Related papers: Digital terrain modeling with the Chebyshev polyno…
Flood extent mapping plays a crucial role in disaster management and national water forecasting. In recent years, high-resolution optical imagery becomes increasingly available with the deployment of numerous small satellites and drones.…
Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of…
We introduce a numerical method for computing spectral densities, and apply it to the evaluation of the local density of states (LDOS) of sparse Hamiltonians derived from tight-binding models. The approach, which we call the high-order…
A spectral element method (SEM) is developed to solve polarized radiative transfer in multidimensional participating medium. The angular discretization is based on the discrete-ordinates approach, and the spatial discretization is conducted…
Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and the natural sciences. In particular, SDEs and Kolmogorov…
Deep neural networks have recently been recognized as one of the powerful learning techniques in computer vision and medical image analysis. Trained deep neural networks need to be generalizable to new data that was not seen before. In…
We develop a spectrally accurate numerical method to compute solutions of a model partial differential equation used in plasma physics to describe diffusion in velocity space due to Fokker-Planck collisions. The solution is represented as a…
Two combined numerical methods for solving semilinear differential-algebraic equations (DAEs) are obtained and their convergence is proved. The comparative analysis of these methods is carried out and conclusions about the effectiveness of…
High resolution Digital Elevation Models(DEMs) are an important requirement for many applications like modelling water flow, landslides, avalanches etc. Yet publicly available DEMs have low resolution for most parts of the world. Despite…
Digital Elevation Model (DEM), while providing a bare earth look, is heavily used in many applications including construction modeling, visualization, and GIS. Their registration techniques have not been explored much. Methods like…
Analytic expressions for the Fourier transforms of the Chebyshev and Legendre polynomials are derived, and the latter is used to find a new representation for the half-order Bessel functions. The numerical implementation of the so-called…
This paper presents a parallel algorithm for calculating the eight-directional (D8) up-slope contributing area in digital elevation models (DEMs). In contrast with previous algorithms, which have potentially unbounded inter-node…
Density-equalizing map (DEM) serves as a powerful technique for creating shape deformations with the area changes reflecting an underlying density function. In recent decades, DEM has found widespread applications in fields such as data…
The purpose of this study is to utilize the Chebyshev spectral method neural network(CSNN) model to solve differential equations. This approach employs a single-layer neural network wherein Chebyshev spectral methods are used to construct…
The shortage of high-resolution urban digital elevation model (DEM) datasets has been a challenge for modelling urban flood and managing its risk. A solution is to develop effective approaches to reconstruct high-resolution DEMs from their…
This work is unique in the use of discrete wavelets that were built from or derived from Chebyshev polynomials of the second and third kind, filter the Discrete Second Chebyshev Wavelets Transform (DSCWT), and derive two effective filters.…
We propose an implementation of the Smooth Selection Embedding Method (SSEM) in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain / collocation method which solves boundary value problems in complex domains by…
Having good knowledge of terrain information is essential for improving the performance of various downstream tasks on complex terrains, especially for the locomotion and navigation of legged robots. We present a novel framework for neural…
In this paper, an online multiscale model reduction method is presented for stochastic partial differential equations (SPDEs) with multiplicative noise, where the diffusion coefficient is spatially multiscale and the noise perturbation…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…