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 harmonic wavelets. The connection coefficients are explicitly computed and characterized by a set of differential equations. Thus the popagation is considered as a superposition of wavelets at different sclae 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.
Multiscale Analysis of Wave Propagation in Composite Materials
CATTANI, Carlo
2003-01-01
Abstract
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 harmonic wavelets. The connection coefficients are explicitly computed and characterized by a set of differential equations. Thus the popagation is considered as a superposition of wavelets at different sclae 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
