Some Practical Aspects of Parallel Adaptive BDDC Method
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2012
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Jakub Šístek, Jan Mandel, Bedřich Sousedík: Some practical aspects of parallel adaptive BDDC method, Proceedings of Applications of Mathematics 2012, Prague, Czech Republic, May 2-5, 2012, J. Brandts, J. Chleboun, S. Korotov, K. Segeth, J. Šístek, T. Vejchodský (eds.), Institute of Mathematics AS CR, 253-266, 2012
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Abstract
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.