Naslov
On some projections of the homogenised coefficients in stationary diffusion equation

Autori
Antonić, Nenad ; Vrdoljak, Marko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Annual Scientific Conference GAMM 2003 / Schrefler, Bernard i drugi - Padova : GAMM, 2003, 195-195

Skup
Annual Scientific Conference GAMM 2003

Mjesto i datum
Padova, Italija, 24.03.2003. - 28.03.2003

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
stationary diffusion equation; homogenization

Sažetak
We consider the stationary diffusion equation $$ -{\rm div}(A\nabla u)=f\, , $$ where $A$ is conductivity matrix function corresponding to a mixture of two phases (possibly anisotropic). The mathematical theory of homogenisation introduces the notion of composite materials, as fine mixture limits of different phases. Given the local proportion $\theta$ of the first material, the set of all possible composite materials is denoted by ${\cal K}(\theta)$. For some applications in optimal shape design problems, optimisation over the set ${\cal K}(\theta)$ (which is in fact unknown in some situations), could be changed to optimisation over a simpler set, knowing the characterisation of the set ${\cal K}(\theta)e$ for any vector $e$. This set actually corresponds to the first column of effective conductivity matrix. We address the question of describing two columns of these matrices, or more precisely the set $\{(A e, A f):A \in{\cal K}(\theta)\}$, for two vectors $e$ and $f$. Thanks to geometric interpretation, it is possible to solve the problem, although the solution involves tedious computations. Some interesting properties of the set under consideration are proved.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA