Loading [MathJax]/jax/output/HTML-CSS/jax.js
prikaz prve stranice dokumenta Redukcijski modeli dinamike fluida s primjenama
  Download
PDF 4.05 MB
master's thesis
Redukcijski modeli dinamike fluida s primjenama
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:231905
Kozić, Kristina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kozić, K. (2018). Redukcijski modeli dinamike fluida s primjenama (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:231905

Kozić, Kristina. "Redukcijski modeli dinamike fluida s primjenama." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:231905

Kozić, Kristina. "Redukcijski modeli dinamike fluida s primjenama." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:231905

Kozić, K. (2018). 'Redukcijski modeli dinamike fluida s primjenama', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:231905

Kozić K. Redukcijski modeli dinamike fluida s primjenama [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2025 March 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:231905

K. Kozić, "Redukcijski modeli dinamike fluida s primjenama", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:231905

Metadata
TitleRedukcijski modeli dinamike fluida s primjenama
AuthorKristina Kozić
MentorZlatko Drmač (mentor)
Committee memberZlatko Drmač (predsjednik povjerenstva)
Committee memberMarko Vrdoljak (član povjerenstva)
Committee memberEduard Marušić-Paloka (član povjerenstva)
Committee memberDamir Bakić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavamo metode redukcije dimenzije sustava: pravu ortogonalnu dekompoziciju (POD), diskretnu empirijsku interpolacijsku metodu DEIM i q-DEIM, modificiranu verziju DEIM-a. Prilikom konstrukcije nižedimenzionalnog sustava, najčešće se koristi projekcija na potprostor niže dimenzije l<<n. Upravo je POD jedna od metoda koja konstruira ortonormiranu bazu dimenzije l na koju će se projicirati originalni sustav. Štoviše, aproksimacija podataka ranga l dobivena POD... More metodom je najbolja medu svim mogućim aproksimacijama ranga l. Problem je formuliran kao optimizacijski problem čije rješenje nalazimo uz pomoć metode Lagrangeovih multiplikatora. U konačnodimenzionalnom slučaju POD se svodi na dekompoziciju singularnih vrijednosti (SVD). Ukoliko polazni sustav sadrži nelinearni član, tada je rješavanje nelinearnog dijela složenosti kao i rješavanje originalnog sustava. Tu poteškoću nadilazi DEIM na način da koristi POD bazu prostora generiranog nelinearnom funkcijom te bira indekse kojima interpolira polazne podatke. Osnovna razlika q-DEIM u odnosu na DEIM je odabir interpolacijskih indekasa i bolja ocjena na grešku aproksimacije. Predstavili smo oba algoritma i usporedili ih na konkretnom primjeru. Less
Abstract (english)
In this paper, we study proper orthogonal decomposition (POD), discrete empirical interpolation method (DEIM) as well as its modified version q-DEIM and their applications, to obtain reduced order models. While constructing a reduced order system we usually apply projection on the subspace of lower dimension l<<n. POD constructs lower dimensional subspace on which we project original system. Moreover, POD approximation represents a set of data better than any other... More representation of its rank. We set POD problem as an optimization problem and we solve it within Lagrangian framework. In finite dimensional case it comes down to singular value decomposition (SVD). If original system contains nonlinear term, the cost of solving it is the same as solving the original system. DEIM overcomes that problem. It uses POD base of space generated by nonlinear function and by selecting indexes interpolates original data. q-DEIM has different approach to select indexes and as a result it has a better error upper bound. We demonstrate both algorithms and compare them on concrete example. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:231905
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-05-27 10:52:41
accessibility

closeAccessibilityrefresh

If you wish to permanently save changes, click on Save, if not - your settings will be reset when you restart the browser.