ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Seminar on Applied Mathematics

 

PROGRAM


Matematički Institut
Matematički fakultet
Fakultet organizacionih nauka
JUPIM

SEMINAR ZA PRIMENJENU I INDUSTRIJSKU MATEMATIKU

MI SANU, Knez Mihailova 35, sala 2

PLAN RADA SEMINARA ZA MART 2007. GODINE

Utorak, 06.03.2007. u 16:15, Sala 2, MI SANU:


SEDNICA PREDSEDNIšTVA JUPIM-a

Utorak, 13.03.2007. u 14:15, SALA 2, MI SANU:

Žarko Mijajlović, Matematički fakultet, Beograd, Tatjana Davidović, Matematički institut SANU, Beograd
PROGRAMIRANJE NA KLASTERU

Sadrzaj: Zahvaljujuci Ministarstvu za nauku i zastitu zivotne sredine, Matematicki institut je u procesu nabavke novog paralelnog racunara, viseprocesorskog klastera sa 16+16 dvomesnih procesora. To prakticno znaci da ce korisnicima na raspolaganju biti 64 procesne jedinice od kojih svaka ima svoju lokalnu memoriju i disk. Racunar ce raditi pod Linux operativnim sistemom i bice namenjen za paralelna izracunavanja u raznim oblastima. Ocekuje se da racunar stigne i bude instaliran u prvoj polovini godine.

U okviru ovog predavanja osvrnucemo se najpre na istorijat paralelnog procesiranja u Matematickom institutu, zatim ce biti opisane tehnicke karakteristike racunara i prateci softver. Predvidjeno je i upoznavanje sa specificnostima paralelnog procesiranja, a bice izlozena i prakticna iskustva u koriscenju slicnih klastera.

Utorak, 20.03.2006. u 14:15, sala 2 MI SANU:

Jozef Kratica, Matematički institut SANU, Beograd, Zorica Stanimirovic, Matematički fakultet u Beogradu
SOLVING THE UNCAPACITATED MULTIPLE ALLOCATION P-HUB CENTER PROBLEM BY GENETIC ALGORITHM

Abstract: In this talk we describe a genetic algorithm (GA) for the uncapacitated multiple allocation p-hub center problem (UMApHCP). Binary coding is used and genetic operators adapted to the problem are constructed and implemented in our GA. Computational results are presented for the standard hub instances from the literature. It can be seen that proposed GA approach reaches all solutions that are proved to be optimal so far. The solutions are obtained in a reasonable amount of computational time, even for problem instances of higher dimensions.

Utorak, 27.03.2007. u 14:15, sala 2, MI SANU:

Endre S¨uli, University of Oxford
DISCONTINUOUS GALERKIN FINITE ELEMENT APPROXIMATION: ANALYSIS AND APPLICATIONS

Abstract: We develop the convergence analysis of discontinuous Galerkin finite element approximations to second-order quasilinear elliptic and hyperbolic systems of partial differential equations of the form, respectively,
$$ -\sum_{\alpha=1}^{d}\partial_{x_\alpha}S_{i\alpha}(\nabla u(x))=f_i(x), \;\;\; i=1,\ldots,d, $$
and
$$ \partial_t^2u_i-\sum_{\alpha=1}^{d}\partial_{x_\alpha}S_{i\alpha}(\nabla u(t,x))=f_i(t,x), \;\;\; i=1,\ldots,d, $$
with $\partial_{x_\alpha}=\partial/\partial x_\alpha$, in a bounded spatial domain in $\mathbb{R}^d$, subject to mixed Dirichlet-Neumann boundary conditions, and assuming that $S = (S_{i\alpha})$ is uniformly monotone on $\mathbb{R}^{d\times d}$. The associated energy functional is then uniformly convex. An optimal order bound is derived on the discretization error in each case without requiring the global Lipschitz continuity of the tensor $S$. We then further relax our hypotheses: using a broken G°arding inequality we extend our optimal error bounds to the case of quasilinear hyperbolic systems where, instead of assuming that $S$ is uniformly monotone, we only require that the fourth-order tensor $A = \nabla S$ is satisfies a Legendre-Hadamard condition. The associated energy functional is then only rank-1 convex. Evolution problems of this kind arise as mathematical models in nonlinear elastic wave propagation.



RUKOVODIOCI SEMINARA

Vera Kovačević-Vujčić
Milan Dražić