Wavelet decompositions on nonuniform grids

2008 ◽  
pp. 23-42 ◽  
Author(s):  
Yu. K. Dem′yanovich
Keyword(s):  
Nonuniform Grids ◽  
Wavelet Decompositions

scholarly journals On the Convexity Preservation of a Quasi C3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 310 ◽  
Author(s):  
Pedro Ortiz ◽  
Juan Carlos Trillo
Keyword(s):  
Initial Data ◽  
Numerical Experiments ◽  
Approximation Order ◽  
Piecewise Polynomial ◽  
Nonuniform Grids ◽  
Uniform Grids ◽  
Reconstruction Operator ◽  
Convexity Properties ◽  
Second Degree

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.

scholarly journals Wavelet Frames for Distributions in Anisotropic Besov Spaces

2005 ◽  
Vol 12 (4) ◽  
pp. 637-658
Author(s):  
Dorothee D. Haroske ◽  
Erika Tamási
Keyword(s):  
Large Class ◽  
Besov Spaces ◽  
Studia Math ◽  
Wavelet Frames ◽  
Anisotropic Besov Spaces ◽  
Wavelet Decompositions

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].

Nested spline–wavelet decompositions

2012 ◽  
Vol 184 (3) ◽  
pp. 282-294
Author(s):  
Yu. K. Dem’yanovich ◽  
I. D. Miroshnichenko
Keyword(s):  
Spline Wavelet ◽  
Wavelet Decompositions

Construction of Wavelet Decompositions for Tomographic Images

1993 ◽  
pp. 105-122
Author(s):  
F. Peyrin ◽  
M. Zaim ◽  
R. Goutte
Keyword(s):  
Tomographic Images ◽  
Wavelet Decompositions

scholarly journals Orthogonal-based wavelet analysis of wind turbulence and correlation between turbulence and forces

2007 ◽  
Vol 29 (2) ◽  
pp. 73-82 ◽  
Author(s):  
Le Thai Hoa ◽  
Nguyen Dong Anh
Keyword(s):  
Wavelet Transforms ◽  
Discrete Wavelet ◽  
Time Frequency ◽  
Existing Problems ◽  
Physical Measurements ◽  
Force Relation ◽  
Wind Turbulence ◽  
Time Frequency Localization ◽  
Physical Simulations ◽  
Wavelet Decompositions

Recent models of wind turbulence and turbulence-force relation as well still contain uncertainties. Further studies on them are needed to gain the better knowledge to refine the existing problems from analytical computations to wind tunnel's physical simulations in the wind engineering. The continuous and discrete wavelet transforms have been applied as powerful transformation tools to represent time series into the time-frequency localization. This paper will apply the orthogonal-based wavelet decomposition to investigate the intermittency of the turbulence and to detect the turbulence-force correlation in the both temporal-spectral information using proposed cross energy of wavelet decompositions. Analyzing data have been obtained by physical measurements on model from the wind tunnel tests.

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