Distributed Solution of Laplacian Eigenvalue Problems

Antti Hannukainen*, Jarmo Malinen, Antti Ojalammi

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

The purpose of this article is to approximately compute the eigenvalues of the symmetric Dirichlet Laplacian within an interval (0, Lambda). A novel domain decomposition Ritz method, partition of unity condensed pole interpolation, is proposed. This method can be used in distributed computing environments where communication is expensive, e.g., in clusters running on cloud computing services or networked workstations. The Ritz space is obtained from local subspaces consistent with a decomposition of the domain into subdomains. These local subspaces are constructed independently of each other, using data only related to the corresponding subdomain. Relative eigenvalue error is analyzed. Numerical examples on a cluster of workstations validate the error analysis and the performance of the method.

Original languageEnglish
Pages (from-to)76-103
Number of pages28
JournalSIAM Journal on Numerical Analysis
Volume60
Issue number1
DOIs
Publication statusPublished - 2022
MoE publication typeA1 Journal article-refereed

Keywords

  • eigenvalue problem
  • domain decomposition
  • dimension reduction
  • subspace method
  • APPROXIMATION
  • COMPUTATION

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