Generalized multiple scale reproducing kernel particle methods
type: Item
instance of: scholarly article
title: Generalized multiple scale reproducing kernel particle methods
zbMATH Open document ID: 0896.76069
DOI: 10.1016/S0045-7825(96)01081-X
author: J. Ning
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1998-10-11T00:00:00Z
review text: An approach to unify reproducing kernel methods and an extension to include time and spatial shifting are proposed. The groundwork is set by revisiting the Fourier analysis of discrete systems. The multiresolution concept, its significance in devising the reproducing kernel methods and its discrete counterpart, reproducing kernel particle methods, are explained. An edge detection technique based on multiresolution analysis is developed. This wavelet approach, together with particle methods, gives rise to a straightforward \(h\)-adaptivity algorithm. By using this framework, a Hermite reproducing kernel method is also proposed, and its relation to wavelet methods is presented. It is also shown that the new approach generalizes existing kernel methods, and it can easily be degenerated into other widely used methods. Finally, multiple-scale methods based on frequency and wave number shifting techniques are presented, together with a stability analysis for Newmark time-integration schemes for the low frequency equation.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 1087125
zbMATH Keywords: Fourier analysis of discrete systems
zbMATH Keywords: edge detection technique
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: wavelet approach
zbMATH Keywords: particle methods
zbMATH Keywords: wave number shifting techniques
zbMATH Keywords: stability analysis
zbMATH Keywords: Newmark time-integration schemes
zbMATH Keywords: low frequency equation
MaRDI profile type: Publication
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full work available at URL: s0045-7825(96)01081-x
OpenAlex ID: W1991553895
description: scientific article; zbMATH DE number 1087125