaging modality that uses angularly varying illumination to extend a system performance beyond the limit defined by its optical elements. The FPM technique applies a novel…
This manuscript studies the numerical solution of the time-fractional Burgers-Huxley equation in a reproducing kernel Hilbert space. The analytical solution of the equation is obtained in terms of a convergent series with easily computable…
We study the forward self-similar solutions to the $2$D hypodissipative Navier-Stokes equation with fractional diffusion $(-\Delta)^\alpha$ for $\frac{1}{2}<\alpha<1$. We first show that for arbitrarily large $(1-2\alpha)$-homogeneous…
In this paper we analyze and implement a second-order-in-time numerical scheme for the three-dimensional phase field crystal (PFC) equation. The numerical scheme was proposed in [46], with the unique solvability and unconditional energy…
The hyperanalytic signal is the straight forward generalization of the classical analytic signal. It is defined by a complexification of two canonical complex signals, which can be considered as an inverse operation of the Cayley-Dickson…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…
The challenge of imaging low-density objects in an electron microscope without causing beam damage is significant in modern TEM. This is especially true for life science imaging, where the sample, rather than the instrument, still…
The far field refractor problem with a discrete target is solved with a numerical scheme that uses and simplify ideas from Caffarelli, Kochengin and Oliker. A numerical implementation is carried out and examples are shown.
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…
Holography relies on the interference between a known reference and a signal of interest to reconstruct both the amplitude and phase of that signal. Commonly performed with photons and electrons, it finds numerous applications in imaging,…