National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Fourier-Galerkin Method for Stochastic Homogenization of Elliptic Partial Differential Equations
Vidličková, Eva ; Zeman, Jan (advisor) ; Chleboun, Jan (referee)
This thesis covers the basics in the stochastic homogenization of elliptic partial differential equations, from underlying theory up to numerical ap- proaches. In particular, we introduce and analyze a combination of the Fourier-Galerkin method in the spatial domain with a collocation method in the stochastic domain. The material coefficients are assumed to depend on a finite number of random variables. We present a comparison of the Monte Carlo method with the full tensor grid and sparse grid collocation method for two applications. The first one is the checkerboard problem with continuous random variables, the other considers the material coefficients to be described in terms of an autocorrelation function.
Discrete differential geometry and its applications
Vidličková, Eva ; Šír, Zbyněk (advisor) ; Hron, Jaroslav (referee)
In this thesis we present an elementary introduction to the Discrete differen- tial geometry. We will work with both discrete curves and discrete surfaces. Firstly some basic definitions and theorems from classic Differential geometry will be mentioned and then we will translate these concepts to the discrete setting, so that some important global structures are still preserved. At the end we implement mean curvature flow defined on discrete surfaces and run it on two meshes, that show its area-minimizing feature. This can be used for denoising the discrete surfaces. 1

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