Arkadiusz Czader

Abstract:

The project focuses on optimizing the shape of a 2D air chamber using velocity field obtained from LBM simulations. The goal is to develop a code that finds the optimal chamber shape regarding equal velocity distribution. Due to the large computational domain, finding the optimal shape for most optimization functions is time-consuming. To address this, several methods for identifying potentially profitable changes were implemented. The code allows simple change of optimized functions and optimization constraints.

Petr Filip

Abstract:

This contribution will discuss theoretical and computational behavior of curves moving by curvature in the normal direction in plane and space. The motion will be solved numerically using the parametric approach and finite difference method. The natural and asymptotically uniform redistribution of points along the curve will be compared in various examples of solution in the plane and in generalized form in space.

František Gašpar, Jaromír Kukal

Abstract:

A novel constrained convolution schema (CCS) is introduced as a robust alternative to Monte Carlo simulations for diffusive processes over fractal sets. Unlike stochastic methods, CCS is a deterministic numerical algorithm tailored for grid-based set models, including random sets, ensuring reproducibility and computational efficiency. CCS is designed to yield the complete distribution of diffusion processes within a specified timeframe, offering comprehensive insights into the dynamics of diffusion phenomena. This contribution not only outlines the theoretical framework of CCS but also provides illustrative examples demonstrating its applicability across a diverse range of fractal sets. Through its deterministic nature and versatility, CCS emerges as a valuable tool for exploring diffusion phenomena in complex systems with enhanced precision and computational tractability.

Tomáš Halada, Tomáš Oberhuber, Jakub Klinkovský

Abstract:

Particle methods for solution of partial differential equations are an effective tool for a number of problems where the mesh based methods are difficult to employ. This includes for example free surface flows or problem with moving boundaries. We present a parallel GPU implementation of structures for particle computations, a general particle solver and implementation of SPH method and mesh-free finite difference methods for fluid dynamics problems. The tools are implemented as a submodule of the TNL library: TNL-SPH. Implementation of particle methods brings a number of challenges related to a neighbor search procedures or domain decomposition. We present our solution to these problems  along with a tool for easy implementation of numerical schemes of particle methods or particle methods in general. 

Dominik Horák

Abstract:

The work deals with the mathematical modeling of non-isothermal turbulent flow of incompressible Newtonian fluids. The aim of the work is to implement and test heat transfer and investigate usage of coupled LBM-LBM scheme for solving Navier-Stokes equations and advection-diffusion equation. In the theoretical part, the mathematical model of non-isothermal flow of Newtonian fluids is presented together with the description of turbulent flow. In the second part, the reader is introduced to the lattice Boltzmann method (LBM), and the last part discusses the results of the application of LBM with implemented heat transfer to~the mathematical model. The implementation of heat transfer was successful, and the method produces satisfactory results.

Lenka Horvátová

Abstract:

This research project deals with mathematical modeling of problems arising during myocardial perfusion using the contrast agent. The description of the transport and transfer of the contrast agent from vascular bed to extravascular medium is divided into two tasks. First, the velocity in the vascular system is computed based on pressures. Then, a contrast agent with a given concentration is injected into the vascular system. The transfer of the contrast agent from the vascular system to the extravascular system is modeled using convolution with the Dirac delta function. In the second step, the concentration in both media is calculated. For this mathematical model, we consider an incompressible Newtonian fluid that is not subject to any external forces. The extravascular environment is considered to be porous and rigid. The main goal of this project is to solve the problem of transport and transfer of contrast agent in the vascular system of healthy and unhealthy myocardium using the finite volume method, and in the extravascular medium using the finite difference method.

Kryštof Jakůbek

Abstract:

We introduce the Allen-Cahn equation, describing phase transition in undercooled media, as a method for solving the Stefan problem. Finite difference discretization in two dimensions is performed and the resulting problem is formulated as an explicit and semi-implicit numerical scheme. Subsequently, we investigate errors caused by the operator splitting technique and propose two potential corrections. Finally, we discuss the CUDA implementation and explain several optimized parallel algorithms employed.

Ondřej Marek

Abstract:

This contribution discusses the application of lattice Boltzmann method (LBM) on compressible fluid flow in two dimensions. First, a brief introduction to fluid dynamics and weakly compressible LBM is given. Subsequently, possible extensions of LBM to compressible fluid flow are covered with focus on entropic LBM models for which an analytical single-speed model D2Q9 is derived and Newton method for model D2Q49 is formulated. Finally, both models are verified on the problem of Poiseuille flow in 2D and demostrated on fluid flow in a channel with an obstacle.

Maneesh Narayanan, Michal benes

Abstract:

This paper presents a computational investigation into the dynamics of space curves, utilizing parametric method and flowing finite volume techniques. The parametric approach is employed to solve the equations governing the curves,\begin{equation}\label{Narayanan:1}\partial_t {X}  &=& \alpha {T} + \beta {N} + \gamma {B} + {F},~~~~~~~~{X}(0)&=&{X}_0\end{equation} with a focus on discretization. The evolution equation is then solved using the method of lines. To mitigate instability issues inherent in the computation process, both natural redistribution and uniform redistribution techniques are implemented. Furthermore, the study introduces a special force term to examine its effect on curve dynamics. By integrating this term into the computational framework, we explore its impact on the behaviour and shape evolution of space curves. Through these computational methodologies and techniques, this research contributes to a deeper understanding of space curve dynamics, offering insights into their behaviour under various conditions and the influence of external forces.

Matěj Pokorný

Abstract:

Texture-based analysis of two- and three-dimensional images is a field of immense importance, which keeps rising every year, especially because of the need for fast and reliable analysis of biomedical imaging data. The Fourier transform-based approaches are useful, when we want to compute rotationally invariant image features. We introduce a fast method of producing local translationally-rotationally-mirroring (TRM) invariant local image features through the frequency domain convolution of orthonormal Zernike polynomials with two- or three-dimensional images. In a direct continuation, we also define the global statistical characteristics that will act as textural image features and input data for various image classifiers.

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Neda Bagheri Renani

Abstract:

This study examines the pricing of options in marketing, focusing on two assets with risk and one asset without risk. The Black-Scholes model and European options applicable at the due date are utilized for this investigation. To determine the appropriate price for the European option, it is necessary to solve an equation with partial derivatives involving two spatial variables. Finite differences are employed for these equations. For one-dimensional equations, finite differences typically result in a three-diagonal set that can be solved with calculation costs O(n), where n is the number of discrete points. However, in this case, as the problems are two-dimensional, the Alternating Direction Implicit (ADI) and Alternating Direction Explicit (ADE) methods are used to reduce calculation costs. These methods offer advantages at the discrete points level and demonstrate acceptable stability. Despite their equal ease of calculation, evaluating these methods in option pricing reveals that the ADI method is sensitive to discontinuity or non-derivability, which is a common property of income functions.

Aaron Schick

Abstract:

This work examines the use of diffusive PDEs for image processing, specifically the Allen-Cahn equation and its modification on rectangular domains. Namely, a segmentation model is presented, and we show its application to test cardiac MRI data. Additionally, the Sobolev gradient method is introduced in the context of the calculus of variations, and its properties are demonstrated in the numerical results.

Richard Schlösinger

Abstract:

This work focuses on finding the conditions resulting in a celestial body, previously ejected perpendicularly to the galactic accretion disc from a solar system, being recaptured into an orbit, tilted 60 degrees to the accretion disc. Using simulations based on the laws of classical physics, if such recapture is proven possible, the work may provide one more way of explaining excessive inclinations of planetary systems to the galactic plane and the origin of planets orbiting greatly inclined to their system’s plane of reference, like, for example, WASP 79b with its near-polar orbit around WASP 79.

Adam Štampach, Pavel Strachota

Abstract:

This work focuses on the segmentation of microscopic images of cross-sections of zirconium fuel cladding of a nuclear reactor, on which high temperature experiments were conducted. These experiments result into changes in the internal structure of the zirconium. A thresholding method was used to segment the metal and oxide classes. A neural network was used to segment the alpha and beta classes. The training data set was created by a combination of specialized algorithms and manual interventions. To ensure the correct functioning of the model, appropriate data preprocessing algorithms were implemented, consisting of geometric transformation, brightness normalization and image subdivision into blocks. Three neural network models were trained and compared on the created data set. After obtaining the resulting feature map, the quantitative characteristics of the examined sample were calculated, such as the minimum, maximum and average height of the oxide layer. The result of segmentation are documents containing these characteristics and a visual map of the segmented areas of the image.

Jan Thiele

Abstract:

Magnetic Resonance Imaging (MRI) phantoms are crucial for calibrating, testing, and

validating MRI systems and mathematical models. Traditional methods for constructing

phantoms are time-consuming and inflexible. 3D printing provides a new way to create

customizable and modular MRI phantoms efficiently. Our research focuses on designing and

creating a modular MRI phantom frame and assessing the suitability of various 3D printing

materials for building these phantoms.

Dalibor Trampota

Abstract:

This work focuses on computer graphics, more precisely on the web using WebGL. The main goal is to explore the possibilities of WebGL and the Three.js library and create a voxel game similar to Minecraft.

Nichita Vatamaniuc

Abstract:

This contribution focuses on processing and classification of data gained from motion sensors applied to the human body which suffers from neurological disease that leads to musculoskeletal system disorders. The signal generated by human movement is then transformed into the frequency spectrum and used to get the power spectral features. The power spectral features are classified into two classes depending on whether the patient is healthy. The classification step is performed by different classification algorithms with performance comparison.

František Voldřich, O. Luschykov, O. Harwot

Abstract:

Anomaly detection has numerous applications across various fields, including the space industry. A spacecraft must continuously monitor the health of its subsystems to detect non-nominal situations, but transmitting all telemetry data to ground for analysis is not feasible due to limited transmission capacity and potential delays. Therefore, autonomous fault and anomaly detection is essential for timely response to unexpected events and ensuring the mission’s success. The conventional approach in Space Operations involves using Out-of-Limits (OOL) alarms for anomaly detection. which may prove unsufficient in identifying and responding to complex anomalies or unforseen novelties within the range of nominal values. This talk proposes a Machine Learning approach for anomaly/novelty detection embedded into the radiation-tolerant LEON 3 processor for the HERA mission.

Filip Voženílek

Abstract:

The qualitative theory of differential equations investigates the behaviour of solutions without the need for explicit solution methods. We give an overview of some qualitative theory of periodic solutions and behaviour of solutions in proximity of fixed points. The concepts will be illustrated on instructive examples.