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doctoral thesis
Adaptive numerical modeling of engineering problems using hierarchical Fup basis functions and Control Colume IsoGeometric Analysis
doctoral dissertation
2021. urn:nbn:hr:123:049655
Kamber, Grgo
University of Split
Faculty of Civil Engineering, Architecture and Geodesy
Department of Engineering Mechanics

Cite this document

Kamber, G. (2021). Adaptive numerical modeling of engineering problems using hierarchical Fup basis functions and Control Colume IsoGeometric Analysis : doctoral dissertation (Doctoral thesis). Split: University of Split, Faculty of Civil Engineering, Architecture and Geodesy. Retrieved from https://urn.nsk.hr/urn:nbn:hr:123:049655

Kamber, Grgo. "Adaptive numerical modeling of engineering problems using hierarchical Fup basis functions and Control Colume IsoGeometric Analysis : doctoral dissertation." Doctoral thesis, University of Split, Faculty of Civil Engineering, Architecture and Geodesy, 2021. https://urn.nsk.hr/urn:nbn:hr:123:049655

Kamber, Grgo. "Adaptive numerical modeling of engineering problems using hierarchical Fup basis functions and Control Colume IsoGeometric Analysis : doctoral dissertation." Doctoral thesis, University of Split, Faculty of Civil Engineering, Architecture and Geodesy, 2021. https://urn.nsk.hr/urn:nbn:hr:123:049655

Kamber, G. (2021). 'Adaptive numerical modeling of engineering problems using hierarchical Fup basis functions and Control Colume IsoGeometric Analysis : doctoral dissertation', Doctoral thesis, University of Split, Faculty of Civil Engineering, Architecture and Geodesy, accessed 16 February 2025, https://urn.nsk.hr/urn:nbn:hr:123:049655

Kamber G. Adaptive numerical modeling of engineering problems using hierarchical Fup basis functions and Control Colume IsoGeometric Analysis : doctoral dissertation [Doctoral thesis]. Split: University of Split, Faculty of Civil Engineering, Architecture and Geodesy; 2021 [cited 2025 February 16] Available at: https://urn.nsk.hr/urn:nbn:hr:123:049655

G. Kamber, "Adaptive numerical modeling of engineering problems using hierarchical Fup basis functions and Control Colume IsoGeometric Analysis : doctoral dissertation", Doctoral thesis, University of Split, Faculty of Civil Engineering, Architecture and Geodesy, Split, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:123:049655

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Metadata
TitleAdaptive numerical modeling of engineering problems using hierarchical Fup basis functions and Control Colume IsoGeometric Analysis : doctoral dissertation
Title (croatian)Adaptivno numeričko modeliranje inženjerskih problema koristeći hijerarhijske Fup bazne funkcije i Izogeometrijsku analizu kontrolnih volumena : disertacija
AuthorGrgo Kamber
MentorVedrana Kozulić (mentor)
MentorHrvoje Gotovac (komentor)
Committee memberMijo Nikolić (predsjednik povjerenstva)
Committee memberŽeljan Lozina (član povjerenstva)
Committee memberNino Krvavica (član povjerenstva)
GranterUniversity of Split
Faculty of Civil Engineering, Architecture and Geodesy
(Department of Engineering Mechanics)
Split
Defense date and country2021-02-08, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Civil Engineering
Supporting Structures
Universal decimal classification
(UDC)		51 - Mathematics
624/625 - Civil and structural engineering. Civil engineering of land transport. Railway engineering. Highway engineering
Abstract
The main objective of this thesis is to utilize the powerful approximation properties of Fup basis functions for numerical solutions of engineering problems with highly localized steep gradients while controlling spurious numerical oscillations and describing different spatial scales. The concept of isogeometric analysis (IGA) is presented as a unified framework for multiscale representation of the geometry and solution. This fundamentally high-order approach enables the description of all fields as continuous and smooth functions by using a linear combination of spline basis functions. Classical IGA usually employs Galerkin or collocation approach using B-splines or NURBS as basis functions. However, in this thesis, a third concept in the form of control volume isogeometric analysis (CV-IGA) is used with Fup basis functions which represent infinitely smooth splines. Novel hierarchical Fup (HF) basis functions is constructed, enabling a local hp-refinement such that they can replace certain basis functions at one resolution level with new basis functions at the next resolution level that have a smaller length of the compact support (h-refinement), but also higher order (p-refinement). This hp-refinement property enables spectral convergence which is significant improvement in comparison to the hierarchical truncated B-splines which enable h-refinement and polynomial convergence. Thus, in domain zones with larger gradients, the algorithm uses smaller local spatial scales, while in other region, larger spatial scales are used, controlling the numerical error by the prescribed accuracy. The efficiency and accuracy of the adaptive algorithm is verified with some classic 1D and 2D benchmark test cases with application to the engineering problems with highly localized steep gradients and advection-dominated problems.
Abstract (croatian)
Glavni cilj ove teze je iskoristiti moćna aproksimacijska svojstva Fup baznih funkcija za numeričko modeliranje inženjerskih problema s izrazito lokaliziranim gradijentima uz kontrolu numeričkih oscilacija. Predstavljen je koncept izogeometrijske analize (IGA) kao cjeloviti pristup za višerezolucijsko modeliranje geometrije i rješenja. Pristup fundamentalno višeg reda omogućuje opis različitih polja kao kontinuiranih i glatkih funkcija koristeći linearnu kombinaciju spline baznih funkcija. Klasična IGA obično koristi Galerkinov ili kolokacijski pristup koristeći B-spline ili NURBS kao bazne funkcije. Međutim, u ovoj tezi se koristi treći koncept u obliku izogeometrijske analize kontrolnih volumena (CV-IGA) uz primjenu Fup baznih funkcija koje predstavljaju beskonačno glatke spline funkcije. Konstruirane su nove hijerarhijske Fup (HF) bazne funkcije koje omogućuju lokalno hp-poboljšanje tako da zamjenjuju određene bazne funkcije na jednom nivou novim baznim funkcijama na višem nivou gdje imaju manju duljinu kompaktnog nosača (h-poboljšanje), ali i viši red (p-poboljšanje). Svojstvo hp-poboljšanja je da omogućuje spektralnu konvergenciju što predstavlja značajan doprinos u odnosu na modificirane hijerarhijske B-splineove koji omogućavaju h-poboljšanje i polinomsku konvergenciju. Dakle, u dijelovima domene gdje su rješenja najzahtjevnija, algoritam koristi bazne funkcije višeg reda s manjim kompaktnim nosačem, dok u ostalim dijelovima koristi rjeđi raspored baznih funkcija nižeg reda kontrolirajući numeričku pogrešku s definiranom točnošću. Učinkovitost i točnost adaptivnog algoritma provjerena je na nekim od klasičnih 1D i 2D referentnih numeričkih testova.
Keywords
Keywords (croatian)
Languageenglish
DOIhttps://doi.org/10.31534/DocT.051.KamG
URN:NBNurn:nbn:hr:123:049655
Promotion2021
ProjectNumber: UIP-2013-11-8103
Title: Modeliranje toka podzemnih voda u krškim vodonosnicima
Title: Groundwater flow modelling in karst aquifers
Acronym: Karst modelling
Leader: Hrvoje Gotovac
Jurisdiction: Croatia
Funder: HRZZ
Funding stream: UIP
Study programmeTitle: Civil Engineering
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje tehničkih znanosti, polje građevinarstvo (doktor/doktorica znanosti, područje tehničkih znanosti, polje građevinarstvo)
Catalog URLhttp://library.foi.hr/lib/knjiga.php?B=422&H=&E=&V=&lok=&zbi=&item=14871
Type of resourceText
ExtentXXIII, 115 str. : tabele, graf. prikazi, ilustr. u bojama ; 30 cm
File originBorn digital
Access conditionsOpen access
Embargo expiration date: 2022-02-08
Terms of useLicence In copyright icon
Created on2021-03-04 14:34:10