Primjena pohlepnog algoritma za redukciju dimenzije 1d elastičnih struktura

master's thesis

• Author: Vinka Račić
• Mentor: Josip Tambača (mentor)
• Committee member: Josip Tambača (predsjednik povjerenstva)
• Committee member: Mladen Jurak (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-07-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Metode redukcije baze koriste se za smanjenje reda visokodimenzionalnog modela pretraživanjem njegova konačnog skupa rješenja. Na manjem skupu parametara, koji određuju visokodimenzionalni model, pohlepnim algortimom gradi se reducirana baza, kojoj se u svakom koraku algortima dodaje jedan od vektora rješenja visokodimenzionalnog modela. Cilj je iz početnog problema dobiti reducirani model, čija je dimenzija puno manja u odnosu na dimenziju visokodimenzionalnog modela. Tada se za svaki parametar iz skupa nad kojim se reducirana baza gradi, može brzo i efikasno izračunati rješenje koje aproksimira rješenje visokodimenzionalnog problema do na definiranu točnost. U prvom poglavlju opisana je teorijska pozadina metode i pohlepni algoritam koji se koristi. U drugom poglavlju formuliramo Euler-Bernoullijev model elastičnog štapa i metodu konačnih elemenata koju koristimo za aproksimaciju štapa u konačnodimenzionalnom prostoru. U trećem poglavlju dani su numerički primjeri i primjene metode redukcije dimenzije na modelu poprečnog pomaka štapa.

Abstract (english)

Reduced basis methods are used to reduce the order of high-fidelity problem by searching a finite set of high-fidelity solutions. The greedy algorithm iteratively assembles reduced basis by adding one high-fidelity solution in each step. The algorithm is applied on small set of parameters, which determine a high-fidelity model. The aim is to get a model whose dimension is much smaller than initial problem dimension. A solution that approximates the high-fidelity solution can be calculated quickly and efficiently for each parameter within a parameter set, for a prescribed tolerance. The first chapter presents a theoretical background and a greedy algorithm that is used. The second chapter formulates Euler-Bernoulli beam problem and finite element method which is used for high-fidelity approximation of elastic beam. The third chapter presents numerical examples and the application of greedy algorithm for the construction of reduced basis spaces.

• Keywords: metode redukcije baze; visokodimenzionalni model; Euler-Bernoullijev model elastičnog štapa; metoda konačnih elemenata
• Keywords (english): reduced basis methods; high-fidelity model; Euler-Bernoulli beam problem; finite element method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:191269
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-11-27 11:29:33