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Rovnice vedení tepla ve fyzice planetek a meteoroidů
Pohl, Leoš ; Brož, Miroslav (advisor) ; Vokrouhlický, David (referee)
Non-gravitational forces caused by thermal emission of photons can significantly change orbits and spin states of asteroids in the long term. A solution of the Heat Conduction Equation (HCE) in an asteroid is necessary to evaluate the forces. Finite Difference Methods (FDMs) are implemented in a Fortran numerical HCE solver to calculate a temperature distribution within a system of 1-dimensional slabs which approximate the asteroid. We compare the methods w.r.t. convergence, accuracy and computational efficiency. The numerical results are compared with a simplified steady-state analytical solution. We calculate the non-gravitational accelerations and resulting semimajor axis drift from the numerical results. The implemented FDMs are shown to be convergent with denser grids and the best method has been selected. The analytical solution provides a good first-guess estimate of the temperature amplitude. The drift in semimajor axis of the tested asteroids, which is due to the non-gravitational forces, is in order-of-magnitude agreement with more accurate models and observational data.
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A Brief Design of Optical Resonators
Hubík, Daniel ; Nešpor, Dušan (referee) ; Kadlec, Radim (advisor)
This bachelor thesis is focused on analysis of split-ring resonators in THz region. Simulations were made by finite elements method and by finite-difference time-domain method. At first we created a resonating structure that works in GHz region. Then we were observing a dependence of movement of resonant frequency on the size of resonator. In the final chapter we assigned frequency dependent values of permitivity to such structure. As the result we simulated working resonator at frequency 500THz. All simulations have been made in program HFSS ANSYS and Lumerical FDTD Solutions.
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Simulation of the Heat Diffusion with a Time-Varying Source on GPUs
Hála, Pavel ; Záň, Drahoslav (referee) ; Jaroš, Jiří (advisor)
This bachelor's thesis deals with the simulation of the heat transfer inside human tissue injected by an external time varying heat source. The proposed implemented simulation is based on a 4th order in space and 1st order in time finite-difference time domain method. First, a multithreaded CPU version was implemented. Subsequently, several GPU accelerated versions were implemented taking into account architecture aspect of the GPU. The experimental results showed that the fastest GPU kernel was the naive one using only the GPU global memory. Next, the usefulness of the Gauss-Seidel's method was investigated. The CPU implementation of the method was evaluated as usable because of being only 13% slower while saving up to 50% of memory resources. However, the GPU implementation was twice as slow as the naive version mainly due to shared memory size limits. The peak performance in terms of GFLOPS reached 32 and 135 on CPU and GPU, respectively. This corresponds to 10% and 9% of the theoretical potential of given architectures.
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Heat Diffusion Simulation on GPU
Hradecký, Michal ; Vašíček, Zdeněk (referee) ; Jaroš, Jiří (advisor)
This thesis deals with the simulation of heat diffusion in human tissues. The proposed algorithm uses a finite-difference time-domain method, which is applied on the governing equation describing the system. A modern graphics card is used to accelerate the simulation. The performance achieved on the GPU card is compared with the implementation exploiting a modern multicore CPU. The output of this thesis is a set of differently optimized algorithms targeted on NVIDIA graphics cards. The experimental results reveal that the use of shared memory is contraproductive and the best performance is achieved by a register based implementation. The overall speedup of 18.5 was reached when comparing a NVIDIA GeForce GTX 580 with a quad-core Intel Core i7 920 CPU. This nicely corresponds with the theoretical capabilities of both architectures.
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The Selected Stochastic Programs in Engineering Design
Čajánek, Michal ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
Two-stage stochastic programming problem with PDE constraint, specially elliptic equation is formulated. The computational scheme is proposed, whereas the emphasis is put on approximation techniques. We introduce method of approximation of random variables of stochastic problem and utilize suitable numerical methods, finite difference method first, then finite element method. There is also formulated a mathematical programming problem describing a membrane deflection with random load. It is followed by determination of the acceptableness of using stochastic optimization rather than deterministic problem and assess the quality of approximations based on Monte Carlo simulation method and the theory of interval estimates. The resulting mathematical models are implemented and solved in the general algebraic modeling system GAMS. Graphical and numerical results are presented.
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Techniques of time-domain analysis of interconnects.
Lábsky, Balázs ; Petržela, Jiří (referee) ; Brančík, Lubomír (advisor)
This work deals with techniques of time-domain analysis of interconnects. After a studying crucial issue of time-domain analysis of interconnects methods of modeling and simulation simple interconnects in electrotechnics are described. For transient effect analysis two elementary methods can be used: the state variable method and the FDTD (Finite - Difference Time - Domain) method. The FDTD method can be used to solve partial differential equations in time domain, for instance equations of transmission lines. The method is very effective and delivers satisfactory results in case of linear and non-linear lines with a single “live” conductor. The method can be easily programmed in Matlab.
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Engineering Optimization
Kokrda, Lukáš ; Hrabec, Dušan (referee) ; Popela, Pavel (advisor)
The bachelor thesis deals with convex optimization and in particular, it processes a design of the optimal support of a loaded beam. For better understanding of the terms used, the bachelor thesis contains the brief introduction to the convex optimization problems, explanation of the basic therms of ordinary dierential equations and theory of elasticity. When the original model is built, then the results are obtained by computations in the MATLAB software.
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Optimization in engineering problems
Klepáč, Jaromír ; Popela, Pavel (referee) ; Mrázková, Eva (advisor)
This bachelor thesis deals with optimization in engineering problems. In particular, it focuses on a task of optimal dimensions design of continuously loaded beam with specic requirements on nal beam weight and rigidity. For the purpose of well understanding of all the terms used during solving of an illustrative task, the thesis contains a brief introduction into the optimization problems, ordinary dierential equations, and theory of elasticity as well. Results obtained through optimization in the GAMS software will be checked by analytic solution and compared with an alternative calculation in the ANSYS software.
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