Parallel preprocessing with subdomain's shape control for domain decomposition methods
Résumé
Solving highly heterogeneous structural mechanic problems with a large number of degrees of freedom (HPC simulations) is a real issue in engineering work, because of the required time and memory. Non overlapping domain decomposition methods such as the Finite Element Tearing and Interconnecting (FETI) or Balanced Domain Decomposition (BDD) methods have been developed in order to allocate the problems on distributed memory clusters with a large number of processors and to make mechanical calculations parallel. Two difficulties are encountered when applying domain decomposition methods. First, the mesh generation is most often a sequential process applied to the full domain. Second, the linear system resulting from the partitioning of the mesh may be poorly conditioned, leading to slow convergence. Recently developed techniques such as adapted coarse spaces (e.g. FETI-GenEO) or multipreconditioning (e.g. AMPFETI) enable to restore good convergence rate, at the cost of extra computations. In this study, we try to mitigate these two difficulties by proposing a new hierarchical substructuring method which aims at making the mesh preprocessing step parallel and at improving the condition number of the linear system to be solved by generating regular interfaces adapted to the heterogeneity.
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