Journal ArticleDOI
Solving PDEs using wavelets
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This article is published in Computers in Physics.The article was published on 1998-09-01. It has received 39 citations till now.read more
Citations
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Applications of B-splines in atomic and molecular physics
TL;DR: In this article, the main properties of B-spline basis sets and why they are useful to solve different problems in atomic and molecular physics are discussed and an extensive reference list of theoretical works that have made use of them up to 2000 is provided.
Journal ArticleDOI
Solving differential equations with radial basis functions: multilevel methods and smoothing
TL;DR: Some of the meshless radial basis function methods used for the numerical solution of partial differential equations are reviewed and the important role of smoothing within a multilevel framework is demonstrated.
Journal ArticleDOI
Multiresolution analysis of electronic structure: semicardinal and wavelet bases
TL;DR: In this paper, a review of recent developments in multiresolution analysis that make it a powerful tool for the systematic treatment of the multiple length scales inherent in the electroniic structure of matter is presented.
Journal ArticleDOI
Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets
TL;DR: A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed and the prowess and computational efficiency are demonstrated for the solution of a number of two-dimensional test problems.
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Stochastic coherent adaptive large eddy simulation method
TL;DR: In this article, a stochastic coherent adaptive large eddy simulation (SCALES) method is proposed, which takes advantage of both the coherent vortex simulation (CVS) and large-scale simulation (LES) methods.
References
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The lifting scheme: A construction of second generation wavelets
TL;DR: The lifting scheme is presented, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function, and can be adapted to intervals, domains, surfaces, weights, and irregular samples.
Journal ArticleDOI
The lifting scheme: a construction of second generation wavelets
TL;DR: The lifting wavelet as discussed by the authors is a simple construction of second generation wavelets that can be adapted to intervals, domains, surfaces, weights, and irregular samples, and it leads to a faster, in-place calculation of the wavelet transform.
Journal ArticleDOI
Fast wavelet transforms and numerical algorithms I
TL;DR: The algorithms presented here are based on the recently developed theory of wavelets and are applicable to all Calderon-Zygmund and pseudo-differential operators, and indicate that many previously intractable problems become manageable with the techniques presented here.
Book
Adapted wavelet analysis from theory to software
TL;DR: This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data.
Journal Article
Solving hyperbolic pdes using interpolating wavelets
TL;DR: In this paper, a method based on an interpolating wavelet transform using polynomial interpolation on dyadic grids is presented for adaptively solving hyperbolic PDEs.