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Multiscale analysis of wave propagation in composite materials. (English) Zbl 1109.74332
Summary: 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.
MSC:
74J05Linear waves (solid mechanics)
74S30Other numerical methods in solid mechanics
65T60Wavelets (numerical methods)
35Q72Other PDE from mechanics (MSC2000)
74E30Composite and mixture properties