DOI QR코드

DOI QR Code

다중프론트 해법의 공유메모리 병렬화

Parallelization of Multifrontal Solution Method for Shared Memory Architecture

  • 김민기 (서울대학교 기계항공공학부 대학원) ;
  • 김정호 (인하대학교 항공우주공학과) ;
  • 박찬익 (국방과학연구소) ;
  • 김승조 (한국항공우주연구원)
  • 투고 : 2012.08.30
  • 심사 : 2012.10.04
  • 발행 : 2012.11.01

초록

본 논문은 유한요소 구조해석의 선형해법으로 널리 사용되는 다중프론트 해법의 공유메모리 환경하의 병렬화 방법을 논의한다. 다중프론트 해법은 병렬성이 내재되어 있어서 여타 해법보다 상대적으로 병렬화가 용이한 방법이다. 다중프론트 해법의 공유메모리 컴퓨터에서 최적의 성능을 내도록 병렬 계산을 수행하기 위한 기법들이 제시되었다. 주로 독립적인 계산 작업 시에 필요한 주 메모리 용량을 줄이는 데 초점을 맞춘 방법들로서 프론트 행렬 연성화와 행렬 분리로 명명된 두 기법에 대해 자세히 설명한다. 개발된 방법으로 기존의 알고리즘과의 성능 비교를 수행하여 본지에 제안한 방법이 현대의 다중코어 컴퓨터에서 훨씬 더 효율적인 기법임을 입증하였다.

This paper discusses the parallelization of multifrontal solution method, widely used for finite element structural analyses, for a shared memory architecture. Multifrontal method is easier than other linear solution methods because the solution procedure implies that unknowns can be eliminated simultaneously. Two innovative ideas are introduced to achieve optimal solver performance on a shared memory computer. Those are pairing two frontal matrices and splitting the frontal matrix in order to reduce the temporal memory space required by independent computing tasks. Performance comparisons between original algorithm and proposed one prove that proposed method is more computationally efficient on current multicore machines.

키워드

참고문헌

  1. Bhardwaj, M., et al. "Salinas: a scalable software for high-performance structural and solid mechanics simulations," IEEE Computer Society Press, 2002.
  2. Farhat, C., M. Lesoinne, and K. Pierson, "A scalable dual-primal domain decomposition method," Numerical linear algebra with applications, Vol. 7, 2000, pp. 687-714. https://doi.org/10.1002/1099-1506(200010/12)7:7/8<687::AID-NLA219>3.0.CO;2-S
  3. Nakajima, K. and H. Okuda, "Parallel iterative solvers for unstructured grids using a directive/MPI hybrid programming model for the GeoFEM platform on SMP cluster architectures," Concurrency and Computation-Practice & Experience, Vol. 14, 2002, pp. 411-429. https://doi.org/10.1002/cpe.622
  4. Nakajima, K., "Parallel iterative solvers for finite-element methods using an OpenMP/MPI hybrid programming model on the Earth Simulator," Parallel Computing, Vol. 31, 2005, pp. 1048-1065. https://doi.org/10.1016/j.parco.2005.03.011
  5. Yoshimura, S., et al., "Advanced general-purpose computational mechanics system for large-scale analysis and design," Journal of computational and applied mathematics, Vol. 149, 2002, pp. 279-296. https://doi.org/10.1016/S0377-0427(02)00536-8
  6. Miyamura, T., et al., "Elastic-plastic analysis of nuclear structures with millions of DOFs using the hierarchical domain decomposition method," Nuclear engineering and design, Vol. 212, 2002, pp. 335-355. https://doi.org/10.1016/S0029-5493(01)00497-6
  7. 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
  8. 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
  9. Kim, J.H. and S.J. Kim, "Multifrontal solver combined with graph partitioners," AIAA journal, Vol. 37, 1999, pp. 964-970. https://doi.org/10.2514/2.817
  10. Kim, M.K and S.J. Kim, "High performance hybrid direct-iterative solution method for large scale structural analysis problems," International Journal for Aeronautical and Space Science, Vol. 9, 2008, pp. 79-86 https://doi.org/10.5139/IJASS.2008.9.2.079
  11. Duff, I.S. and J.K. Reid, "The Multifrontal Solution of Indefinite Sparse Symmetric Linear-Equations," ACM Transactions on Mathematical Software, Vol. 9, 1983, pp. 302-325. https://doi.org/10.1145/356044.356047
  12. Irons, B.M., "A frontal solution program for finite element analysis," International Journal for Numerical Methods in Engineering, Vol. 2, 1970, pp. 5-32. https://doi.org/10.1002/nme.1620020104
  13. Karypis, G. and V. Kumar, "A fast and high quality multilevel scheme for partitioning irregular graphs," SIAM Journal on Scientific Computing, Vol. 20, 1998, pp. 359-392. https://doi.org/10.1137/S1064827595287997
  14. Kim, M.K. and S.J. Kim, "Parallelization of bisection mesh partitioning routine for parallel multifrontal solver," ICCES Special Symposium of Meshless and Other Novel Computational Methods, 2010. pp. 58-58.
  15. http://www.openmp.org/
  16. http://threadingbuildingblocks.org/

피인용 문헌

  1. Scheduling and Load Balancing Methods of Multithread Parallel Linear Solver of Finite Element Structural Analysis vol.42, pp.5, 2014, https://doi.org/10.5139/JKSAS.2014.42.5.361
  2. An Out of Core Linear Direct Solution Method for Large Scale Structural Analysis vol.42, pp.6, 2014, https://doi.org/10.5139/JKSAS.2014.42.6.445