A highly scalable parallel implementation of balancing domain decomposition by constraints

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29 Citations (Scopus)

Abstract

In this work we propose a novel parallelization approach of two-level balancing domain decomposition by constraints preconditioning based on overlapping of fine-grid and coarsegrid duties in time. The global set of MPI tasks is split into those that have fine-grid duties and those that have coarse-grid duties, and the different computations and communications in the algorithm are then rescheduled and mapped in such a way that the maximum degree of overlapping is achieved while preserving data dependencies among them. In many ranges of interest, the extra cost associated to the coarse-grid problem can be fully masked by fine-grid related computations (which are embarrassingly parallel). Apart from discussing code implementation details, the paper also presents a comprehensive set of numerical experiments that includes weak scalability analyses with structured and unstructured meshes for the three-dimensional Poisson and linear elasticity problems on a pair of state-of-the-art multicore-based distributed-memory machines. This experimental study reveals remarkable weak scalability in the solution of problems with thousands of millions of unknowns on several tens of thousands of computational cores.

Original languageEnglish
Pages (from-to)C190–C218
Number of pages29
JournalSIAM Journal on Scientific Computing
Volume36
Issue number2
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

Keywords

  • BDDC
  • Coarse-grid correction
  • Domain decomposition
  • MPMD
  • Overlapping
  • Parallelization
  • Scalability

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