Przybyłowicz, Paweł
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Item type:Article, Access status: Open Access , Thermal-mechanical finite element simulation of flat bar rolling coupled with a stochastic model of microstructure evolution(Wydawnictwa AGH, 2022) Szeliga, Danuta; Czyżewska, Natalia; Kusiak, Jan; Kuziak, Roman; Morkisz, Paweł M.; Oprocha, Piotr; Pietrzyk, Maciej; Piwowarczyk, Michał; Poloczek, Łukasz; Przybyłowicz, Paweł; Rauch, Łukasz; Wolańska, NataliaIt is generally recognized that the kinetics of phase transformations during the cooling of steel products depends to a large extent on the state of the austenite after rolling. Austenite deformation (when recrystallization is not complete) and grain size have a strong influence on the nucleation and growth of low-temperature phases. Thus, the general objective of the present work was the formulation of a numerical model which simulates thermal, mechanical and microstructural phenomena during multipass hot rolling of flat bars. The simulation of flat bar rolling accounting for the evolution of a heterogeneous microstructure was the objective of the work. A conventional finite-element program was used to calculate the distribution of strains, stresses, and temperatures in the flat bar during rolling and during interpass times. The FE program was coupled with the stochastic model describing austenite microstructure evolution. In this model, the random character of the recrystallization was accounted for. Simulations supplied information about the distributions of the dislocation density and the grain size at various locations through the thickness of the bars.Item type:Doctoral Dissertation, Access status: Open Access , Złożoność obliczeniowa całkowania stochastycznego w sensie Itô(Data obrony: 2011-11-30) Przybyłowicz, Paweł
Wydział Matematyki StosowanejIn the thesis we study the computational complexity of the stochastic Itô integration. We first investigate the optimal approximation of Itô integrals when linear information about the Wiener process B, consisting of certain Riemann integrals of its trajectories, is available. We show upper and lower bounds on the complexity which, in some cases, turn out to be optimal. Obtained results indicates that algorithms which use integral information are more efficient than algorithms which use only discrete values of the Wiener process B. In the second part of the thesis we deal with the numerical approximation of stochastic Itô integrals of regular and singular deterministic functions $f:[0,T]->R$. In the regular case we show that the nonadaptive Ito-Taylor algorithm is optimal. In the singular case we show that any nonadaptive algorithm cannot efficiently handle such a problem, even in the case of a single singularity. Hence, in the case of a single singularity, we construct an adaptive Itô-Taylor algorithm which has the optimal error known from the regular case. Next, we consider the case of multiple singularities and we show that even adaptive algorithms cannot preserve the optimal rate of convergence known from the regular case. We show that also in the asymptotic setting nonadaptive algorithms cannot preserve the optimal error known from the regular case.