Direct solvers performance on h-adapted grids

Maciej Paszynski, David Pardo, Victor M. Calo

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.
Original languageEnglish (US)
Pages (from-to)282-295
Number of pages14
JournalComputers & Mathematics with Applications
Volume70
Issue number3
DOIs
StatePublished - May 28 2015

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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