A high-performance implementation of a robust preconditioner for heterogeneous problems

Linus Seelinger, Anne Reinarz, Robert Scheichl

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish
Title of host publicationParallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Revised Selected Papers
EditorsRoman Wyrzykowski, Konrad Karczewski, Ewa Deelman, Jack Dongarra
Number of pages12
ISBN (Print)9783030432287
Publication statusPublished - 2020
Event13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019 - Bialystok, Poland
Duration: 8 Sep 201911 Sep 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12043 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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