Multigrid metoda za numeričko rješavanje Poissonove jednadžbe

Lužanac, Ivan (2015) Multigrid metoda za numeričko rješavanje Poissonove jednadžbe. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

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.

Item Type: Thesis (Diploma thesis)
Supervisor: Bosner, Nela
Date: 2015
Number of Pages: 30
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 21 Oct 2015 09:40
Last Modified: 21 Oct 2015 09:40
URI: http://digre.pmf.unizg.hr/id/eprint/4294

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