About a differential method of factorization in complex macro-, micro- and nano-structures

Abstract

The differential method of factorization is developed for an aggregate of different adjoining domains called block structures. Such structures are natural generalization for layered structures and they are the most widely spread ones in the environment. They can be regarded as separate parts of complex structures of natural or man-caused origin. They can have different scales — from nano- and micro-scales in materials science and electronics, to macro-scales used in construction when assessing seismic stability of structures, in geology, and seismology. When solving boundary-value problems with the application of differential factorization method for the above aggregates of domains, we have to face certain peculiarities, which differ from traditional approaches. For example, boundary conditions in the differential factorization method cannot be satisfied in the traditional form simply by introducing limiting values of solutions and their derivatives on the domain boundary into the given boundary conditions. In this work we show possible ways of overcoming the difficulties connected with the application of the differential method of factorization in block structures, an example is given.