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REDUCED ORDER SIMULATIONS OF THE BURGERS' EQUATION USING CENTROIDAL VORONOI TESSELLATION
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 이형천 | - |
| dc.contributor.author | 이성환 | - |
| dc.date.accessioned | 2022-11-29T03:01:23Z | - |
| dc.date.available | 2022-11-29T03:01:23Z | - |
| dc.date.issued | 2005 | - |
| dc.identifier.other | 350 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/21101 | - |
| dc.description | 학위논문(석사)--아주대학교 대학원 :수학과,2005 | - |
| dc.description.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. | - |
| dc.description.tableofcontents | Contents Chapter 1 Introduction = 1 Chapter 2. Centroidal Voronoi Tessellation = 5 2.1 Definition of CVTs for discrete data sets = 5 2.2 Minimization Property of CVTs = 7 2.3 Algorithms for constructing discrete CVTs = 7 Chapter 3. CVT-based model reduction for the Burgers equation = 10 3.1 Generating a Snapshot = 10 3.1.1 The Galerkin Method and the Weak Form = 11 3.1.2 The Finite Element Approximation = 11 3.2 Reduced Order Modelling via CVT = 16 Chapter 4. Computational Experiments = 20 4.1 Setting Up the Problem = 20 4.2 A Comparison to FEM Solutions = 22 Chapter 5. Conclusions = 40 | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | REDUCED ORDER SIMULATIONS OF THE BURGERS' EQUATION USING CENTROIDAL VORONOI TESSELLATION | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.alternativeName | Lee, SungHwan | - |
| dc.contributor.department | 일반대학원 이학계열 | - |
| dc.date.awarded | 2005. 2 | - |
| dc.description.degree | Master | - |
| dc.identifier.localId | 564246 | - |
| dc.identifier.url | http://dcoll.ajou.ac.kr:9080/dcollection/jsp/common/DcLoOrgPer.jsp?sItemId=000000000350 | - |
| dc.description.alternativeAbstract | 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. | - |
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- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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