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2차원 열전도 문제 경계요소법의 대규모 선형시스템에 대한 GMRES 해법 적용 연구 Application of GMRES Solver for the Large Scale Linear Systems from Boundary Element Method of the 2D Heat Conduction Problems

최창용
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한국기계기술학회지 (韓國機械技術學會誌)
제21권 제1호 (2019.02)
pp.34-41
한국기계기술학회 (Korean Society of Mechanical Technology)
초록

Boundary element solution method is introduced for radiation heat transfer problem with objects inside a 2-D enclosure, where shadow zone exists. Surfaces are assumed as diffuse gray in a transparent medium. Boundary integral and boundary element equations were derived from radiation transfer equation, and their theory is reviewed. Also the process of solution methods to implement the boundary element method is analysed and explained with consideration of shadow effects. BEM solution results are compared with two test problems and are found to be good agreements with the both analytic and ANSYS Fluent numerical solutions. Therefore the current BEM analysis for radiation heat transfer problem can be considered as verified, and their efficacy with engineering applicability is established as a result.

키워드
Boundary element method(경계요소법)GMRES iterative solver(Generalized Minimal Residual Method 반복 솔버)Krylov subspace(Krylov 부분공간)Arnoldi process(Arnodi 과정)Upper Hessenberg matrix(우 Hessenberg 행렬)2D Heat conduction problem(2차원 열전도 문제)
목차
ABSTRACT
 1. 서 론
 2. 경계요소식의 구성
 3. GMRES 해법
 4. Preconditioning
 5. Preconditioned GMRES 알고리즘
  5.1 재시작 전 반복 횟수 설정
  5.2 외부 루프 시작과 초기조건 설정
  5.3 내부 루프 시작
  5.4 Arnoldi 과정 시작
  5.5 내부 루프의 수렴 체크
  5.6 근사해의 계산
  5.7 외부 루프의 수렴 체크
 6. 결과 및 고찰
 7. 결 론
 후 기
 References
저자
  • 최창용(Jeonju University) | Chang-Yong Choi Corresponding Author