An efficient algorithm for the parallel solution of high-dimensional differential equations

Stefan Klus, Tuhin Sahai*, Cong Liu, Michael Dellnitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

The study of high-dimensional differential equations is challenging and difficult due to the analytical and computational intractability. Here, we improve the speed of waveform relaxation (WR), a method to simulate high-dimensional differential-algebraic equations. This new method termed adaptive waveform relaxation (AWR) is tested on a communication network example. Further, we propose different heuristics for computing graph partitions tailored to adaptive waveform relaxation. We find that AWR coupled with appropriate graph partitioning methods provides a speedup by a factor between 3 and 16.

Original languageEnglish
Pages (from-to)3053-3062
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume235
Issue number9
DOIs
Publication statusPublished - 1 Mar 2011

Keywords

  • Adaptive windowing
  • Graph partitioning
  • Parallel algorithms
  • Petri nets
  • Waveform relaxation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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