Open AccessMULTISCALE ANALYSIS OF WAVE PROPAGATION IN COMPOSITE MATERIALS
Author(s) -
Carlo Cattani
Publication year - 2003
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2003.9637229
Subject(s) - wavelet , superposition principle , connection (principal bundle) , mathematics , mathematical analysis , harmonic , scale (ratio) , differential equation , physics , computer science , geometry , quantum mechanics , artificial intelligence
The multiscale solution of the Klein‐Gordon equations in the linear theory of (two‐phase) materials with microstructure is defined by using a family of wavelets based on the harmonic wavelets. The connection coefficients are explicitly computed and characterized by a set of differential equations. Thus the propagation is considered as a superposition of wavelets at different scale of approximation, depending both on the physical parameters and on the connection coefficients of each scale. The coarse level concerns with the basic harmonic trend while the small details, arising at more refined levels, describe small oscillations around the harmonic zero‐scale approximation.