Geodesic
Hybrid parallelization of an adaptive finite element code
Kybernetika, Tome 46 (2010) no. 2, pp. 316-327.

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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.
Classification : 35K55, 65M55, 65M60, 65N30, 65Y05
Keywords: adaptive finite elements; parallelization; OpenMP; MPI 
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     author = {Voigt, Axel and Witkowski, Thomas},
     title = {Hybrid parallelization of an adaptive finite element code},
     journal = {Kybernetika},
     pages = {316--327},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2010},
     mrnumber = {2663603},
     zbl = {1195.65135},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a6/}
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Voigt, Axel; Witkowski, Thomas. Hybrid parallelization of an adaptive finite element code. Kybernetika, Tome 46 (2010) no. 2, pp. 316-327. http://geodesic.mathdoc.fr/item/KYB_2010__46_2_a6/