scholarly journals Discrete Fractional COSHAD Transform and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Hongqing Zhu ◽  
Zhiguo Gui ◽  
Yu Zhu ◽  
Zhihua Chen
Keyword(s):  
High Accuracy ◽  
Kernel Functions ◽  
Piecewise Smooth ◽  
Reconstruction Method ◽  
Accurate Approximation ◽  
Finite Set ◽  
Orthogonal Transforms ◽  
Stability And Accuracy ◽  
Polynomial Reconstruction ◽  
Inverse Polynomial Reconstruction Method

In recent years, there has been a renewed interest in finding methods to construct orthogonal transforms. This interest is driven by the large number of applications of the orthogonal transforms in image analysis and compression, especially for colour images. Inspired by this motivation, this paper first introduces a new orthogonal transform known as a discrete fractional COSHAD (FrCOSHAD) using the Kronecker product of eigenvectors and the eigenvalues of the COSHAD kernel functions. Next, this study discusses the properties of the FrCOSHAD kernel function, such as angle additivity. Using the algebra of quaternions, the study presents quaternion COSHAD/FrCOSHAD transforms to represent colour images in a holistic manner. This paper also develops an inverse polynomial reconstruction method (IPRM) in the discrete COSHAD/FrCOSHAD domains. This method can effectively recover a piecewise smooth signal from the finite set of its COSHAD/FrCOSHAD coefficients, with high accuracy. The convergence theorem has proved that the partial sum of COSHAD provides a spectrally accurate approximation to the underlying piecewise smooth signal. The experimental results verify the numerical stability and accuracy of the proposed methods.

Open-boundary spectral and flux-balance Vlasov simulation

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
Alexander J. Klimas ◽  
Adolfo F. Viñas
Keyword(s):  
Periodic Boundary ◽  
Gibbs Phenomenon ◽  
Periodic Boundary Conditions ◽  
Simulation System ◽  
Open Boundary ◽  
Reconstruction Method ◽  
One Dimensional ◽  
Flux Balance ◽  
Polynomial Reconstruction ◽  
Inverse Polynomial Reconstruction Method

Simulations of one-dimensional Vlasov–Maxwell solutions with non-periodic boundary conditions are discussed. Results obtained using a recently developed filtered flux-balance simulation system are compared to those obtained using a filtered, Fourier–Fourier transformed system. Excellent agreement is confirmed except for the appearance of the Gibbs phenomenon on the discontinuous simulated solutions of the transformed system. Recovery of the flux-balance results from the Fourier transformed results using the inverse polynomial reconstruction method is demonstrated.

scholarly journals LNG Tank Sloshing Simulation of Multidegree Motions Based on Modified 3D MPS Method

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Chunhui Wang ◽  
Chunyu Guo ◽  
Fenglei Han
Keyword(s):  
Free Surface ◽  
Weighted Average ◽  
Kernel Functions ◽  
Computational Stability ◽  
Mps Method ◽  
Fluid Sloshing ◽  
Particle Hydrodynamics ◽  
Moving Particle ◽  
Lng Tank ◽  
Stability And Accuracy

Modified 3D Moving Particle Semi-Implicit (MPS) method is used to complete the numerical simulation of the fluid sloshing in LNG tank under multidegree excitation motion, which is compared with the results of experiments and 2D calculations obtained by other scholars to verify the reliability. The cubic spline kernel functions used in Smoothed Particle Hydrodynamics (SPH) method are adopted to reduce the deviation caused by consecutive two times weighted average calculations; the boundary conditions and the determination of free surface particles are modified to improve the computational stability and accuracy of 3D calculation. The tank is under forced multidegree excitation motion to simulate the real conditions of LNG ships, the pressures and the free surfaces at different times are given to verify the accuracy of 3D simulation, and the free surface and the splashed particles can be simulated more exactly.

scholarly journals Reconstruction of Piecewise Smooth Multivariate Functions from Fourier Data

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 88
Author(s):  
David Levin
Keyword(s):  
Fourier Series ◽  
Fourier Coefficients ◽  
Order Approximation ◽  
High Accuracy ◽  
Rectangular Domain ◽  
High Order ◽  
Piecewise Smooth ◽  
Multidimensional Case ◽  
Order Spline ◽  
The Given

In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a method for deriving high order approximation to f using a Padé-like method. Namely, we do this by fitting some Fourier coefficients of the approximant to the given Fourier coefficients of f. Given the Fourier series coefficients of a function on a rectangular domain in Rd, assuming the function is piecewise smooth, we approximate the function by piecewise high order spline functions. First, the singularity structure of the function is identified. For example in the 2D case, we find high accuracy approximation to the curves separating between smooth segments of f. Secondly, simultaneously we find the approximations of all the different segments of f. We start by developing and demonstrating a high accuracy algorithm for the 1D case, and we use this algorithm to step up to the multidimensional case.

The Circle-End-Face Centering Device Based on Image Processing

2014 ◽  
Vol 926-930 ◽  
pp. 3447-3450
Author(s):  
Yong Bo Li ◽  
Yun Zhao Xu ◽  
Jia He
Keyword(s):  
Image Processing ◽  
Digital Image Processing ◽  
High Stability ◽  
Least Square Method ◽  
High Accuracy ◽  
Concentric Circle ◽  
Least Square ◽  
Programmable Logic ◽  
Edge Extraction ◽  
Stability And Accuracy

The circle-end-face centering device which is in the base of image processing accomplishes the center of the cylinders end face by digital image processing. Through edge extraction and doing the matching in the calculation of the least square method, the coordinate of the central of the circle can be calculated. At last, the drill will be moved to the central of the circle and do the punching by the actuator. This equipment is in the high accuracy and speed compared with the traditional way and the concentric circle laser of marking with the center. Meanwhile, the actuator consists of the programmable logic controller, touch panel and servo drivers which is in the high stability and accuracy. Certainly it is easy to be controlled by the method.

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