Računanje rezonantnih modova u sustavu BEM++

master's thesis

• Author: Marko Dominković
• Mentor: Luka Grubišić (mentor)
• Committee member: Luka Grubišić (predsjednik povjerenstva)
• Committee member: Vjeran Hari (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-02-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U radu je opisana jedna od metoda za računanja rezonanci i pseudospektra. Bazira se na iterativnom računanju najmanje singularne vrijednosti operatora raspršenja. Implementacija algoritma je odrađena u BEM++ kroz Python sučelje. U prvom poglavlju opisana je matematička notacija akustičnog raspršenja. Definirali smo pseudospektar. Pseudospektar je idealan alat za prikazati svojstvo normalnosti operatora. Nadalje, prikazali smo neke od osnovnih metoda za korištenje BEM++: način konstruiranje rešetke, definiranje funkcija na njima i implementacija operatora raspršenja. Zadnje poglavlje obrađuje konkretan primjer; opis algoritma za traženje najmanje singularne vrijednosti, računanje pseudospektra te traženje rezonance. Na jediničnoj kugli izračunali smo rezonance i prikazali rezonantne modove.

Abstract (english)

In this thesis is described one of methods for computing resonance and pseudospectra. It is based on iterative calculation of smallest singular value for scatter operator. Whole implementation is done in BEM++ with Python interface. First chapter describes mathematical notation of acoustic scattering. We defined pseudospectra. Pseudospectra is the ideal instrument to describe normality of operators. Further, we showed some of a basic method for BEM++ usage: grid construction, defining grid functions and implementation of scatter operators. The last chapter deals with concrete example; describing algorithm for searching the smallest singular value, calculating pseudospecta and looking for resonance. On unit sphere we have found resonances and plot resonance modes.

• Keywords: računanje rezonanci; računanje pseudospektra; iterativno računanje; BEM++; Python
• Keywords (english): computing resonance; computing pseudospectra; iterative calculation; BEM++; Python
• Language: croatian
• URN:NBN: urn:nbn:hr:217:919410
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2020-01-18
• Created on: 2019-07-18 12:13:48