Numeričko rješavanje problema u elektrostatici pomoću programskog jezika Julia

master's thesis

• Title (english): Numerical problem solving in electrostatics using the Julia programming language
• Author: Tin Biršić
• Mentor: Davor Horvatić (mentor)
• Committee member: Davor Horvatić (predsjednik povjerenstva)
• Committee member: Katarina Jeličić (član povjerenstva)
• Committee member: Ivica Smolić (član povjerenstva)
• Committee member: Željko Skoko (član povjerenstva)
• Committee member: Petar Žugec (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2024-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Tradicionalno, problemi iz područja elektrostatike rješavaju se analitičkim metodama. Međutim, s porastom složenosti sustava, analitička rješenja postaju nedostupna ili previše kompleksna za izvođenje. U takvim situacijama, numeričke metode postaju neophodan alat za analizu električnih polja i potencijala. Ovaj rad prikazuje primjenu numeričkih metoda u rješavanju problema iz elektrostatike korištenjem programskog jezika Julia. Korištenjem metode momenata (MoM, eng. Method of Moments) i metode... More konačnih elemenata (FDM, eng. Finite Difference Method) prikazali smo mogućnost rješavanja Laplaceove jednadžbe numeričkim metodama koje su nam omogućile da dobijemo aproksimacije potencijala i raspodjele naboja tamo gdje analitička rješenja postaju suviše kompleksna. Implementacija u Juliji pokazala se efikasnom i brzom za izračune te vizualizaciju rezultata, što potvrđuje vrijednost Julije kao alata u znanstvenim i tehničkim područjima. Less

Abstract (english)

Traditionally, problems in the field of electrostatics are solved using analytical methods. However, as the complexity of systems increases, analytical solutions become unavailable or too complex to carry out. In such situations, numerical methods become an essential tool for the analysis of electric fields and potentials. This work presents the application of numerical methods in solving electrostatic problems using the Julia programming language. By utilizing the Method of Moments (MoM) and... More the Finite Difference Method (FDM), we demonstrated the capability to solve Laplace’s equation with numerical methods that allowed us to obtain approximations of potentials and charge distributions where analytical solutions become too complex. The implementation in Julia proved to be efficient and fast for computations and visualization of results, confirming the value of Julia as a tool in scientific and technical fields. Less

• Keywords: elektrostatika; numeričke metode; Laplaceova jednadžba; Julia; metoda momenata; metoda konačnih elemenata
• Keywords (english): electrostatics; numerical methods; Laplace’s equation; Julia; method of moments; finite difference method
• Language: croatian
• URN:NBN: urn:nbn:hr:217:409361
• Study programme: Title: The Integrated University Undergraduate and Graduate Programme in Physics and Computer Science Education; specializations in: Physics and informatics; Course: Physics and informatics; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: sveučilišni magistar edukacije fizike i informatike (sveučilišni magistar edukacije fizike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2025-02-01 08:43:47