BDDC
Parallel implementation of multilevel BDDC 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.
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References in zbMATH (referenced in 10 articles , 1 standard article )
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Sorted by year (- Badia, Santiago; Martín, Alberto F.; Principe, Javier: Multilevel balancing domain decomposition at extreme scales (2016)
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- Xi, Yuanzhe; Li, Ruipeng; Saad, Yousef: An algebraic multilevel preconditioner with low-rank corrections for sparse symmetric matrices (2016)
- Zampini, Stefano: PCBDDC: a class of robust dual-primal methods in petsc (2016)
- Heinlein, A.; Hetmaniuk, U.; Klawonn, A.; Rheinbach, O.: The approximate component mode synthesis special finite element method in two dimensions: parallel implementation and numerical results (2015)
- Šístek, J.; Mandel, J.; Sousedík, B.; Burda, P.: Parallel implementation of multilevel BDDC (2013)
- Sousedík, Bedřich: Nested BDDC for a saddle-point problem (2013)
- Sousedík, Bedřich; Šístek, Jakub; Mandel, Jan: Adaptive-multilevel BDDC and its parallel implementation (2013)