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Center for Nonlinear Studies |
In the first part of the talk, basic concepts of iterative substructuring will be recalled along with a very brief survey of domain decomposition preconditioners. The components of the Balancing Domain Decomposition based on Constraints (BDDC) method will be explained in detail. The method solves large sparse systems of linear equations resulting from discretization of PDEs. In the second part of the talk, the algorithm of Adaptive-Multilevel BDDC will be described. It is based on a combination of two extensions of the standard BDDC method: The Adaptive BDDC, which aims at problems with severe numerical difficulties, generates constraints based on prior analysis of the problem and eliminates the worst modes from the space of admissible functions. The Multilevel BDDC is a recursive application of the BDDC method to successive coarse problems aiming at very large problems solved using thousands of compute cores. A crucial component in substructuring is represented by interface weights for averaging the discontinuous solution from neighbouring subdomains. Several existing approaches will be recalled and compared to two proposed choices. Finally, the parallel implementation of these concepts within our open-source BDDCML package will be presented. Performance of the solver is analysed on several benchmark and engineering problems, and main issues with an efficient implementation of both Adaptive and Multilevel extensions are discussed. This is joint work with Jan Mandel, Bedrich Sousedik and Marta Certikova.
Host: Ondrej Certik