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Parallel Implementation of Multilevel BDDC

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • J. Šístek

    (Academy of Sciences of the Czech Republic, Institute of Mathematics)

  • J. Mandel

    (University of Colorado Denver, Department of Mathematical and Statistical Sciences)

  • B. Sousedík

    (University of Southern California, Department of Aerospace and Mechanical Engineering)

  • P. Burda

    (Czech Technical University, Department of Mathematics, Faculty of Mechanical Engineering)

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.

Suggested Citation

  • J. Šístek & J. Mandel & B. Sousedík & P. Burda, 2013. "Parallel Implementation of Multilevel BDDC," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 681-689, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_72
    DOI: 10.1007/978-3-642-33134-3_72
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