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.
Isogeometric analysis is a quickly emerging alternative ot the standard, polynomial-based finite element analysis. It is only the question of time, when it will be implemented into major software packages and will be intensively used by engineering community to the analysis of complex realistic problems. Computational demands of such analyses, that may likely exceed the capacity of a single computerk can be parallel processing requires usuall an appropriate decomposition of the investigated problem to the individual processing units. In the case of he isogeometric analysis, the decomposition corresponds to the spatial partitioning of the underlying spatial discretization. While there are several matured graphs-based decomposers which can be readily applied to the subdivison of finite element meshes, their use in the context of the isogeometric analysis is not straightforward because of a rather complicated construction of the graph corresponding to the computational isogeometric mesh. In this paper, a new technology for the construction of the dual graph of a two-dimensional NURBS-based (non-uniform rational B-spline) isogeometric mesh is introduced. This makes the partitioning of the isogeometric meshes for parallel processing accessible for the standard graph-based partitioning of the isogeometric meshes for parallel processing accessible for the standard graph-based partitioning approaches. and Obsahuje seznam literatury