REDUCED ORDER SIMULATIONS OF THE BURGERS' EQUATION USING CENTROIDAL VORONOI TESSELLATION

Author(s)
이성환
Alternative Author(s)
Lee, SungHwan
Advisor
이형천
Department
일반대학원 이학계열
Publisher
The Graduate School, Ajou University
Publication Year
2005
Language
eng
Abstract
Centroidal Voronoi tessellation (CVT)는 연관된 generating point들이 대응하는 Voronoi region들의 무게중심이 되는 성질을 만족하는 주어진 집합의 Voronoi tessellation이다. 이 논문에서, CVT는 시간에 의존하는 버거스 방정식에 대한 reduced-order model을 유도하기 위해 이용된다. 그리고 나서, 그 결과들이 유한요소법 (finite element method)을 이용한 결과들 그리고 proper orthogonal decomposition (POD)를 이용한 결과들과 비교된다.
Alternative Abstract
A centroidal Voronoi tessellation (CVT) is a Voronoi Tessellation of a given set such that the associated generating points are centroids (centers of mass) of the corresponding Voronoi regions. In this thesis, CVT is utilized to derive reduced-order models for the time-dependent Burgers equation. Then, CVT-based algorithms are compared with numerical results obtained from finite-element discretization and proper orthogonal decomposition (POD)-based algorithms.
URI
https://dspace.ajou.ac.kr/handle/2018.oak/21101
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Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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