Title:
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Hybrid parallelization of an adaptive finite element code (English) |
Author:
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Voigt, Axel |
Author:
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Witkowski, Thomas |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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46 |
Issue:
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2 |
Year:
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2010 |
Pages:
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316-327 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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. (English) |
Keyword:
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adaptive finite elements |
Keyword:
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parallelization |
Keyword:
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OpenMP |
Keyword:
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MPI |
MSC:
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35K55 |
MSC:
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65M55 |
MSC:
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65M60 |
MSC:
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65N30 |
MSC:
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65Y05 |
idZBL:
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Zbl 1195.65135 |
idMR:
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MR2663603 |
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Date available:
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2010-09-13T16:41:39Z |
Last updated:
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2013-07-30 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140746 |
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Reference:
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[1] Backofen, R., Rätz, A., Voigt, A.: Nucleation and growth by a phase-field crystal (PFC) model.Phil. Mag. Lett. 87 (2007), 813–820. 10.1080/09500830701481737 |
Reference:
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[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). |
Reference:
|
[3] Davis, T. A.: Algorithm 832: UMFPACK, an unsymmetric-pattern multifrontal method.ACM Trans. Math. Software 30 (2004), 2 196–199. MR 2075981, 10.1145/992200.992206 |
Reference:
|
[4] Dziuk, G., Elliott, C. M.: Finite elements on evolving surfaces.IMA J. Numer. Anal. 27 (2007), 262–292. Zbl 1120.65102, MR 2317005, 10.1093/imanum/drl023 |
Reference:
|
[5] Elder, K. R., Katakowski, M., Haataja, M., Grant, M.: Modeling elasticity in crystal growth.Phys. Rev. Lett. 88 (2002), 245701. 10.1103/PhysRevLett.88.245701 |
Reference:
|
[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. |
Reference:
|
[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. |
Reference:
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[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. MR 2535657 |
Reference:
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[9] Rätz, A., Ribalta, A., Voigt, A.: Surface evolution of elastically stressed films under deposition by a diffuse interface model.J. Comput. Phys. 214 (2006), 187–208. MR 2208676, 10.1016/j.jcp.2005.09.013 |
Reference:
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[10] Schloegel, K., Karypis, G., Kumar, V.: Parallel static and dynamic multi-constraint graph partitioning.Concurrency and Computation: Practice and Experience 14 (2002), 3, 219–240. Zbl 1012.68146, 10.1002/cpe.605 |
Reference:
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[11] Schmidt, A., Siebert, K. G.: Design of adaptive finite element software.(Lecture Notes in CSE 42.) Springer, Heidelberg 2005. Zbl 1068.65138, MR 2127659 |
Reference:
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[12] Teeffelen, S. van, Backofen, R., Voigt, A., Löwen, H.: Derivation of the phase field crystal model for colloidal solidification.Phys. Rev. E. 79 (2009), 051404. 10.1103/PhysRevE.79.051404 |
Reference:
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[13] Vey, S., Voigt, A.: Adaptive full domain covering meshes for parallel finite element computations.Computing 81 (2007), 53–75. Zbl 1132.65107, MR 2369421, 10.1007/s00607-007-0243-1 |
Reference:
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[14] Vey, S., Voigt, A.: AMDiS – adaptive multidimensional simulations.Comput. Visual Sci. 10 (2007), 57–67. MR 2295934, 10.1007/s00791-006-0048-3 |
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