Generalized symmetric interpolating wavelets

Shi, Zhongchao; Kouri, Donald J.; Wei, Guannan; Hoffman, David K.

doi:10.1016/s0010-4655(99)00185-x

Cited by 27 publications

(16 citation statements)

References 48 publications

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“…For this reason, this wavelet Ž . family is called interpolating Lagrange wa®elet Shi et al, 1999 . The polynomial degree, n, is related to the wavelet order, ms nq1, which means that the interpolation only involves m neighborhood points.…”

Section: Multiresolution Representation Of Datamentioning

confidence: 99%

2‐D wavelet‐based adaptive‐grid method for the resolution of PDEs

et al. 2003

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Section: Multiresolution Representation Of Datamentioning

confidence: 99%

2‐D wavelet‐based adaptive‐grid method for the resolution of PDEs

et al. 2003

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“…The ISF originate from a multiresolution analysis associated with interpolating (spline) wavelets [27,28,29]. The ISF have a finite support whose width is determined by the order of the underlying interpolating polynomial and the resolution level (the mesh step).…”

Section: Discussionmentioning

confidence: 99%

“…In this paper we present a treatment of reactive scattering based on the wave function representation in the basis of interpolating scaling functions corresponding to interpolating (spline) wavelets [28]. Basis functions are generated from a single function, called the scaling function, by appropriate scalings and shifts of its argument.…”

Section: Introductionmentioning

confidence: 99%

An application of the interpolating scaling functions to wave packet propagation

Borisov

2004

Computer Physics Communications

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Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an equidistantly spaced grid. They have compact support of the size determined by the order of the underlying interpolating polynomial that is used to generate ISF. In this basis the potential energy matrix is diagonal and the kinetic energy matrix is sparse and, in the 1D case, has a band-diagonal structure. An important feature of the basis is that matrix elements of a Hamiltonian are exactly computed by means of simple algebraic transformations efficiently implemented numerically. Therefore the number of grid points and the order of the underlying interpolating polynomial can easily be varied allowing one to approach the accuracy of pseudospectral methods in a regular manner, similar to high order finite difference methods. The results of numerical simulation of a H+H 2 collinear collision show that the ISF provide one with an accurate and efficient representation for use in the wave packet propagation method.

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“…The basic characteristics of interpolating wavelets require that the mother scaling function satisfies the following condition [6]:…”

Section: B Deslauriers-dubuc Interpoletsmentioning

confidence: 99%

Analysis of Beams and Thin Plates Using the Wavelet-Galerkin Method

Burgos¹,

Santos²,

Silva³

2015

IJET

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Abstract-The use of wavelets has become increasingly popular in the development of numerical schemes for the solution of partial differential equations (PDEs), especially for problems with local high gradient. In this work, the Galerkin Method has been adapted for the direct solution of differential equations in a meshless formulation using Daubechies wavelets and Deslauriers-Dubuc interpolating functions (Interpolets). This approach takes advantage of wavelet properties like compact support, orthogonality and exact polynomial representation, which allow the use of a multiresolution analysis. Several examples based on typical differential equations for beams and thin plates were studied successfully.Index Terms-Wavelets, interpolets, wavelet-galerkin method, beam on elastic foundation, thin plates.

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Generalized symmetric interpolating wavelets

Cited by 27 publications

References 48 publications

2‐D wavelet‐based adaptive‐grid method for the resolution of PDEs

2‐D wavelet‐based adaptive‐grid method for the resolution of PDEs

An application of the interpolating scaling functions to wave packet propagation

Analysis of Beams and Thin Plates Using the Wavelet-Galerkin Method

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