Vladimir Fuka, Klára Jurčáková

Abstract:

Soňa Kiliánová, Daniel Ševčovič, Maria Trnovska

Abstract:

We consider a problem of dynamic stochastic portfolio optimization based on expected terminal as well as intermediate utility optimization, which leads to solving a Hamilton-Jacobi-Bellman (HJB) equation. The HJB equation is transformed to a simpler quasi-linear PDE by means of the so-called Riccati transformation. Since this problem can be sensitive to the input data, we can modify the problem from fixed input parameters to worst-case optimization over convex or discrete uncertainty sets both for asset returns and covariance matrix. We also look at how solutions change if we allow for non-constant risk aversion parameter.

Miroslav Kolář

Abstract: TBA

Jaromír Kukal

Abstract:

The infinitesimal generator is an n-dimensional radially symmetric random variable, which is useful for the analysis of diffusion processes. Based on spatial convolution and Pareto distribution, we can simulate a multidimensional alpha-stable distribution and therefore an anomalous diffusion of particles under various boundary conditions. But we can also developed adequate analytical solutions as expansions in orthonormal bases in particular cases. Resulting Green functions correspond with a method of images in the case of rectangular domains with periodic or von Neumann boundary conditions. But we obtained new analytical solutions for disc, ball and  spherical surface. The results of Monte Carlo simulations are included.

Tomáš Oberhuber, Jakub Klinkovský, Aleš Wodeki, Radek Fučík

Abstract: We will present Template Numerical Library (www.tnl-project.org) as a tool for development of numerical algorithms for modern parallel architectures especially for GPUs. We will concentrate mainly on linear algebra and BLAS like functions. We will demonstrate use of modern features of C++ like templates, lambda functions or expression templates. Such approach is more intuitive and it does not affect performance. We present performance comparison with BLAS and cuBLAS.

Petr Pauš, Jiří Chludil, Radek Richtr

Abstract:

In cooperation with the Institute of History and the Philosophical Faculty of the University of Hradec Králové, we work on the digitization of the historical city center. Our goal is to create a platform for storage and presentation of the digital data (i.e., 3D models, textures, desktop and mobile apps). The contribution deals with the problems arising during the development (such as server back-end solutions, front-end difficulties, etc.) and also with automatic model modification according to the weather, season, daytime.

Michal Sněhota, Andreas Pohlmeier, John Koestel, Tomas Princ, Martina Sobotkova, Prof. Milena Cislerova

Abstract:

Magnetic resonance imaging (MRI) of freezing and thawing process was performed on two samples of different porous materials, each one in two replicates. The soil freeze sample assembly consisted of two Plexiglas cylinders, the outer dimensions of the set-up was 6 cm in diameter and 12.5 cm high. The inner cylindrical container (3 cm in diameter, 6 cm high) was filled with the sample material. The inner cylinder was insulated by vacuum. On the top of the porous media, a glass disk (2.8 cm in diameter, 1 cm thickness) was placed to define the upper boundary of a material during freezing and thawing. One inflow tube and two outflow tubes at the top of the inner cylinder were used for circulation of cold nitrogen gas as a freezing medium to the top of the sample. The temperatures of the freezing medium were continuously recorded by the temperature sensors located outside of the MR coil. The first sample packing consisted of 72 glass beads, 0.8 cm in diameter immersed in the 1 mM/L GdDTP2-2Na+. In the second sample, the coarse sand was packed in 0.5 cm thick layers in the same sample solute. Total eight freezing-thawing cycles were performed and recorded on the samples. As a result, time-lapse series of 3D MR images were obtained. The geometric distortion of these 4D MR images due to magnetic field inhomogeneity had to be elaborated prior to the process analysis. The analyses of the freezing-thawing process on glass beads revealed interesting effects while thawing, where the thin layers on the glass beads surface exhibited faster melting in otherwise homogeneous ice. The impact of MRI heat transfers has to be evaluated. The freezing-thawing fronts recorded of sand samples were relatively uniform. Small changes in sand structure as a consequence of volumetric ice-water changes are studied. The spatiotemporal analysis of the frozen water volume is done. The data are available for a two-phase ice-water simulation models evaluation.

Martina Sobotková

Abstract:

Horizontal freezing and thawing of water were carried out in the laboratory on fully saturated packed sand sample (15 cm in diameter and 20 cm in height). The experimental setup consisted of plastic tube covered on its sides and bottom by insulation layers. The sample assembly was placed into the precisely controlled freezer chamber. The top of the sample was covered by a stainless steel plate. Initially the sample was equilibrated at +10 $^\circ$C then the temperature inside the chamber was changed to -10 $^\circ$C. The inner temperature of sand sample was monitored in three depths by thin temperature sensors (109 SS, Campbell Scientific) horizontally inserted into the sample. Temperature development in three temperature sensors was obtained during freezing and thawing cycles. The experiment aims to provide information on freezing dynamics and thermo-mechanical changes during the freezing and thawing cycles. The data were compared with simulations obtained by a numerical model. The model is based on the heat balance within the sample assembly and a modified heat equation for the porous medium temperature allowing for the phase transition below the freezing point depression. The comparisons of the thermal behavior show good agreements both in quantitative and qualitative sense and are presented.

Pavel Strachota

Abstract: This contribution gives an overview of the available High Performance Computing (HPC) systems at the department of Mathematics, FNSPE CTU in Prague. The hardware architecture and the design of the software environment are presented with focus on the two main systems: the HELIOS cluster and the HYPERION cluster. The audience will briefly learn about the installed features and how to use them. The topics of interest include remote access using console and graphical desktop, job submission and monitoring, parallel programming with MPI and OpenMP, GPGPU programming in CUDA, accelerated remote visualization by VirtualGL, and machine learning using TensorFlow and CUDA. Design of interactive and batch jobs for MATLAB, Mathematica, R, and ANSYS is also discussed. This talk is aimed primarily at employees and students o! f the department, as well as at external collaborators who can also gain access to the HPC systems. For others, it may serve as an inspiration and presentation of what today's HPC can offer.

Robert Straka

Abstract:

After years of painful work, the derivation of  an equivalent finite difference scheme (EFDS) for a macroscopic quantity which advection-diffusion evolution is solved by the D1Q3 Lattice Boltzmann Method with cascaded (or central moment) collision operator will be presented. This EFDS is further analyzed (for the case of single relaxation time approach) to check how much we can control error terms and how we can increase the accuracy of the solutions.

Daniel Ševčovič, Jose Cruz

Abstract:

Using the theory of abstract semilinear parabolic equations we proved existence and uniqueness of solutions of a class of partial integro-differential equations in the Bessel potential space. Our aim is to generalize known existence results for a wide class of Levy measures including those having strong singular kernel. We also prove existence and uniqueness of solutions to the penalized PIDE representing approximation of the linear complementarity problem.

Kyoko Tomoeda, Kaname Matsue

Abstract: There are experimental results of suspension by Zhou et al. (2005): A suspension of polydisperse glass beads (diameter 250-425 mm) flows on an acrylic plate with an inclination angle $\alpha$ ($0^{\circ}<\alpha <90^{\circ}$), then the surface of the suspension is characterized by three patterns. (a) At low inclination angles and the particle volume fraction, the particles settle to the substrate and the clear silicone oil flows over the particle bed. (b) At high inclination angles and the particle volume fraction, the particles accumulate at near the contact line forming a particle-rich ridge. (c) At intermediate inclination angles and the particle volume fraction, the particles remain well-mixed in the fluid. Zhou et al. (2005) and Cook et al. (2008) derived a system of conservation laws (lubrication model) to analyze the formation mechanism of a particle-rich ridge in pattern (b). Moreover Zhou et al. show by numerical simulations that the ridge formation is due to the double shock wave (1-shock wave and 2-shock wave). In this talk we deal with the Riemann problem of lubrication model. We show that the weak solution does not have $1$-shock wave under certain conditions. Also we introduce a double shock wave with a profile different from the shock wave shown by Zhou et al. (2005). Our results suggest that the formation of a particle-rich ridge may be due to factors other than shock waves.

Quang Van Tran

Abstract:

Voigt distribution is a convolution of a Cauchy distribution and a Gaussian distribution which has been so far widely used in technical disciplines. The inclusion of the Cauchy distribution into the mixture makes it a possible alternative for modeling heavy tail properties commonly present in financial data. Despite of the existence of the close form of probability density function (PDF),  it does not provide any practical usage for the parameter maximum likelihood estimation (MLE) due to its numerical complexity. Therefore, we propose the use of Fast Fourier Transform (FFT) to make the parameter estimation via MLE technique numerically more convenient. We investigate the accuracy of this method compared to the one used the PDF. This approach is then verified on the returns of cryptocurrencies which tend to have more heavy tails than those of ordinary heavy tail distributions.

Jan Valášek

Abstract: The talk will focus on the numerical simulation of the flow induced sound generated by the vibration of vocal folds. The two-dimensional fluid-structure interaction (FSI) problem is modelled with the aid of linear elastic problem coupled to the incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. The propagation of sound sources is described either by the Lighthill acoustic analogy or by the Perturbed Convective Wave Equation method. It means, that the sound sources are calculated from the FSI results according to chosen aeroacoustic analogy and then they are used as sources on the right hand of the wave-like equation. All partial differential equations, describing the elastic, fluid and acoustic subproblems, are solved by the finite element method. However, only the numerical realization of aeroacoustic problem is shown. For the purpose of computation cost reduction the interpolation between fluid and acoustic computational mesh is performed. Finally, the numerical results of frequency spectra for phonation of vowel [u:] are presented.