Аннотації

О ПАРАЛЛЕЛЬНЫХ РЕШАТЕЛЯХ В КОНЕЧНОЭЛЕМЕНТНЫХ ПРОГРАММНЫХ КОМПЛЕКСАХ, ОРИЕНТИРОВАННЫХ НА МНОГОЯДЕРНЫЕ КОМПЬЮТЕРЫ С ОБЩЕЙ ОПЕРАТИВНОЙ ПАМЯТЬЮ

Автор(и):
Фиалко С.Ю.
Автор(и) (англ)
Fialko S.Yu.
Дата публікації:

02.01.2016

Анотація (укр):

Обговорюються прямі методи розв’язування систем лінійних алгебраїчних рівнянь з симетричними розрідженими матрицями, що виникають при застосуванні методу скінчених елементів до завдань механікі конструкцій та механікі деформованого твердого тіла. Головна увага приділяється методам досягнення високої продуктивності на багатоядерних комп’ютерах з загальною пам’яттю (sharedmemorycomputers).

Анотація (рус):

Рассматриваются прямые методы решения систем линейных алгебраических уравнений с симметричными разреженными матрицами, возникающими при применении метода конечных элементов к задачам строительной механики и механики деформированного твердого тела. Основное внимание уделяется методам достижения высокой производительности на многоядерных компьютерах с общей оперативной памятью (sharedmemorycomputers).

Анотація (англ):

The direct methods for solution of linearequation sets arising when the finite element method is applied to problems of structural and solid mechanics are considered. Main attention is paid to achievement of high performance on multicore shared memory computers.We confine ourselves to the consideration of the multifrontal and supernodal methods, present a brief description and emphasize their advantages and disadvantages for the considered class of problems on shared memory multicore computers. We compare the performance of Boeing sparse direct solver implemented in famous ANSYS 15.0 finite element software, supernodal solver PARDISO from Intel Math Kernel Library with block substructure multifrontal solver BSMFM and supernodal parallel finite element solver PARFES, implemented in SCAD software (www.scadsoft.com). Then, we present the stable speed up and performance on computer with 16-core AMD Opteron 6276 processordemonstrated by PARFES.

Література:

  1. Matrixcomputations/ G.H. Golub, C.F. VanLoan, Thirded. –John Hopkins University Press, 1996, 694 p.
  2. Численное решение больших разреженных систем уравнений / А. Джордж, Дж. Лю. – М.: Мир, 1984. – 333 с.
  3. Applied numerical linear algebra / J.W. Demmel. – Philadelphia, SIAM, 1997. – 421 p.
  4. Прямые методы решения систем линейных уравнений в современных МКЭ-комплексах / С.Ю. Фиалко. – М.: СКАД СОФТ, 2009. – 160 с.
  5. DuffI. S., ReidJ. K.Themultifrontalsolutionofindefinitesparsesymmetriclinearsystems. – ACMTransactionsonMathematicalSoftware. – 1983. – Vol. 9. – P. 302–325.
  6. Dobrian F., Kumfert G., Pothen A. The Design of Sparse Direct Solvers using Object-Oriented Techniques –In: BruasetA.M., Langtangen H.P., Quak E. (eds.) –Modern Software Tools in Scientific Computing. Springer-Verlag,2000,P 89–131.
  7. Intel® Math Kernel Library Reference Manual – BLAS Routines. https://software.intel.com/sites/products/documentation/doclib/iss/2013/....
  8. Goto K., Van DeGeijn R.A. Anatomy of High-Performance Matrix Multiplication. – ACM Transactions on Mathematical Software. – 2008. –Vol34. No. 3/ – P. 1–25.
  9. Amestoy P.R., Duff I.S., L’Excellent J.Y. Multifrontal parallel distributed symmetric and unsymmetric solvers. –  Comput. Meth. Appl. Mech. Eng. – 2000. –Vol. 184. – P. 501–520.
  10. Фиалко С.Ю. К исследованию напряженно-деформированного состояния тонкостенных оболочек с массивными ребрами. – Прикл. Механика. – т. 40. –, № 4. – С. 84–92.
  11. Fialko S. A Sparse Shared-Memory Multifrontal Solver in SCAD Software. IEEE Xplore Digital Library. Computer Science and Information Technology, 2008. IMCSIT 2008. InternationalMulticonferenceon.20 – 22 Oct. – 2008. – P. 277 – 283. Doi:10.1109/IMCSIT.2008.4747252 .
  12. Chen Y., Davis T.A., Hager W.W., Rajamanickam S. Algorithm 8xx: CHOLMOD,supernodal sparse Cholesky factorization and update/downdate. – Technical report TR-2006-005. – CISE Dept, Univ. of Florida, Gainesville, FL. – 2006. URL:http://www.cise.ufl.edu/tr/DOC/REP-2006-290.pdf (Accessed 20.12.2014).
  13. Demmel J.W., Eisenstat S.C., Gilbert J.R., Li X.S., Liu J.W.H. A supernodal approach for sparse partial pivoting. – SIAM J. Matrix Anal. Appl. – 1999. – Vol 20. – No. 3. – P. 720 – 755.
  14. Protkin V., Toledo S. The design and implementation of a new out-of-core sparse Cholesky factorization method. – ACM Transactions on Mathematical Software. – 2004. – Vol. 30. – No.1. – P. 19 – 46.
  15. Schenk O., Gartner K. Two-level dynamic scheduling in PARDISO: Improved scalability on shared memory multiprocessing systems. – Parallel Computing. – 2002. –Vol. 28. – P. 187–197.
  16. Pardo D., MyungJin Nam, Carlos Torres-Verdín, Michael G. Hoversten, Iñaki Garay. Simulation of marine controlled source electromagnetic measurements using a parallel Fourier hp-finite element method. – Comput. Geosci. – 2011. – Vol. 15. P. 53–67.
  17. Fialko S. PARFES: A method for solving finite element linear equations on multi-core computers. – Advances in engineering software. – 2010. – Vol.40. – No.12. – P. 1256 – 1265.
  18. Fialko S. Parallel Finite Element Solver for Multi-Core Computers. IEEE Xplore Digital Library. Computer Science and Information Technology (FedCSIS), 2012 Federated Conference on. – P. 525 – 532. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6354298.
  19. Fialko S. Application of AVX (Advanced Vector Extensions) for Improved Performance of the PARFES – Finite Element Parallel Direct Solver. IEEE Xplore Digital Library.Computer Science and Information Systems (FedCSIS), 2013 Federated Conference on. – P. 447 – 454.http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6644039&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6644039
  20. Karypis G., Kumar V. METIS: Unstructured Graph Partitioning and Sparse Matrix Ordering System. – Technical report. – Department of Computer Science. – University of Minnesota. Minneapolis. – 1995.
 

References:

  1. Matrixcomputations/ G.H. Golub, C.F. VanLoan, Thirded. –John Hopkins University Press, 1996, 694 p.
  2. Computer solution of sparse positive definite systems / A.George, J.W.H. Liu. – Moscow, Mir, 1984, 333 p. (In Russian)
  3. Applied numerical linear algebra / J. W. Demmel. – Philadelphia, SIAM, 1997. – 421 p.
  4. The direct methods for solution of the linear equation sets in modern FEM software / S. Fialko. – Moscow, SCAD SOFT, 2009, 160 p. (in Russian).
  5. DuffI. S., ReidJ. K.Themultifrontalsolutionofindefinitesparsesymmetriclinearsystems. – ACMTransactionsonMathematicalSoftware. – 1983. – Vol. 9. – P. 302–325.
  6. Dobrian F., Kumfert G., Pothen A. The Design of Sparse Direct Solvers using Object-Oriented Techniques –In: Bruaset A.M., Langtangen H.P., Quak E. (eds.) –ModernSoftwareToolsinScientificComputing. Springer-Verlag, 2000,P 89–131.
  7. Intel® Math Kernel Library Reference Manual – BLAS Routines. https://software.intel.com/sites/products/documentation/doclib/iss/2013/....
  8. Goto K., Van DeGeijn R. A. Anatomy of High-Performance MatrixMultiplication. – ACM Transactions on Mathematical Software. – 2008. –Vol34. No. 3/ – P. 1–25.
  9. Amestoy P.R., Duff I.S., L’Excellent J.Y. Multifrontal parallel distributed symmetric and unsymmetric solvers. –  Comput. Meth. Appl. Mech. Eng. – 2000. –Vol. 184. – P. 501–520.
  10. Fialko S. Stress-Strain Analysis of Thin-Walled Shells with Massive Ribs. – Int. App. Mech. – 2004. Stress-Strain Analysis of Thin-Walled Shells with Massive Ribs. Int. App. Mech. – 2004. –Vol. 4. – No 4. – P. 432–439.
  11. Fialko S. A Sparse Shared-Memory Multifrontal Solver in SCAD Software. IEEE Xplore Digital Library. Computer Science and Information Technology, 2008. IMCSIT 2008. InternationalMulticonferenceon. 20 – 22 Oct. – 2008. – P. 277 – 283. Doi:10.1109/IMCSIT.2008.4747252 .
  12. Chen Y., Davis T.A., Hager W.W., Rajamanickam S. Algorithm 8xx: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate. – Technical report TR-2006-005. – CISE Dept, Univ. of Florida, Gainesville, FL. – 2006. URL:http://www.cise.ufl.edu/tr/DOC/REP-2006-290.pdf (Accessed 20.12.2014).
  13. Demmel J.W., Eisenstat S.C., Gilbert J.R., Li X., Liu J.W.H. A supernodal approach for sparse partial pivoting. – SIAM J. Matrix Anal. Appl. – 1999. – Vol 20. – No. 3. – P. 720 – 755.
  14. Protkin V., Toledo S. The design and implementation of a new out-of-core sparse Cholesky factorization method. – ACM Transactions on Mathematical Software. – 2004. – Vol. 30. – No.1. – P. 19 – 46.
  15. Schenk O., Gartner K. Two-level dynamic scheduling in PARDISO: Improved scalability on shared memory multiprocessing systems. – Parallel Computing. – 2002. –Vol. 28. – P. 187–197.
  16. Pardo D., MyungJin Nam, Carlos Torres-Verdín, Michael G. Hoversten, Iñaki Garay. Simulation of marine controlled source electromagnetic measurements using a parallel Fourier hp-finite element method. – Comput. Geosci. – 2011. – Vol. 15. P. 53–67.
  17. Fialko S. PARFES: A method for solving finite element linear equations on multi-core computers. – Advances in engineering software. – 2010. – Vol.40. – No.12. – P. 1256 – 1265.
  18. Fialko S. Parallel Finite Element Solver for Multi-Core Computers. IEEE Xplore Digital Library. Computer Science and Information Technology (FedCSIS), 2012 Federated Conference on. – P. 525 – 532. http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6354298.
  19. Fialko S. Application of AVX (Advanced Vector Extensions) for Improved Performance of the PARFES – Finite Element Parallel Direct Solver. IEEE Xplore Digital Library. Computer Science and Information Systems (FedCSIS), 2013 Federated Conference on. – P. 447 – 454. http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6644039&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6644039
  20. Karypis G., Kumar V. METIS: Unstructured Graph Partitioning and Sparse Matrix Ordering System. – Technical report. – Department of Computer Science. – University of Minnesota. Minneapolis. – 1995.