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master's thesis
Multigrid metoda za numeričko rješavanje Poissonove jednadžbe
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:400565
Lužanac, Ivan
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Lužanac, I. (2015). Multigrid metoda za numeričko rješavanje Poissonove jednadžbe (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:400565

Lužanac, Ivan. "Multigrid metoda za numeričko rješavanje Poissonove jednadžbe." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:400565

Lužanac, Ivan. "Multigrid metoda za numeričko rješavanje Poissonove jednadžbe." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:400565

Lužanac, I. (2015). 'Multigrid metoda za numeričko rješavanje Poissonove jednadžbe', Master's thesis, University of Zagreb, Faculty of Science, accessed 05 October 2024, https://urn.nsk.hr/urn:nbn:hr:217:400565

Lužanac I. Multigrid metoda za numeričko rješavanje Poissonove jednadžbe [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 October 05] Available at: https://urn.nsk.hr/urn:nbn:hr:217:400565

I. Lužanac, "Multigrid metoda za numeričko rješavanje Poissonove jednadžbe", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:400565

Metadata
TitleMultigrid metoda za numeričko rješavanje Poissonove jednadžbe
AuthorIvan Lužanac
MentorNela Bosner (mentor)
Committee memberNela Bosner (predsjednik povjerenstva)
Committee memberBojan Basrak (član povjerenstva)
Committee memberZvonimir Bujanović (član povjerenstva)
Committee memberNikola Sarapa (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Osnovna ideja ovoga rada nam je bila Multigrid metoda, tj. njezina usporedba sa ostalim iterativnim metodama. Testiranje metoda smo provodili isključivo koristeći Poissonovu jednadžbu sa homogenim rubnim uvjetom, premda to nije bilo nužno. Također, koristili smo legitimnu pretpostavku da nam je promatrani prostor dimenzije 1D, zbog složenosti postavljanja problema u višim dimenzijama. Radi lakšeg snalaženja, rad smo podijelili na tri osnovne cjeline: Uvod, Poissonova jednadžba, te Multigrid. U prvoj cjelini smo iskazali osnovne matematičke pojmove koje smo koristili, dok smo u drugoj klasificirali Poissonovu jednažbu. Posljednja, glavna cjelina se sastoji od motivacije i općenitih razmatranja koja su dovela do razvijanja Multigrida, osnovnih elemenata Multigrida koje smo morali u konačnici povezati, te naposljetku od pseudokoda algoritma i grafičkog prikaza rezultata. Poseban naglasak smo stavili na rezultate, koji su nam sa pragmatičnog stajališta, najbitniji dio rada. Nismo vršili detaljnu interpretaciju rezultata, radi jasnoće MATLAB-ovskih grafičkih prikaza. Kod uz pomoć kojega su dobiveni rezultati, je pisan posebno u MATLABU, te nam je omogućio usporedbu Multigrida sa osnovnim metodama poput Jacobijeve.
Abstract (english)
Basic idea of this work is Multigrid method, i.e. comparison with other basic iterative methods. Method testing was carried out exclusively using Poisson equation with homogeneous boundary condition, although that was not necessary. Also, we used legitimate assumption that our space has dimension 1D, due to complex set up in higher dimensions. Conveniently, our work is split in three basic units: Introduction, Poisson equation, and Multigrid. In first unit, we have expressed basic mathematical terms which we used, while in second unit we classified Poisson equation. Last, the most significant unit consists of motivation and general considerations which led us to develop Multgrid, basic elements of Multigrid, which we had to connect in the end, and finally algorithm pseudocode and graphical display of results. Special emphasis is made on the results, which are from pragmatical viewpoint, most important part of our work. We did not performed detailed interpretation of our results, because of distinct clearness of MATLAB graphical displays. Code which obtained our results, is written in MATLAB, and allow us comparison of Multigrid with basic iterative methods like Jacobi.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:400565
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 on2019-02-28 13:22:48