Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Further Improvement of Direct Solution-based FETI Algorithm

직접해법 기반의 FETI 알고리즘의 개선

  • Kang, Seung-Hoon (Department of Aerospace Engineering, Seoul National University) ;
  • Gong, DuHyun (Department of Aerospace Engineering, Seoul National University) ;
  • Shin, SangJoon (Institute of Advanced Aerospace Technology, Seoul National University)
  • 강승훈 (서울대학교 항공우주공학과) ;
  • 공두현 (서울대학교 항공우주공학과) ;
  • 신상준 (서울대학교 항공우주신기술연구소)
  • Received : 2022.06.10
  • Accepted : 2022.07.22
  • Published : 2022.10.31
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Abstract

This paper presents an improved computational framework for the direct-solution-based finite element tearing and interconnecting (FETI) algorithm. The FETI-local algorithm is further improved herein, and localized Lagrange multipliers are used to define the interface among its subdomains. Selective inverse entry computation, using a property of the Boolean matrix, is employed for the computation of the subdomain interface stiffness and load, in which the original FETI-local algorithm requires a full matrix inverse computation of a high computational cost. In the global interface computation step, the original serial computation is replaced by a parallel multi-frontal method. The performance of the improved FETI-local algorithm was evaluated using a numerical example with 64 million degrees of freedom (DOFs). The computational time was reduced by up to 97.8% compared to that of the original algorithm. In addition, further stable and improved scalability was obtained in terms of a speed-up indicator. Furthermore, a performance comparison was conducted to evaluate the differences between the proposed algorithm and commercial software ANSYS using a large-scale computation with 432 million DOFs. Although ANSYS is superior in terms of computational time, the proposed algorithm has an advantage in terms of the speed-up increase per processor increase.

본 논문은 직접해법 기반 FETI 알고리즘의 개선 방안을 제시하였다. 개선 대상은 FETI-local로, 해당 알고리즘은 국부 Lagrange 승수를 통해 부영역 간 경계 문제를 정의한다. 부영역 경계 강성 및 하중 계산 단계의 경우, 전체 역행렬 계산 등 과도한 비용을 요구했던 기존 알고리즘을 Boolean 행렬 특성을 활용한 선택적 역행렬 성분 계산으로 개선하였다. 전역 경계 행렬식 계산 단계의 경우, 기존 단일 프로세서 연산을 다중 프론탈 기법 기반 병렬 연산으로 대체하였다. 제시된 FETI-local 알고리즘의 성능 개선은 64만 자유도 수치 예제를 통해 검증되었으며, 기존 대비 최대 97.8%의 계산 시간 감소가 달성되었다. 또한, 기존 대비 안정적이고 개선된 확장성이 가속 지표를 통해 확인되었다. 추가로, 432만 자유도의 대용량 계산 성능 비교가 제시된 알고리즘과 상용 프로그램인 ANSYS 간에 수행되었다. 그 결과, 계산 시간 측면에선 ANSYS가 우수하였으나, 프로세서 수에 따른 가속 성능 증가율 측면에선 제시된 알고리즘이 우수한 것이 확인되었다.

Keywords

Acknowledgement

본 논문은 2022년도 정부(과학기술통신부)의 재원으로 한국연구재단의 지원을 받아 수행된 연구입니다(No. 2021R1A5A1031868, 2021R1A2C1007352).

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