A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

Maciej R. Paszyński, Victor M. Calo, David Pardo

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)1140-1151
Number of pages12
JournalComputers and Mathematics with Applications
Volume65
Issue number8
DOIs
StatePublished - Apr 2013

ASJC Scopus subject areas

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

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