Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Scheduling and Load Balancing Methods of Multithread Parallel Linear Solver of Finite Element Structural Analysis

유한요소 구조해석 다중쓰레드 병렬 선형해법의 스케쥴링 및 부하 조절 기법 연구

  • Received : 2013.11.25
  • Accepted : 2014.03.31
  • Published : 2014.05.01
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Abstract

In this paper, task scheduling and load balancing methods of multifrontal solution methods of finite element structural analysis in a modern multicore machine are introduced. Many structural analysis problems have generally irregular grid and many kinds of properties and materials. These irregularities and heterogeneities lead to bottleneck of parallelization and cause idle time to analysis. Therefore, task scheduling and load balancing are desired to reduce inefficiency. Several kinds of multithreaded parallelization methods are presented and comparison between static and dynamic task scheduling are shown. To reduce the idle time caused by irregular partitioned subdomains, computational load balancing methods, Balancing all tasks and minmax task pairing balancing, are invented. Theoretical and actual elapsed time are shown and the reason of their performance gap are discussed.

본 논문은 최근에 널리 사용되는 다중코어 컴퓨팅 환경에서 병렬 다중프론트 해법의 스케쥴링 및 부하조절 기법에 대해 논의한다. 통상적으로 구조해석 문제들은 불규칙한 격자계와 혼재된 물성 때문에 병렬화 알고리즘 구현 시 병목현상을 일으키고 불필요한 유휴시간을 초래한다. 따라서 이를 극복하며 효율성을 향상시키기 위해 다중쓰레드 기반 환경에 걸맞는 작업 스케쥴링 및 부하 분산 기법의 적용이 필수적이다. 본 논문에서 제시된 정적, 동적 스케줄링 기법과 정적 전 임무 분산, 최소최대 임무 결합 등의 부하 분산 기법들에 대한 이론적, 실제 결과를 제시함으로서 그 유용성을 논의하고자 한다.

Keywords

References

  1. Duff, I. S., and Reid, J. K. "The Multifrontal Solution of Indefinite Sparse Symmetric Linear-Equations," ACM Transactions on Mathematical Software, Vol. 9, No. 3, 1983, pp. 302-325. https://doi.org/10.1145/356044.356047
  2. Irons, B. M. "A frontal solution program for finite element analysis," International Journal for Numerical Methods in Engineering, Vol. 2, No. 1, 1970, pp. 5-32. https://doi.org/10.1002/nme.1620020104
  3. P. R. Amestoy, I. S. Duff, J. Koster, and J. -Y. L'Excellent, "A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling," SIAM Journal of Matrix Analysis and Applications, Vol 23, No. 1, 2001, pp. 15-41. https://doi.org/10.1137/S0895479899358194
  4. T. A. Davis, "Algorithm 832 : UMFPACK, An Unsymmetric-Pattern Multifrontal Method," ACM Transaction on Mathematical Software, Vol 30, No. 2, 2004, pp. 196-199. https://doi.org/10.1145/992200.992206
  5. Kim, J.H., C.S. Lee, and S.J. Kim, "High-performance domainwise parallel direct solver for large-scale structural analysis," AIAA journal, Vol. 43, 2005, pp. 662-670. https://doi.org/10.2514/1.11171
  6. Kim, S.J., C.S. Lee, and J.H. Kim, "Large-scale structural analysis by parallel multifrontal solver through Internet-based personal computers," AIAA journal, Vol. 40, 2002, pp. 359-367. https://doi.org/10.2514/2.1654
  7. M.K. Kim, J.H. Kim, C.Y. Park and S.J. Kim, "Parallelization of Multifrontal Solution Method for Shared Memory Architecture", KSAS Journal, Vol. 40, No. 11, 2012, pp 972-978. https://doi.org/10.5139/JKSAS.2012.40.11.972
  8. Kim, M.K, Kim, S.J, "Hybrid Parallelism of Multifrontal Linear Solution Algorithm with Out Of Core Capability for Finite Element Analysis", CMES, Vol. 84, 2012, pp. 297-331.
  9. M.K. Kim, "Studies of Scheduling and Load Balancing Ways of the Parallel Direct Solution Method in Multicore Computers for Large Scale Structural Analysis", KSAS Autumn Conference, 2013, pp. 201-204.
  10. http://software.intel.com/en-us/intel-mkl
  11. http://openmp.org/wp/
  12. https://www.threadingbuildingblocks.org/
  13. http://software.intel.com/en-us/intel-cilk-plus
  14. Agullo, E., Demmel, J., Dongarra, J., Hadri, B., Kurzak, J., Langou, J., Ltaief, H., Luszczek, P., Tomov, S. "Numerical linear algebra on emerging architectures: The PLASMA and MAGMA projects," Journal of Physics: Conference Series, Vol. 180, 2009.