Related papers: Fourier series (based) multiscale method for compu…
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…
Controlling waves by actively changing the material parameters of a medium enables the development of new acoustic and electrical devices. Modulating the material breaks classical properties like reciprocity and the conservation of energy,…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
This paper introduces an Algebraic MultiScale method for simulation of flow in heterogeneous porous media with embedded discrete Fractures (F-AMS). First, multiscale coarse grids are independently constructed for both porous matrix and…
Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion…
We propose a general physics-based deep learning architecture for wave-based imaging problems. A key difficulty in imaging problems with a varying background wave speed is that the medium "bends" the waves differently depending on their…
Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…
With the rapid advancement of intelligent driving and remote sensing, oriented object detection has gained widespread attention. However, achieving high-precision performance is fundamentally constrained by the Angle Boundary Discontinuity…
This study presents a generalized theory for the diffusion of Brownian particles in shear flows. By solving the Langevin equations using stochastic instead of classical calculus, we propose a new mathematical formulation that resolves the…
This note presents a rigorous introduction to a selection of distributions along with their Fourier transforms, which are commonly encountered in signal processing and, in particular, magnetic resonance imaging (MRI). In contrast to many…
In this work, we numerically study the higher-ordered/extended Boussinesq system describing the propagation of water-waves over flat topography. A reformulation of the same order of precision that avoids the calculation of high order…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
We describe a generalized formalism, addressing the fundamental problem of reflection and transmission of complex optical waves at a plane dielectric interface. Our formalism involves the application of generalized operator matrices to the…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…