Hybrid parallelization of an adaptive finite element code

Axel Voigt; Thomas Witkowski

Kybernetika (2010)

  • Volume: 46, Issue: 2, page 316-327
  • ISSN: 0023-5954

Abstract

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We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the large problem and the smaller sub-problems, sufficiently fast we make use of a hierarchical mesh structure. The partitioning is done on a coarser mesh level, resulting in a very fast method that shows good computational balancing results. Numerical experiments show that both parallelization methods achieve good scalability in computing solution of nonlinear, time dependent, higher order PDEs on large domains. The parallelization is realized in the adaptive finite element software AMDiS.

How to cite

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Voigt, Axel, and Witkowski, Thomas. "Hybrid parallelization of an adaptive finite element code." Kybernetika 46.2 (2010): 316-327. <http://eudml.org/doc/197081>.

@article{Voigt2010,
abstract = {We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the large problem and the smaller sub-problems, sufficiently fast we make use of a hierarchical mesh structure. The partitioning is done on a coarser mesh level, resulting in a very fast method that shows good computational balancing results. Numerical experiments show that both parallelization methods achieve good scalability in computing solution of nonlinear, time dependent, higher order PDEs on large domains. The parallelization is realized in the adaptive finite element software AMDiS.},
author = {Voigt, Axel, Witkowski, Thomas},
journal = {Kybernetika},
keywords = {adaptive finite elements; parallelization; OpenMP; MPI; adaptive finite elements; parallelization; OpenMP; MPI; phase field crystal model; computational material science; domain decomposition; error estimation; numerical experiments; software AMDiS},
language = {eng},
number = {2},
pages = {316-327},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Hybrid parallelization of an adaptive finite element code},
url = {http://eudml.org/doc/197081},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Voigt, Axel
AU - Witkowski, Thomas
TI - Hybrid parallelization of an adaptive finite element code
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 2
SP - 316
EP - 327
AB - We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the large problem and the smaller sub-problems, sufficiently fast we make use of a hierarchical mesh structure. The partitioning is done on a coarser mesh level, resulting in a very fast method that shows good computational balancing results. Numerical experiments show that both parallelization methods achieve good scalability in computing solution of nonlinear, time dependent, higher order PDEs on large domains. The parallelization is realized in the adaptive finite element software AMDiS.
LA - eng
KW - adaptive finite elements; parallelization; OpenMP; MPI; adaptive finite elements; parallelization; OpenMP; MPI; phase field crystal model; computational material science; domain decomposition; error estimation; numerical experiments; software AMDiS
UR - http://eudml.org/doc/197081
ER -

References

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  1. Backofen, R., Rätz, A., Voigt, A., 10.1080/09500830701481737, Phil. Mag. Lett. 87 (2007), 813–820. DOI10.1080/09500830701481737
  2. Balay, S., Buschelman, K., Gropp, W. D., Kaushik, D., Knepley, M. G., McInnes, L. C., Smith, B. F., Zhang, H., PETSc Web page, http://www.mcs.anl.gov/petsc (2009). 
  3. Davis, T. A., 10.1145/992200.992206, ACM Trans. Math. Software 30 (2004), 2 196–199. MR2075981DOI10.1145/992200.992206
  4. Dziuk, G., Elliott, C. M., 10.1093/imanum/drl023, IMA J. Numer. Anal. 27 (2007), 262–292. Zbl1120.65102MR2317005DOI10.1093/imanum/drl023
  5. Elder, K. R., Katakowski, M., Haataja, M., Grant, M., 10.1103/PhysRevLett.88.245701, Phys. Rev. Lett. 88 (2002), 245701. DOI10.1103/PhysRevLett.88.245701
  6. Gottschling, P., Wise, D. S., Adams, M. D., Representation-transparent matrix algorithms with scalable performance, In: ICS ’07: Proc. 21st Annual Internat. Conference on Supercomputing 2007, pp. 116–125. 
  7. Kotakemori, H., Hasegawa, H., Performance evaluation of a parallel iterative method library using OpenMP, In: ACM Proc. Eighth Internat. Conference on High-Performance Computing in Asia–Pacific Region 2005, pp. 432–437. 
  8. Li, B., Lowengrub, J., Rätz, A., Voigt, A., Geometric evolution laws for thin crystalline films: Modeling and numerics, Comm. Comput. Phys. 6 (2009), 433–482. MR2535657
  9. Rätz, A., Ribalta, A., Voigt, A., 10.1016/j.jcp.2005.09.013, J. Comput. Phys. 214 (2006), 187–208. MR2208676DOI10.1016/j.jcp.2005.09.013
  10. Schloegel, K., Karypis, G., Kumar, V., 10.1002/cpe.605, Concurrency and Computation: Practice and Experience 14 (2002), 3, 219–240. Zbl1012.68146DOI10.1002/cpe.605
  11. Schmidt, A., Siebert, K. G., Design of adaptive finite element software, (Lecture Notes in CSE 42.) Springer, Heidelberg 2005. Zbl1068.65138MR2127659
  12. Teeffelen, S. van, Backofen, R., Voigt, A., Löwen, H., 10.1103/PhysRevE.79.051404, Phys. Rev. E. 79 (2009), 051404. DOI10.1103/PhysRevE.79.051404
  13. Vey, S., Voigt, A., 10.1007/s00607-007-0243-1, Computing 81 (2007), 53–75. Zbl1132.65107MR2369421DOI10.1007/s00607-007-0243-1
  14. Vey, S., Voigt, A., 10.1007/s00791-006-0048-3, Comput. Visual Sci. 10 (2007), 57–67. MR2295934DOI10.1007/s00791-006-0048-3

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