Numerical differentiation for two-dimensional functions by a Fourier extension method

2019 ◽  
Vol 28 (1) ◽  
pp. 126-143
Author(s):  
Zehong Meng ◽  
Zhenyu Zhao ◽  
Duan Mei ◽  
Yongxiong Zhou
Keyword(s):  
Numerical Differentiation ◽  
Two Dimensional ◽  
Extension Method ◽  
Fourier Extension

scholarly journals Boundary operation of 2D non-separable oversampled lapped transforms

2016 ◽  
Vol 5 ◽  
Author(s):  
Kosuke Furuya ◽  
Shintaro Hara ◽  
Kenta Seino ◽  
Shogo Muramatsu
Keyword(s):  
Discrete Cosine Transform ◽  
Local Control ◽  
Lattice Structure ◽  
Experimental Results ◽  
Perfect Reconstruction ◽  
Operation Technique ◽  
Two Dimensional ◽  
Hard Thresholding ◽  
Extension Method ◽  
Iterative Hard Thresholding

This paper proposes a boundary operation technique of two-dimensional (2D) non-separable oversampled lapped transforms (NSOLT). The proposed technique is based on a lattice structure consisting of the 2D separable block discrete cosine transform and non-separable redundant support-extension processes. The atoms are allowed to be anisotropic with the oversampled, symmetric, real-valued, compact-supported, and overlapped property. First, the blockwise implementation is developed so that the atoms can be locally controlled. The local control of atoms is shown to maintain perfect reconstruction. This property leads an atom termination (AT) technique as a boundary operation. The technique overcomes the drawback of NSOLT that the popular symmetric extension method is invalid. Through some experimental results with iterative hard thresholding, the significance of AT is verified.

A quadratic formulation for two-dimensional elastoplastic analysis using the boundary integral equation method

1986 ◽  
Vol 21 (3) ◽  
pp. 159-175 ◽  
Author(s):  
K H Lee ◽  
R T Fenner
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Numerical Differentiation ◽  
Approximate Solutions ◽  
Boundary Integral ◽  
Test Problems ◽  
Two Dimensional ◽  
Element Analysis ◽  
Perfectly Plastic

An isoparametric quadratic formulation of the boundary integral equation (BIE) method for two-dimensional elasto-plastic analysis is presented. The initial strain approach is adopted but, unlike in finite element analysis, it is capable of accurately treating perfectly-plastic and weakly strain-hardening materials. Two methods of evaluating internal stress and strain rates, namely, via the elementwise numerical differentiation of the displacement rates, and the pointwise use of integral identities, are included in the solution algorithm, and their relative efficiency is discussed. The use of correction factors is suggested in some cases to ensure that the von Mises flow rules are implemented in a consistent manner. Results to test problems are given and compared with exact or existing approximate solutions.

scholarly journals Numerical differentiation for two-dimensional scattered data on arbitrary domain base on Hermite extension with an implicit iteration process

2022 ◽  
Vol 7 (4) ◽  
pp. 5991-6015
Author(s):  
Benxue Gong ◽  
◽  
Zhenyu Zhao ◽  
Tiao Bian ◽  
Yingmei Wang ◽  
...  
Keyword(s):  
Iteration Method ◽  
Input Data ◽  
Solution Process ◽  
Iteration Process ◽  
Numerical Differentiation ◽  
Scattered Data ◽  
Two Dimensional ◽  
Arbitrary Domain ◽  
Approximation Process ◽  
Implicit Iteration

<abstract><p>In this paper, we develop a method for numerical differentiation of two-dimensional scattered input data on arbitrary domain. A Hermite extension approach is used to realize the approximation and a modified implicit iteration method is proposed to stabilize the approximation process. For functions with various smooth conditions, the numerical solution process of the method is uniform. The error estimates are obtained and numerical results show that the new method is effective. The advantage of the method is that it can solve the problem in any domain.</p></abstract>

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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