Wavelet=Galerkin discretization of hyperbolic equations

Restrepo, Juan M.; Leaf, Gary K.

doi:10.2172/432435

Cited by 6 publications

(8 citation statements)

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“…This yields an equation relating a moment of ϕ ( t ) to the connection coefficients. Efficient computation schemes for evaluation of the connection coefficients have been suggested by Beylkin (1992), Restrepo and Leaf (1995), Romine and Peyton (1997), etc. The tables of connection coefficients for Daubechies' family can also be found in these references.…”

Section: Wavelet Finite Element Methodsmentioning

confidence: 99%

Wavelet basis finite element solution of structural dynamics problems

Gopikrishna

Shrikhande

2011

Engineering Computations

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PurposeThe purpose of this paper is to present a new hierarchical finite element formulation for approximation in time.Design/methodology/approachThe present approach using wavelets as basis functions provides a global control over the solution error as the equation of motion is satisfied for the entire duration in the weighted integral sense. This approach reduces the semi‐discrete system of equations in time to be solved to a single algebraic problem, in contrast to step‐by‐step time integration methods, where a sequence of algebraic problems are to be solved to compute the solution.FindingsThe proposed formulation has been validated for both inertial and wave propagation types of problems. The stability and accuracy characteristics of the proposed formulation has been examined and is found to be energy conserving.Originality/valueThe paper presents a new hierarchical finite element formulation for the solution of structural dynamics problems. This formulation uses wavelets as the analyzing basis for the desired transient solution. It is found to be very well behaved in solution of wave‐propagation problems.

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Section: Wavelet Finite Element Methodsmentioning

confidence: 99%

Wavelet basis finite element solution of structural dynamics problems

Gopikrishna

Shrikhande

2011

Engineering Computations

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“…Without loss of generality the mesh size is set to unity b 0 = 1. In our consideration of the DWT representation (44) applied to hydrodynamic turbulence, in contrast to many schemes applied for numerical simulation of the NSE [35,10], we have no a priory arguments to assume a mutual orthogonality of the basis functions ψ j k . To keep the wavelet decomposition (44) unique, the orthogonality of basic functions is not required.…”

Section: Energy Dissipation and Energy Transfermentioning

confidence: 99%

Multiscale theory of turbulence in wavelet representation

Altaisky

2006

Dokl. Phys.

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We present a multiscale description of hydrodynamic turbulence in incompressible fluid based on a continuous wavelet transform (CWT) and a stochastic hydrodynamics formalism. Defining the stirring random force by the correlation function of its wavelet components, we achieve the cancellation of loop divergences in the stochastic perturbation expansion. An extra contribution to the energy transfer from large to smaller scales is considered. It is shown that the Kolmogorov hypotheses are naturally reformulated in multiscale formalism. The multiscale perturbation theory and statistical closures based on the wavelet decomposition are constructed.Comment: LaTeX, 27 pages, 3 eps figure

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“…Although the slow decay in the space domain, their sharp localization in frequency, is a good property especially for the analysis of wave evolution problems (see e.g. [13,10,13,15,16,25,32,33]. In the search for numerical approximation of dierential problems, the main idea is to approximate the unknown so-lution by some wavelet series and then by computing the integrals (or derivatives) of the basic wavelet functions, to convert the starting dierential problem into an algebraic system for the wavelet coecients (see e.g.…”

Section: Introductionmentioning

confidence: 99%

A Review on Harmonic Wavelets and Their Fractional Extension

Cattani

2018

J. ADV. ENG. COMPUT.

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In this paper a review on harmonic wavelets and their fractional generalization, within the local fractional calculus, will be discussed. The main properties of harmonic wavelets and fractional harmonic wavelets will be given, by taking into account of their characteristic features in the Fourier domain. It will be shown that the local fractional derivatives of fractional wavelets have a very simple expression thus opening new frontiers in the solution of fractional differential problems.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

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Wavelet=Galerkin discretization of hyperbolic equations

Cited by 6 publications

References 0 publications

Wavelet basis finite element solution of structural dynamics problems

Wavelet basis finite element solution of structural dynamics problems

Multiscale theory of turbulence in wavelet representation

A Review on Harmonic Wavelets and Their Fractional Extension

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