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The paper examines local approximation errors of finite difference schemes in electromagnetic analysis. Despite a long history of the subject, several accuracy-related issues have been overlooked and/or remain controversial. For example,…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
This article addresses a fundamental concern regarding the incompressible approximation of fluid motions, one of the most widely used approximations in fluid mechanics. Common belief is that its accuracy is $O(\epsilon)$ where $\epsilon$…
Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing…
The optical aberrations of a system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersection…
We performed a series of three-dimensional numerical simulations of supersonic homogeneous Euler turbulence with adaptive mesh refinement (AMR) and effective grid resolution up to 1024^3 zones. Our experiments describe non-magnetized driven…
We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $d=2$ and $3$. This requires to approximate first the scattering field, for some incident…
Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms…
The spectral element method constructed by the $Q^k$ ($k\geq 2$) continuous finite element method with $(k+1)$-point Gauss-Lobatto quadrature on rectangular meshes is a popular high order scheme for solving wave equations in various…
The secular equation for surface acoustic waves propagating on an orthotropic incompressible half-space is derived in a direct manner, using the method of first integrals.
Adaptive gradient methods like AdaGrad are widely used in optimizing neural networks. Yet, existing convergence guarantees for adaptive gradient methods require either convexity or smoothness, and, in the smooth setting, only guarantee…
The structure of discrete resonances in water-wave turbulence is studied. It is shown that the number of exact 4-wave resonances is huge (hundreds million) even in comparatively small spectral domain when both scale and angle energy…
This paper analyzes the well-known L1 scheme for fractional wave equations with nonsmooth data. A new stability estimate is obtained, and the temporal accuracy $ \mathcal O(\tau^{3-\alpha}) $ is derived for the nonsmooth initial data. In…
Many recent loss functions in deep metric learning are expressed with logarithmic and exponential forms, and they involve margin and scale as essential hyper-parameters. Since each data class has an intrinsic characteristic, several…
Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal and random lattices is studied. The adsorption process is modeled by using random sequential adsorption (RSA) algorithm. Objects are adsorbed on one-,…
Staggered grid finite difference scheme is widely used for the first order elastic wave equation, which constitutes the basis for least-squares reverse time migration and full waveform inversion. It is of great importance to improve the…
We consider an initial-boundary value problem for the $n$-dimensional wave equation with the variable sound speed, $n\geq 1$. We construct three-level implicit in time and compact in space (three-point in each space direction) 4th order…
The demand for high-resolution point clouds has increased throughout the last years. However, capturing high-resolution point clouds is expensive and thus, frequently replaced by upsampling of low-resolution data. Most state-of-the-art…
This paper investigates the low-complex linear minimum mean squared error (LMMSE) channel estimation in an extra-large scale MIMO system with the spherical wave model (SWM). We model the extra-large scale MIMO channels using the SWM in the…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…