Some practical aspects of parallel adaptive BDDC method. (English) Zbl 1313.74121

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 2–5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-60-8/pbk). 253-266 (2012).
Summary: We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may represent one class of such challenging problems. The adaptive selection of constraints is shown to significantly increase the robustness of the method for this class of problems. However, since the cost of the set-up of the preconditioner with adaptive constraints is considerably larger than for the standard choices, computational feasibility of the presented implementation is obtained only for large contrasts of material coefficients.
For the entire collection see [Zbl 1277.00031].


74S30 Other numerical methods in solid mechanics (MSC2010)
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation
74B20 Nonlinear elasticity
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