Composites with a periodic structure: Mathematical analysis and numerical treatment (Q1072358)

The authors treat the solution of a partial differential equation describing the behaviour of composites that have a periodic structure. The equation has highly oscillatory periodic coefficients. The technique of homogenization which is appropriate for specific applications and which can be used as the basis for an adaptive model is discussed. The theory is developed for the most general n-dimensional case, but the detailed deduction being worked-out in this paper is one-dimensional. The deduction is derived by using the Fourier transform and the expansion in corresponding powers. The procedure has some advantages from the numerical point of view, especially at the use of finite difference or finite element methods. The procedure is illustrated by numerical examples.