1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
The goal of the course is to introduce students to the fundamentals of homogenization theory and its applications in modeling heterogeneous media. Special emphasis is placed on the variational approach and the periodic homogenization of linear partial differential equations.

COURSE DESCRIPTION AND SYLLABUS:

1. Variational approach to partial differential equations. Weak formulation of elliptic boundary value problems. Convergence in Hilbert spaces and the concept of a solution.
2. Periodic homogenization. The method of two-scale convergence. Derivation of homogenized equations and effective coefficients. Mathematical justification of homogenization. Derivation of Darcy's law by homogenizing the Stokes equations in a porous medium.
3. Extensions and applications of homogenization. G-convergence and H-convergence. Homogenization of non-periodic and nonlinear structures.
4. Numerical approximation of homogenized coefficients. Applications to composite materials and fluid-structure interaction models.

1. An introduction to homogenization, Cioranescu D., Donato P., Oxford Lecture Series in Mathematics and Applications 17, Oxford, 1999.
2. Shape optimization by the homogenization method, Allaire G., Springer Verlag, New York, 2002.
3. Introduction to partial differential equations, Folland, G. B., Princeton University Press, 1995.
4. Homogenization: averaging processes in periodic media, Mathematics and its applications, vol.36, Bakhvalov N., Panasenko G., Kluwer Academic Publishers, Dordrecht, 1990.
5. The General Theory Of Homogenization, Lecture notes of the Unione Matematica Italiana, 7, L. Tartar, Springer, 2010.

Enrollment :
Attended : Lower-Dimensional Models and Homogenization 1

Examination :
Passed : Lower-Dimensional Models and Homogenization 1

Izborni modul Nižedimenzionalni modeli i homogenizacija - Regular study - Applied Mathematics

Izborni modul Nižedimenzionalni modeli i homogenizacija - Regular study - Applied Mathematics

Izborni modul Nižedimenzionalni modeli i homogenizacija - Regular study - Applied Mathematics

Izborni modul Nižedimenzionalni modeli i homogenizacija - Regular study - Applied Mathematics