Homogenization Theory and its Applications in Periodic and Perforated Domains

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Hosseinkhan, Alireza | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 47084 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi Firouzabad, Morteza
Abstract:
Through this thesis the Homogenization Theory for composite materials is studied assuming that the distribution of heterogeneities is periodic. In this theory two scales characterize the problem: microscopic and macroscopic scale. The first method that is used to solve the problem is the classical Asymptotic Expansion method where an error estimate is presented for the solution. The second method which was introduced by Luc Tartar for the first time is Oscillating Test Functions method. In the next chapter after introducing the concept of two-scale convergence, the Two-Scale Convergence method has been introduced. At last the unfolding
periodic method, which is based on the concept of unfolding operator, will be described for perforated domains
Keywords:
Homogenization ; Periodic Domains ; Perforated Domains ; Tartar's Method ; Two Scale Convergence Method