Seminar on
Applied Mathematics
PROGRAM
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