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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:

74J05 Linear waves in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65T60 Numerical methods for wavelets
35Q72 Other PDE from mechanics (MSC2000)
74E30 Composite and mixture properties
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