A parallel space–time boundary element method for the heat equation

Stefan Dohr, Jan Zapletal, Günther Of, Michal Merta, Michal Kravcenko

Research output: Contribution to journalArticlepeer-review


In this paper we introduce a new parallel solver for the weakly singular space–time boundary integral equation for the heat equation. The space–time boundary mesh is decomposed into a given number of submeshes. Pairs of the submeshes represent dense blocks in the system matrices, which are distributed among computational nodes by an algorithm based on a cyclic decomposition of complete graphs ensuring load balance. In addition, we employ vectorization and threading in shared memory to ensure intra-node efficiency. We present scalability experiments on different CPU architectures to evaluate the performance of the proposed parallelization techniques. All levels of parallelism allow us to tackle large problems and lead to an almost optimal speedup.

Original languageEnglish
Pages (from-to)2852-2866
JournalComputers & Mathematics with Applications
Issue number9
Early online date2019
Publication statusPublished - 1 Nov 2019


  • Heat equation
  • Parallelization
  • Space–time boundary element method
  • Vectorization

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Modelling and Simulation

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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