scholarly journals A FAST INVERSE POLYNOMIAL RECONSTRUCTION METHOD BASED ON CONFORMAL FOURIER TRANSFORMATION

2012 ◽  
Vol 122 ◽  
pp. 119-136 ◽  
Author(s):  
Zhe Liu ◽  
Qing Huo Liu ◽  
Chun-Hui Zhu ◽  
Jianyu Yang
Keyword(s):  
Fourier Transformation ◽  
Reconstruction Method ◽  
Polynomial Reconstruction ◽  
Inverse Polynomial Reconstruction Method

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 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.

scholarly journals Alternating Polynomial Reconstruction Method for Hyperbolic Conservation Laws

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1885
Author(s):  
Shijian Lin ◽  
Qi Luo ◽  
Hongze Leng ◽  
Junqiang Song
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Euler Method ◽  
High Order ◽  
High Order Accuracy ◽  
Reconstruction Method ◽  
Hyperbolic Conservation ◽  
High Order Schemes ◽  
Numerical Solver ◽  
Polynomial Reconstruction

We propose a new multi-moment numerical solver for hyperbolic conservation laws by using the alternating polynomial reconstruction approach. Unlike existing multi-moment schemes, our approach updates model variables by implementing two polynomial reconstructions alternately. First, Hermite interpolation reconstructs the solution within the cell by matching the point-based variables containing both physical values and their spatial derivatives. Then the reconstructed solution is updated by the Euler method. Second, we solve a constrained least-squares problem to correct the updated solution to preserve the conservation laws. Our method enjoys the advantages of a compact numerical stencil and high-order accuracy. Fourier analysis also indicates that our method allows a larger CFL number compared with many other high-order schemes. By adding a proper amount of artificial viscosity, shock waves and other discontinuities can also be computed accurately and sharply without solving an approximated Riemann problem.

Mapping of Phase Distribution in Electron Holography with a Stage-Scanning System

2013 ◽  
Vol 750 ◽  
pp. 152-155 ◽  
Author(s):  
Dan Lei ◽  
Kazutaka Mitsuishi ◽  
Ken Harada ◽  
Masayuki Shimojo ◽  
Dong Ying Ju ◽  
...  
Keyword(s):  
Fourier Transformation ◽  
Phase Distribution ◽  
Experimental Results ◽  
Scanning System ◽  
Electron Holography ◽  
Electron Optics ◽  
Reconstruction Method ◽  
Complex Reconstruction ◽  
The One ◽  
Stage Scanning

A new method is proposed for mapping of phase distribution in electron holography. A stage-scanning system was used for moving the specimen to obtain a series of holograms with different specimen positions in a fixed electron-optics configuration. By applying a digital aperture which selects an area on holograms with different specimen positions, an interferogram of the specimen can be obtained directly without a complex reconstruction method such as the one using Fourier transformation. Experimental results for a Co particle demonstrated the practicability of this method.

Three-dimensional reconstruction of the 40S ribosomal subunit from rabbit reticulocytes

1987 ◽  
Vol 45 ◽  
pp. 936-937
Author(s):  
Neng-Yu Zhang ◽  
Terence Wagenknecht ◽  
Michael Radermacher ◽  
Tom Obrig ◽  
Joachim Frank
Keyword(s):  
Three Dimensional ◽  
Ribosomal Subunit ◽  
Uranyl Acetate ◽  
Reconstruction Method ◽  
Single Exposure ◽  
Electron Dose ◽  
Ribosomal Subunits ◽  
40S Ribosomal Subunit ◽  
Dimensional Reconstruction ◽  
Rabbit Reticulocytes

We have reconstructed the 40S ribosomal subunit at a resolution of 4 nm using the single-exposure pseudo-conical reconstruction method of Radermacher et al.Small (40S) ribosomal subunits were Isolated from rabbit reticulocytes, applied to grids and negatively stained (0.5% uranyl acetate) in a manner that “sandwiches” the specimen between two layers of carbon. Regions of the grid exhibiting uniform and thick staining were identified and photographed twice (magnification 49,000X). The first micrograph was always taken with the specimen tilted by 50° and the second was of the Identical area untilted (Fig. 1). For each of the micrographs the specimen was subjected to an electron dose of 2000-3000 el/nm2.Three hundred thirty particles appearing in the L view (defined in [4]) were selected from both tilted- and untilted-specimen micrographs. The untilted particles were aligned and their rotational alignment produced the azimuthal angles of the tilted particles in the conical tilt series.

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