Abstract
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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Acknowledgements
We are grateful to Prof. Blaheta and Dr. Starý (Institute of Geonics AS CR) for providing the geocomposite problem. We are also grateful to Dr. Cirak (University of Cambridge) for providing computer time on Darwin. This work was supported by Ministry of Education, Youth and Sports of the Czech Republic under research project LH11004, by Czech Science Foundation under project 106/08/0403, by the Academy of Sciences of the CR through RVO: 67985840, by grant IAA100760702 of the Grant Agency of AS CR, by DOE through an ASCR grant, and by National Science Foundation under grant DMS-0713876, The research was started during two visits of Jakub Šístek at the University of Colorado Denver and some parts of the work have been performed under the HPC-Europa2 project with the support of the European Commission.
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Šístek, J., Mandel, J., Sousedík, B., Burda, P. (2013). Parallel Implementation of Multilevel BDDC. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_72
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DOI: https://doi.org/10.1007/978-3-642-33134-3_72
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