Computations of Laguerre tessellations with given cell volumes

• Thesis title in Czech: Výpočty Laguerrovy mozaiky se zadanými objemy buněk
• Thesis title in English: Computations of Laguerre tessellations with given cell volumes
• Key words: Laguerrova mozaika|přiřazení|kapacita|Barzilai-Borweinův algoritmus
• English key words: Laguerre tessellation|assignment|capacity|Barzilai-Borwein algorithm
• Academic year of topic announcement: 2020/2021
• Thesis type: Bachelor's thesis
• Thesis language: angličtina
• Department: Department of Probability and Mathematical Statistics (32-KPMS)
• Supervisor: prof. RNDr. Viktor Beneš, DrSc.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 25.08.2020
• Date of assignment: 25.08.2020
• Confirmed by Study dept. on: 27.11.2020
• Date and time of defence: 07.09.2022 08:30
• Date of electronic submission: 18.07.2022
• Date of submission of printed version: 25.07.2022
• Date of proceeded defence: 07.09.2022
• Opponents: RNDr. Jiří Dvořák, Ph.D.
• Advisors: RNDr. Mgr. Filip Seitl, Ph.D.

Guidelines

Student se s pomocí literatury seznámí s pojmem Laguerrova mozaika a jejími vlastnostmi. Bude studovat matematické odvození algoritmu konstrukce Laguerrovy mozaiky se zadanými objemy buněk. Podle tohoto algoritmu připraví počítačový program a provede výpočty na simulovaných vstupních datech.

References

(i) F. Aurenhammer, F. Hoffmann, B. Aronov: Minkowski-type theorems and least-squares clustering. Algorithmica 20 (1998), 61-76.
(ii) J. Kuhn, M. Schneider, P. Sonnweber-Ribic, T. Boelke: Fast methods for computing centroidal Laguerre tessellations for prescribed volume fractions with applications to microstructure generation of polycrystalline materials. Comput. Methods Appl. Mech. Eng. 369 (2020) 113175.