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Marek Netušil - Multiscale Modelling of Aortic Media; Tomáš Gergelits - Introduction to Uncertainty Quantification

Kdy: 20/12/2016 09:00 - 20/12/2016 10:30
Kde: seminárka KNM (Karlín)
Kdy: 20/12/2016 09:00
Kde: seminárka KNM (Karlín)

Marek Netušil - Multiscale Modelling of Aortic Media
Abstrakt:
Homogenization is a popular and modern approach to modelling composite materials. Arterial tissue is an example of such kind of material, consisting of several constituents forming a complex three-dimensional structure. While there has been done a lot in the field of linear PDEs, homogenization in large deformations is still an open problem.
We introduce a simplified representative volume element for the aortic media and a way to attack the problem of nonlinear homogenization will be presented. This approach is based on the linearization of the PDE during the Newton iterative method used in the finite element approximation.


Tomáš Gergelits - Introduction to Uncertainty Quantification
Abstrakt:
Uncertainty Quantification is currently rapidly growing field of quantitative characterization and reduction of uncertainties in both computational and real world applications. After a short introduction we will concentrate on the uncertainty quantification associated with an elliptic PDE with random coefficient and present the numerical method called stochastic Galerkin finite element method. Furthermore, we will outline the possible approach for a posteriori estimation of the total error in practical computations.

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