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Parallel implementation of multilevel BDDC. (English) Zbl 1311.65178

Cangiani, Andrea (ed.) et al., Numerical mathematics and advanced applications 2011. Proceedings of ENUMATH 2011, the 9th European conference on numerical mathematics and advanced applications, Leicester, UK, September 5–9, 2011. Berlin: Springer (ISBN 978-3-642-33133-6/hbk; 978-3-642-33134-3/ebook). 681-689 (2013).
Summary: In application of the Balancing Domain Decomposition by Constraints (BDDC) to a case with many substructures, solving the coarse problem exactly becomes the bottleneck which spoils scalability of the solver. However, it is straightforward for BDDC to substitute the exact solution of the coarse problem by another step of BDDC method with subdomains playing the role of elements. In this way, the algorithm of three-level BDDC method is obtained. If this approach is applied recursively, multilevel BDDC method is derived. We present a detailed description of a recently developed parallel implementation of this algorithm. The implementation is applied to an engineering problem of linear elasticity and a benchmark problem of Stokes flow in a cavity. Results by the multilevel approach are compared to those by the standard (two-level) BDDC method.
For the entire collection see [Zbl 1257.65002].

MSC:

65Y05 Parallel numerical computation
74S30 Other numerical methods in solid mechanics (MSC2010)
76M25 Other numerical methods (fluid mechanics) (MSC2010)
74B05 Classical linear elasticity
76D05 Navier-Stokes equations for incompressible viscous fluids

Software:

BDDC; BDDCML
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