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A High-Performance Implementation of a Robust Preconditioner for Heterogeneous Problems

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12043)


We present an efficient implementation of the highly robust and scalable GenEO (Generalized Eigenproblems in the Overlap) preconditioner [16] in the high-performance PDE framework DUNE [6]. The GenEO coarse space is constructed by combining low energy solutions of a local generalised eigenproblem using a partition of unity. The main contribution of this paper is documenting the technical details that are crucial to the efficiency of a high-performance implementation of the GenEO preconditioner. We demonstrate both weak and strong scaling for the GenEO solver on over 15, 000 cores by solving an industrially motivated problem in aerospace engineering. Further, we show that for highly complex parameter distributions arising in certain real-world applications, established methods become intractable while GenEO remains fully effective.


  • Partial differential equations
  • Domain decomposition
  • Preconditioning
  • High performance computing

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This work was supported by an EPSRC Maths for Manufacturing grant (EP/K031368/1). This research made use of the Balena High Performance Computing Service at the University of Bath. This work used the ARCHER UK National Supercomputing Service (

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Correspondence to Linus Seelinger .

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Seelinger, L., Reinarz, A., Scheichl, R. (2020). A High-Performance Implementation of a Robust Preconditioner for Heterogeneous Problems. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12043. Springer, Cham.

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43228-7

  • Online ISBN: 978-3-030-43229-4

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