Using Algebraic Multigrid in Inexact BDDC Domain Decomposition Methods
A highly scalable implementation of an inexact BDDC (Balancing Domain Decomposition by Constraints) method is presented, and scalability results for linear elasticity problems in two and three dimensions for up to 131,072 computational cores of the JUQUEEN BG/Q are shown. In this method, the inverse action of the partially coupled stiffness matrix is replaced by V-cycles of an AMG (algebraic multigrid) method. The use of classical AMG for systems of PDEs, based on a nodal coarsening approach is compared with a recent AMG method using an explicit interpolation of the rigid body motions (global matrix approach; GM). It is illustrated, that for systems of PDEs an appropriate AMG interpolation is mandatory for fast convergence, i.e., using exact interpolation of rigid body modes in elasticity.
This work was supported in part by the German Research Foundation (DFG) through the Priority Programme 1648 “Software for Exascale Computing” (SPPEXA) under grants KL 2094/4-1, KL 2094/4-2, RH 122/2-1, and RH 122/3-2. The authors also gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, www.lrz.de) and JUQUEEN  at Jülich Supercomputing Centre (JSC, www.fz-juelich.de/ias/jsc). GCS is the alliance of the three national supercomputing centres HLRS (Universität Stuttgart), JSC (Forschungszentrum Jülich), and LRZ (Bayerische Akademie der Wissenschaften), funded by the German Federal Ministry of Education and Research (BMBF) and the German State Ministries for Research of Baden-Württemberg (MWK), Bayern (StMWFK) and Nordrhein-Westfalen (MIWF).
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